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Solid Earth, 1, 25–48, 2010 www.solid-earth.net/1/25/2010/ © Author(s) 2010. This work is distributed under the Creative Commons Attribution 3.0 License. Solid Earth Particle size distributions by laser diffraction: sensitivity of granular matter strength to analytical operating procedures F. Storti and F. Balsamo Dipartimento di Scienze Geologiche, Universit` a “Roma Tre”, Largo S. L. Murialdo 1, 00146 Roma, Italy Received: 6 November 2009 – Published in Solid Earth Discuss.: 21 December 2009 Revised: 24 March 2010 – Accepted: 2 April 2010 – Published: 19 April 2010 Abstract. We tested laser diffraction particle size analy- sis in poorly coherent carbonate platform cataclastic brec- cias and unfaulted quartz-rich eolian sands, representing low- and high-strength granular materials, respectively. We used two different instruments with different sample dispersion and pumping systems and several wet analytical procedures that included different pump speeds, measurement precision tests with and without sample ultrasonication, and different dispersant liquids. Results of our work indicate that high strength material is not strongly affected by analytical op- erating procedures, whereas low strength materials are very sensitive to the pump speed, ultrasonication intensity, and measurement run time. To reduce such a data variability, we propose a workflow of analytical tests preliminary to the set up of the most appropriate SOP. 1 Introduction Particle size distributions provide fundamental information for rock characterization and geological process descrip- tion in earth sciences, including sedimentology, stratigraphy, structural geology, pedology, and volcanology (e.g. Krum- bein, 1941; Irani and Callis, 1963; Engelder, 1974; Fried- man, 1979; Sheridan et al., 1987; Rieu and Sposito, 1991). In the last three decades, laser diffraction particle size analy- sers have proved to be an effective tool for providing particle size distributions of poorly coherent rocks and soils (Weiss and Frock, 1976; McCave et al., 1986; de Boer et al., 1987; Wanogho et al., 1987; Agrawal et al., 1991; Loizeau et al., 1994; Pye and Blott, 2004; Blott and Pye, 2006). This is be- cause they require little time for analysis, cover a wide size range, and require small size samples (e.g. Beuselinck et al., Correspondence to: F. Storti ([email protected]) 1998), thus facilitating very detailed studies of particle size distributions in geological structures. Laser diffraction particle size analysers provide indirect size measurements of spherically equivalent particles, based on the principle that particles of a given size diffract light through a given angle that increases logarithmically with de- creasing size (e.g. Beuselinck et al., 1998). In “wet proce- dures”, a few grams of material are dispersed into a liquid that circulates across a quartz measurement cell illuminated by a laser beam (Fig. 1). Different instruments have dif- ferently designed systems for stirring the dispersant liquid into the tank and ensuring its circulation through the mea- surement cell by mechanical pumping. A wide variety of standard operating procedures (SOP) can be set up in laser diffraction particle size analysers. They include the pump speed, the number of measurement runs, the length of the measurement time, and the use of dispersing agents and/or ultrasonication to aid sample disaggregation and dispersion (e.g. Blott et al., 2004; Sperazza et al., 2004). It follows that measurement results, particularly when dealing with datasets produced by different operators and/or different instruments, can be influenced by the adopted SOP. Sample ultrasonica- tion, for example, can aid particle disaggregation by collision or, in some cases, particle agglomeration (e.g. Mason et al., 2003; Blott et al., 2004). In this study we analysed particle size distributions of un- faulted quartz-rich (83% quartz, 9% plagioclase, and 8% feldspar) eolian sands from the Priverno quarry, on the Tyrrhenian side of the Central Apennines (e.g. Angelucci and Palmerini, 1961), and carbonate cataclastic breccias from the active Assergi extensional fault system, which bounds to the south the Gran Sasso Massif in the Central Apennines, Italy (e.g. D’Agostino et al., 1998). Our results indicate that particle size data measurement by laser diffrac- tion granulometry is not straightforward in fragile granular materials. We provide an analytical workflow for prelimi- nary testing, which is propedeutic to final SOP determination Published by Copernicus Publications on behalf of the European Geosciences Union.
Transcript

Solid Earth, 1, 25–48, 2010www.solid-earth.net/1/25/2010/© Author(s) 2010. This work is distributed underthe Creative Commons Attribution 3.0 License.

Solid Earth

Particle size distributions by laser diffraction: sensitivity ofgranular matter strength to analytical operating procedures

F. Storti and F. Balsamo

Dipartimento di Scienze Geologiche, Universita “Roma Tre”, Largo S. L. Murialdo 1, 00146 Roma, Italy

Received: 6 November 2009 – Published in Solid Earth Discuss.: 21 December 2009Revised: 24 March 2010 – Accepted: 2 April 2010 – Published: 19 April 2010

Abstract. We tested laser diffraction particle size analy-sis in poorly coherent carbonate platform cataclastic brec-cias and unfaulted quartz-rich eolian sands, representing low-and high-strength granular materials, respectively. We usedtwo different instruments with different sample dispersionand pumping systems and several wet analytical proceduresthat included different pump speeds, measurement precisiontests with and without sample ultrasonication, and differentdispersant liquids. Results of our work indicate that highstrength material is not strongly affected by analytical op-erating procedures, whereas low strength materials are verysensitive to the pump speed, ultrasonication intensity, andmeasurement run time. To reduce such a data variability, wepropose a workflow of analytical tests preliminary to the setup of the most appropriate SOP.

1 Introduction

Particle size distributions provide fundamental informationfor rock characterization and geological process descrip-tion in earth sciences, including sedimentology, stratigraphy,structural geology, pedology, and volcanology (e.g. Krum-bein, 1941; Irani and Callis, 1963; Engelder, 1974; Fried-man, 1979; Sheridan et al., 1987; Rieu and Sposito, 1991).In the last three decades, laser diffraction particle size analy-sers have proved to be an effective tool for providing particlesize distributions of poorly coherent rocks and soils (Weissand Frock, 1976; McCave et al., 1986; de Boer et al., 1987;Wanogho et al., 1987; Agrawal et al., 1991; Loizeau et al.,1994; Pye and Blott, 2004; Blott and Pye, 2006). This is be-cause they require little time for analysis, cover a wide sizerange, and require small size samples (e.g. Beuselinck et al.,

Correspondence to:F. Storti([email protected])

1998), thus facilitating very detailed studies of particle sizedistributions in geological structures.

Laser diffraction particle size analysers provide indirectsize measurements of spherically equivalent particles, basedon the principle that particles of a given size diffract lightthrough a given angle that increases logarithmically with de-creasing size (e.g. Beuselinck et al., 1998). In “wet proce-dures”, a few grams of material are dispersed into a liquidthat circulates across a quartz measurement cell illuminatedby a laser beam (Fig. 1). Different instruments have dif-ferently designed systems for stirring the dispersant liquidinto the tank and ensuring its circulation through the mea-surement cell by mechanical pumping. A wide variety ofstandard operating procedures (SOP) can be set up in laserdiffraction particle size analysers. They include the pumpspeed, the number of measurement runs, the length of themeasurement time, and the use of dispersing agents and/orultrasonication to aid sample disaggregation and dispersion(e.g. Blott et al., 2004; Sperazza et al., 2004). It follows thatmeasurement results, particularly when dealing with datasetsproduced by different operators and/or different instruments,can be influenced by the adopted SOP. Sample ultrasonica-tion, for example, can aid particle disaggregation by collisionor, in some cases, particle agglomeration (e.g. Mason et al.,2003; Blott et al., 2004).

In this study we analysed particle size distributions of un-faulted quartz-rich (83% quartz, 9% plagioclase, and 8%feldspar) eolian sands from the Priverno quarry, on theTyrrhenian side of the Central Apennines (e.g. Angelucciand Palmerini, 1961), and carbonate cataclastic brecciasfrom the active Assergi extensional fault system, whichbounds to the south the Gran Sasso Massif in the CentralApennines, Italy (e.g. D’Agostino et al., 1998). Our resultsindicate that particle size data measurement by laser diffrac-tion granulometry is not straightforward in fragile granularmaterials. We provide an analytical workflow for prelimi-nary testing, which is propedeutic to final SOP determination

Published by Copernicus Publications on behalf of the European Geosciences Union.

26 F. Storti and F. Balsamo: Particle size distributions by laser diffraction

LaserLaserbeam

Projectionlens

Fourier lens

Water-particle suspension

Stirring andultrasonication

Tank

Measurecell

Pump

Dete

cto

r

Computer

Fig. 1. Schematic cartoon showing the main components of a laserdiffraction particle size analyser. See text for details.

in granular rocks. The proposed testing procedure can resultappropriate for a wide variety of rock types, including cata-clastic rocks in fault zones and clastic sediments that under-went burial-related grain microfracturing.

2 Instruments overview

Most granulometric analyses were performed with a Mas-tersizer 2000 laser diffraction granulometer and associateddispersion units manufactured by Malvern Instruments Ltd.This laser diffraction particle size analyser is designed formeasuring particle sizes in the 0.02 to 2000 µm range by us-ing a blue (488.0 µm wavelength LED) and red (633.8 µmwavelength He-Ne laser) light dual-wavelength, single-lensdetection system. The light energy diffracted by the di-lute suspension circulating through the cell is measured by52 sensors. The light intensity adsorbed by the material ismeasured asobscurationand indicates the amount of sam-ple added to the dispersant liquid. Light scattering data areaccumulated in 100 size fractions bins, which are analysedat 1000 readings per second, and compiled with Malvern’sMastersizer 2000 software by using either full Mie or Fraun-hofer diffraction theories (de Boer et al., 1987). Light scatter-ing data acquired by the Mastersizer 2000 granulometer wereall mathematically inverted using the Mie theory, which uti-lizes the refractive index (RI) and absorption (ABS) of thedispersed granular material, and RI of the dispersant liquid.This theory is based on the assumption that: (1) particlesare mineralogically homogeneous; (2) particles are spherical;(3) the optical properties of particle and dispersion mediumare known; (4) suspension dilution guarantees that light scat-tered by one particles is measured before being-re-scatteredby other particles.

Particle size distributions were measured from wet disper-sions using both small (Malvern Hydro 2000 S) and large(Malvern Hydro 2000 MU) volume sample dispersion unitsavailable for the Mastersizer 2000 granulometer. The Hy-dro 2000 S unit has a capacity of 50 to 120 ml and is equippedwith a continuously variable single shaft centrifugal pumpand stirrer (up to 3500 revolutions per minute; in the follow-ing rpm), and by a continuously variable ultrasonic probe.The Hydro 2000 MU unit has a dispersion mechanism con-sisting of a sample recirculation head immerged into a stan-dard laboratory beaker (capacity of 600 to 1000 ml), whichcontains a built-in stirrer and sample recirculation centrifu-gal pump (from 600 to 4000 rpm), and a continuously vari-able ultrasonic probe (maximum power is 20 µm of tip dis-placement). A comparative wet analysis was performed bya Cilas 930 laser diffraction granulometer manufactured byCilas, which measures particle size distributions in the 0.2 to500 µm size range of wet dispersions by diffraction of a laserlight of 830 nm wavelength, based either on the Fraunhoferor Mie diffraction theories. Sample recirculation is achievedby two peristaltic pumps.

The analysed carbonate fault breccia sample, namedCABRE3, was collected in the same site of sample CABRE1described in Storti and Balsamo (2010), and was sievedat 500 µm to account for the analytical size range of theCilas 930 laser diffraction particle size analyser. Repro-ducible sub-sampling up to about 20 g weight of the totalsample amount was achieved by using a Quantachrome Siev-ing Riffler-Rotary Sample Splitter. Sub-sample aliquots nec-essary to produce laser obscuration values between 10% and15% were randomly selected from sub-samples (from 0.5 gto few grams) and added into the liquid-filled beaker for anal-ysis.

3 Factors influencing data acquisition and processingfrom dilute suspensions: testing strategy

Both chemical and mechanical factors can influence lightscattering data obtained from dilute suspensions (e.g. Sper-azza et al., 2004). Chemical interactions can in fact oc-cur between dispersion medium, the analysed material and,possibly, dispersing agent. Mechanical sample alterationcan be produced by two major factors: (i) ultrasonicationduring sample recirculation and (ii) centrifugal pump andstirrer speed. Moreover, the conversion of light scatter-ing data into particle size distributions depends on the op-tical properties of both analysed material and dispersant liq-uid. The high variability of the optical properties of rocksand sediments commonly requires iterative data reprocess-ing unless essentially monomineralic materials are analysed(e.g. Sperazza et al., 2004). To investigate on the influenceof parameters listed above, we set up the following testson monomineralic materials like eolian quartz sand (sub-sample aliquots SAND1x) and carbonate cataclastic breccia

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F. Storti and F. Balsamo: Particle size distributions by laser diffraction 27

(sub-sample aliquots CABRE3x): pump speed test, measure-ment precision test (instrument precision test of Blott et al.,2004), ultrasonication test, chemical test, and reprocessingtest.

The pump speed test is labelled Pt -test, wheret is the mea-surement run time (i.e. the number of readings that are aver-aged in a single measurement), and consists of measurementruns performed on a given sub-sample aliquot, at differentstirrer and pump speed (in the following simply referred to aspump speed) for a givent . The test starts with the set up oflaser obscuration values between 10% and 15% at half of themaximum pump speed. The pump speed is then lowered tothe minimum value and few (typically 10) measurement runsare performed before increasing the pump speed (typicallyby 100 rpm). Progressive measurement steps are carried outup to the maximum pump speed. Results are plotted in amean diameter versus pump speed graph to select the mostappropriate rpm value for further analyses. The measurementprecision test is labelled MPtS , whereS is the pump speed,and consists of measurement runs acquired at given pumpspeed and measurement run time during sub-sample recir-culation through the measurement cell. Our MPtS analysestypically consisted of 100 measurement runs, which meanssome hundred thousands of instrument readings. Analysis ofdata trends is included in the measurement precision test tohelp selecting the most appropriate number of measurementruns and to prevent significant mechanical bias. Additionof sub-sample ultrasonication to the measurement precisiontest produces the ultrasonication test US, which is labelledas USdS , whered is the probe tip displacement in the Hy-dro 2000 MU dispersion unit. Chemical effects were inves-tigated by repeating the above mentioned sample tests usingdifferent dispersion liquids. The suffixl is added to the ap-propriate test labelling in order to indicate the dispersion liq-uid used, which can be a solution with a dispersing agent. Wedid not use specific labelling for decalcified tap water by cou-pled magnetic and chemical commercial devices, which wasused in most of our analyses. The reprocessing test consistsof changing the optical properties of both granular materialand dispersant liquid during light scattering data processingof a given analysis by the Mie theory through the Master-sizer 2000 software.

Our preferred workflow (Fig. 2) starts with a pump speedtest to provide indications on the pump speed range for fur-ther testing. Short measurement run times (typically 5 s asa starting value) are used in pump speed analyses, in orderto minimise sub-sample mechanical alteration without com-promising the statistical robustness of the data. Results fromthe P-test provide constraints for MP and US test pairs per-formed at the same pump speed values. More than one testpair can be performed to investigate uncertainties associatedwith the pump test. Cross checking of results from the MPand US tests is commonly achieved by comparing the be-haviour of mean diameters, of the corresponding laser ob-scuration values, and of other statistical parameters including

pump speed range1 n

MPtS1

+USdS1

P testt

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+USdSn

best sample recirculation andmeasure run time parameters

Chemical test

best dispersant liquid

SP testFinalSOP

P = pump speed testMP = measurement precision testUS = Ultrasonication test

t = measurement run times = pump speedd = probe tip displacement

Reprocessing test

Fig. 2. Flow chart illustrating the main steps that constitute the pro-posed workflow to select the most appropriate operating procedurefor analyzing granular materials. See text for details.

the mode and percentiles, among whichD10, D50, andD90are the most common ones. Once the most appropriate pa-rameters in terms of best sample recirculation, measurementrun time, and measurement run number are selected, all in-formation for defining the most appropriate SOP is availablefor a given dispersion liquid. The next step is to check theeffectiveness of the selected dispersion medium by runningthe same test with different dispersion liquids. Comparisonof all results leads to the selection of the final SOP, whichcan be repeated for several sub-samples to perform a sam-pling precision test (Blott et al., 2004) that allows evaluatingmeasurement reproducibility (Fig. 2).

The sequential logic of these tests implies that results fromone test are then used to properly set up the following ones.Consequently, data interpretation is directly provided in sub-sections associated with the corresponding test descriptions.In most tests, for comparative purposes we acquired 100

www.solid-earth.net/1/25/2010/ Solid Earth, 1, 25–48, 2010

28 F. Storti and F. Balsamo: Particle size distributions by laser diffraction

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Fig. 3. Results of the pump speed test P5 performed on sub-sample aliquot SAND1a by the Hydro 2000 MU dispersion unit.(a) Meandiameter value evolution with increasing the pump speed from 600 up to 4000 rpm.(b) Laser obscuration value progression during the sametest.(c) Progression ofD10, D50, andD90 during the same test.(d) Granulometric curves obtained by averaging data from the corresponding10 measurement runs during representative pump speed steps.(e) Distribution of clay, silt, and sand size fractions during the test. Note thatthe sand fraction quickly reaches 100% of the sample material. See text for details.

measurement runs regardless of indications from previoustests. This because of the short time required by laser diffrac-tion particle size analysers to acquire light scattering data,thus encouraging the collection of large datasets from whichsub-sets can then be easily extracted.

4 Pump speed test

Results of the P5-test of sub-sample aliquot SAND1a(i.e. 5000 readings of the scattered light energy distributionfor each measurement run) are illustrated in Fig. 3. Meandiameters show an asymmetric bell-shaped trend character-ized by very low values at 600 and 700 rpm, a maximum at1000 to 1200 rpm, and an almost flat envelope of mean di-ameter values at pump speed higher than 1800 rpm (Fig. 3a).The corresponding laser obscuration values show a muchhigher variability, with a peak at 900 rpm and a minimumat 1300 rpm, followed by a near constant increase at higher

pump speed values (Fig. 3b). The trend ofD10, D50, andD90percentile data points strongly resembles the distribution ofthe mean diameters (Fig. 3c). Granulometric curves averagedover 10 measurement runs indicate a strongly unimodal par-ticle size distribution with some variability of both volumepercentage and modal peak size between 900 and 1500 rpm.Conversely, almost overlapping curves support strongly con-sistent results at pump speed values greater than 2000 rpm(Fig. 3d). The well sorted particle size distribution of thesample is illustrated by the pattern of clay, silt, and sand sizefractions: starting from 700 rpm, the latter includes 100% ofthe analysed material (Fig. 3e).

The P5-test of sub-sample aliquot CABRE3a shows anasymmetric bell-shaped trend characterized by very low val-ues of mean diameters at 600 to 800 rpm, followed by anabrupt increase up to 1100 rpm (Fig. 4a). With increasingthe pump speed, mean diameter values rapidly decrease up to1500 rpm and then continue to overally decrease quite slowly

Solid Earth, 1, 25–48, 2010 www.solid-earth.net/1/25/2010/

F. Storti and F. Balsamo: Particle size distributions by laser diffraction 29

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Fig. 4. Results of the pump speed test P5 performed on sub-sample aliquot CABRE3a by the Hydro 2000 MU dispersion unit.(a) Meandiameter value evolution with increasing the pump speed from 600 up to 4000 rpm.(b) Laser obscuration value progression during the sametest. (c) Progression ofD10, D50, andD90 percentiles during the same test.(d) Granulometric curves obtained by averaging data from thecorresponding 10 measurement runs during representative pump speed steps.(e) Distribution of clay, silt, and sand size fractions during thetest.

up to the maximum pump speed. The corresponding laser ob-scuration values show a rapid initial increase up to about 18%at 1000 rpm, followed by a rapid decrease towards the initialreference value (between 14.8% and 15.2%). A short-livedplateau occurs up to 2000 rpm and then obscuration con-stantly increases with increasing the pump speed (Fig. 4b).The D10, D50, and D90 percentiles show bell-shaped en-velopes, qualitatively similar to that of the mean diameter(Fig. 4c). From 2000 to 4000 rpm, theD90 data point enve-lope shows a constant and significant decrease, whileD50 ischaracterized by a higher scattering and only a slightly de-creasing trend.D10 values decrease as well and at 4000 rpmreach almost half of the value at 2000 rpm. Granulometriccurves averaged over 10 measurement runs, are characterisedby a strongly asymmetric shape that includes a major peakin the coarser fractions and a subordered “long tail” in thefiner ones (Fig. 4d). With increasing the pump speed, theheight of the major peak decreases and shifts towards finer

modal values, and the volume percentage of finer particles(equivalent diameter smaller than about 100 µm) correspond-ingly increases. The pattern of clay, silt, and sand size frac-tion curves indicates an initial dominance of silt sizes, fol-lowed by their abrupt decrease and a corresponding increaseof sand size fractions at pump speed values correspondingto the maximum mean diameter (Fig. 4e). At pump speedvalues higher than 1500 rpm, the sand size fraction slightlyvaries about a plateau value, the silt size fraction slightly de-creases, and the clay size fraction slightly increases.

Results of the P1-test of sub-sample aliquot CABRE3b areillustrated in Fig. 5. The overall behaviour of this test is sim-ilar to the previous one, with a slightly higher scattering ofmean diameter and percentile values. Granulometric curvesdo not show the almost constant shape evolution that charac-terises those acquired at 5 s of measurement run time, despitethe overall trend is comparable with the latter.

www.solid-earth.net/1/25/2010/ Solid Earth, 1, 25–48, 2010

30 F. Storti and F. Balsamo: Particle size distributions by laser diffraction

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Fig. 5. Results of the pump speed test P1 performed on sub-sample aliquot CABRE3b by the Hydro 2000 MU dispersion unit.(a) Meandiameter value evolution with increasing the pump speed from 600 up to 4000 rpm.(b) Laser obscuration value progression during the sametest. (c) Progression ofD10, D50, andD90 percentiles during the same test.(d) Granulometric curves obtained by averaging data from thecorresponding 10 measurement runs during representative pump speed steps.(e) Distribution of clay, silt, and sand size fractions during thetest.

A comparative P5-test of sub-sample aliquot CABRE3cwas performed with the Hydro 2000 S dispersion unit. Theoverall behaviour is quite similar to the previous test, withvery low mean diameter values at 500 rpm, a maximum at1200 rpm, and a decrease up to 2000 rpm. The last steps,with pump speed increments of 500 rpm, show quite smallvariations (Fig. 6a). A P5-test by the Hydro 2000 S dis-persion unit of sub-sample aliquot SAND1b, from 500 to2500 rpm, shows a bell-shaped distribution of mean diametervalues similar to that produced by using the Hydro 2000 MUdispersion unit (Fig. 6b). Comparison of pump speed test re-sults from sample CABRE, acquired at 5 s of measurementrun time by the Hydro 2000 MU and S dispersion units,shows that the former systematically provides higher meandiameter values at low pump speed ranges up to 1100 rpm,including the highest one (Fig. 6c). In the 1200 to 1600 rpmrange, higher mean diameter values are provided by the Hy-dro 2000 S unit. At higher pump speed, values provided bythe two dispersion units are similar.

Interpretation of the pump speed test results

The meaning of the bell-shaped curve provided by pumpspeed tests is not straightforward. Low velocity stirring andpumping favour sedimentation of coarser particles at the bot-tom of the beaker and/or slow motion in the recirculation unitand measurement cell, thus producing initial size distribu-tions biased towards the finer particles. The rapid increaseof mean diameter values derives from the improved recircu-lation of progressively coarser particles with increasing thepump and stirrer speed. The highest mean diameter valuescan either relate to the actual particle size distribution, or toan artefact caused by stagnation/slow motion of coarser ma-terial in the measurement cell. In the first case, the subse-quent decrease of mean diameter values should indicate on-going particle size reduction, accompanied by a significantincrease of laser obscuration at values higher than the ini-tial reference interval. For sub-sample aliquot CABRE3a,such an increase occurs at pump speed values higher than

Solid Earth, 1, 25–48, 2010 www.solid-earth.net/1/25/2010/

F. Storti and F. Balsamo: Particle size distributions by laser diffraction 31

eoliansand

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Fig. 6. (a) Pump speed test P5 performed on sub-sample aliquotCABRE3c by the Hydro 2000 S dispersion unit; mean diame-ter value evolution with increasing the pump speed from 500 upto 3500 rpm. (b) Pump speed test P5 performed on sub-samplealiquot SAND1b by the Hydro 2000 S dispersion unit; mean di-ameter value evolution with increasing the pump speed from 500up to 2500 rpm.(c) Comparison, in the range 500–2000 rpm, of thetrends of mean diameter values obtained from pump speed tests onsample CABRE. The solid line refers to data in Fig. 3a; the brokenline refers to data in Fig. 6a.

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finewardbias

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Fig. 7. Conceptual sketch showing the four main stages character-ising the typical asymmetric bell shaped curve resulting from theprogression of mean diameter values during pump speed tests ofgranular materials. See text for details.

2100 rpm, whereas obscuration remains almost constant andwithin the initial reference interval from 1500 to 2000 rpm(Fig. 4b). This evidence suggests that highest mean diametervalues are coarseward biased through inefficient sample re-circulation, and that values in the plateau characterizing bothmean diameter and laser obscuration values, correspond tothe most likely measurement runs. In CABRE3b the obscu-ration data point plateau adjacent to the maximum value isnot well developed and, conversely, it seems to indicate aslight increase of finer material during measurement. How-ever, analysis of theD10, D50, andD90 percentiles does notindicate significant particle size reduction despite significantscattering.

The behaviour of obscuration values associated with sub-sample aliquot SAND1a is different and this can relate to thedifferent rock type and size. Initial values very close to zerocan be explained by the very good sorting of the sample, al-most totally consisting of sand-size particles that, at very lowpump speed, are almost entirely deposited at the bottom ofthe beaker. The constant increase of laser obscuration valuesat pump speed higher than 1300 rpm indicates an increase ofthe material amount in the dispersion unit. Percentiles, how-ever, would support much smaller size variations (Fig. 3c).This apparently contrasting evidence can be reconciled byadmitting an increase of very fine particles and negligibleoverall particle size reduction. The source of such extremelyfine grained material is likely collision-induced surface pol-ishing of quartz grains, which are originally coated by ironhydroxide thin films imparting them a slightly orange colour.The same colour characterized water in the beaker at the endof the analyses.

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32 F. Storti and F. Balsamo: Particle size distributions by laser diffraction

measurement run number

a

e

b

c

measurement run number

0 20 40 60 80 1000

20

40

60

80

100

measure run number

d

Log Particle Size (mm)

0.01 1 10 100 10000.1

6

12

18

0

Volu

me p

erc

enta

ge

sand size

0 20 40 60 80 100

Linear Fit:

Y = 0.001588220822 * X + 271.6571448

Average Y = 271.737

Residual sum of squares = 84.7112

Regression sum of squares = 0.210183

R-squared = 0.00247503

0

100

200

300

400

500

0 20 40 60 80 100

0

200

400

600

800

D50

D90

D10

Mean diameter (mm)

Volume percentage

Obscuration (%) Diameter (mm)

16

14

10

8

4

2 Measurement run number

Mo

de

(m

m)

0 2 4 6 8 10250

260

270

280

curve 1

curve 100

curve 90

curve 80

curve 70

curve 60

curve 40

curve 30

curve 20

curve 10

curve 50

0 20 40 60 80 100

10

11

12

13

14

measurement run number

Linear fit:

Y = -0.01827272727 * X + 262.8133636

Average Y = 262.704

Residual sum of squares = 4.53526

Regression sum of squares = 0.0367282

R-squared = 0.00803331

Fig. 8. Results of the measurement precision test MP25005 performed on sub-sample aliquot SAND1c by the Hydro 2000 MU dispersionunit. (a) Mean diameter value evolution with increasing the number of measurement runs. Data statistics are provided.(b) Laser obscurationvalue progression during the same test.(c) Progression ofD10, D50, andD90 percentiles during the same test.(d) Granulometric curvesrepresentative of the particle size evolution. Note their virtually perfect overlap. The corresponding modal values (same colour code) areillustrated in the inset graph, whose statistics are also provided. Note how average modal and mean values are very similar.(e) Distributionof the sand size fractions during the test. It represents 100% of the sample, without any significant amount of clay and silt.

Results from the pump speed tests illustrated above can beschematically explained by a composite trend of mean valuesas a function of pump speed values, where four major stagescan be identified (Fig. 7): (1) an initial segment characterizedby very low mean diameter values, which is interpreted to in-dicate fineward bias by ineffective material recirculation intothe dispersion unit and measurement cell; (2) the adjacent,bell-shaped segment containing the maximum mean diame-ter values, which is interpreted to indicate coarseward biasby ineffective material recirculation; (3) the third, flat-lyingor slowly dipping segment, which is interpreted to indicateeffective material recirculation without significant mechani-cal alteration, thus providing the most effective pump speedsize range for further analyses; (4) the fourth segment, char-acterised by progressively decreasing mean diameter valuesindicating the occurrence of significant mechanical alterationand consequent fineward biasing of the sample material data.

The geometry of this last segment might be also influencedby a differential velocity between coarse and fine particles:being the recirculation of the latter faster, this might createthe illusion of a higher content of fines.

5 Measurement precision test

Results from the pump speed test on the SAND1 sample in-dicate negligible influence of this parameter for values higherthan 2000 rpm. We performed a MP25005 test (i.e. 2500 rpmof pump speed and 5 s of measurement run time) on sub-sample aliquot SAND1c (Fig. 8). Mean diameter values dis-play only slight variation between the 100 runs, as do theD10, D50, andD90 percentiles, while obscuration values arescattered and progressively increase. Granulometric curvesselected to monitor the evolution of the test show virtuallyidentical shapes, as supported by the very low variations of

Solid Earth, 1, 25–48, 2010 www.solid-earth.net/1/25/2010/

F. Storti and F. Balsamo: Particle size distributions by laser diffraction 33

100

measurement run number

a

0

100

200

300

400

500

0 20 40 60 80

Linear Fit:Y = -0.3149409241 * X + 220.0308467

Average Y = 204.126Residual sum of squares = 54629.7

Regression sum of squares = 8264.82R-squared = 0.131408

Mean diameter (mm)

e

b12

13

14

15

0 20 40 60 80 100

Residual sum of squares = 0.21348

Regression sum of squares = 4.94862

R-squared = 0.958645

Linear Fit:

Y = 0.007706450645 * X + 13.77582424

0 20 40 60 80 100

0

200

400

600

800

D10

D50

D90

c

measurement run number measurement run number

0 20 40 60 80 1000

20

40

60

80

100

measurement run number

d

Log Particle Size (mm)

Volume percentage

0.01 1 10 100 10000.1

2

4

6

0

Volu

me p

erc

enta

ge

clay sizesilt sizesand size

curve 100

Obscuration (%) Diameter (mm)

1 10 50 100360

380

400

420

440

460

480

500

Mode (m

m)

Measurement run number

curve 1

curve 90

curve 80

curve 70

curve 60

curve 40

curve 30

curve 20

curve 10

curve 50

Fig. 9. Results of the measurement precision test MP20005 performed on sub-sample aliquot CABRE3d by the Hydro 2000 MU dispersionunit. (a) Mean diameter value evolution with increasing the number of measurement runs. Data statistics are provided.(b) Laser obscurationvalue progression during the same test. Data statistics are provided.(c) Progression ofD10, D50, andD90 percentiles during the same test.(d) Granulometric curves representative of the particle size evolution. The corresponding modal values (same colour code) are illustrated inthe inset graph.(e)Distribution of the clay, silt and sand size fractions during the test.

the corresponding mode values (Fig. 8d). This indicates thatno material finer than sand was produced during measure-ment runs (Fig. 8e).

The pump speed test for sample CABRE3 indicates that2000 rpm is the most suitable pump speed value to ensure ef-fective material recirculation without very invasive mechan-ical alteration. Moreover, 5 s of measurement run time areexpected to provide more statistically robust results than 1 s.Accordingly, we initially performed a MP20005, test on sub-sample aliquot CABRE3d (Fig. 9). Mean diameter valuesshow significant scattering and a slightly decreasing trendwith time, while laser obscuration progressively increased.The value ofD50, andD90 percentiles show a pattern simi-lar to the mean diameter, being the scattering of the formerparticularly higher. On the other hand,D10 percentile val-ues are extremely small. Selected granulometric curves arequite similar apart from the first run (Fig. 9d). The corre-sponding modal values show a much higher mode for the

first run, followed by a drop of about 140 µm in the sec-ond one. Slightly higher values characterize runs 3 to 5, andthen very similar values pertain to the following runs (about350 µm) with the exception of the last one, which has a highermode, slightly higher than 400 µm. The distribution of sand,silt and clay size fractions shows a scattered pattern abouta slightly decreasing trend for the sand size, less scatteringabout a slightly increasing trend for the silt size, and negli-gible scattering with near constant values for the clay sizefraction (Fig. 9e).

Data from MP tests at 1200 rpm and 4000 rpm pumpspeed, respectively, performed for comparative purposes onthe influence of pump speed, are illustrated in Fig. 10. Thefirst test is characterised by extremely high data scattering,whereas in the second case scattering is quite small, aver-age diameter values are lower, and laser obscuration val-ues increase at higher rate than the corresponding ones ac-quired at 2000 rpm. Comparative measurement precision

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34 F. Storti and F. Balsamo: Particle size distributions by laser diffraction

a

Linear Fit:

Y = 0.1612023402 * X + 422.9113418

Average Y = 431.052

Residual sum of squares = 92539.3

Regression sum of squares = 2165.3

R-squared = 0.0228637

0

100

200

300

400

500

0 20 40 60 80 100

Mean d

iam

ete

r (m

m)

f

0 20 40 60 80 100

Linear Fit:

Y = -0.3405654845 * X + 197.785317

Average Y = 180.587

Residual sum of squares = 5835.99

Regression sum of squares = 9664.44

R-squared = 0.623495

d

Ob

scu

ratio

n (

%)

b

0 20 40 60 80 100

12

13

14

15

Linear Fit

Y = -0.002659105911 * X + 14.45768485

Residual sum of squares = 19.5907

Regression sum of squares = 0.589178

R-squared = 0.0291964

0 20 40 60 80 1000

200

400

600

800

D90

D50

D10

measure run number

c

Dia

mete

r (m

m)

measure run number measure run number

0 20 40 60 80 100

12

13

14

15

Residual sum of squares = 0.836643

Regression sum of squares = 14.5889

R-squared = 0.945762

Linear Fit:

Y = 0.01323192319 * X + 14.37078788

e

Ob

scu

ratio

n (

%)

0 20 40 60 80 1000

200

400

600

800

measure run number

i

D90

D50

D10

Dia

mete

r (m

m)

1200 rpm

4000 rpm

measure run numbermeasure run number

0

100

200

300

400

500

Mean d

iam

ete

r (m

m)

Fig. 10.Comparison between measurement precision test results performed on sample CABRE3 at the pump speed velocity corresponding tothe mean diameter peak value of the pump speed test (Fig. 3a), and at the maximum pump speed, respectively.(a) Test MP12005 performedon sub-sample aliquot CABRE3e by the Hydro 2000 MU dispersion unit; mean diameter value evolution with increasing the number ofmeasurement runs. Data statistics are provided.(b) Laser obscuration value progression during the same test. Data statistics are provided.(c) Progression ofD10, D50, andD90 percentiles during the same test.(d) Test MP40005 performed on sub-sample aliquot CABRE3f bythe Hydro 2000 MU dispersion unit; mean diameter value evolution with increasing the number of measurement runs. Data statistics areprovided.(e) Laser obscuration value progression during the same test. Data statistics are provided.(f) Progression ofD10, D50, andD90percentiles during the same test. Note the very large difference between the average mean diameter obtained from the first (431.052 µm) andthe second test (180.587 µm), respectively. Both them are affected by strong recirculation-related mechanical bias.

tests designed to investigate the influence of measurementrun time were performed at 2000 rpm pump speed and1 s, 10 s, 20 s, and 40 s of measurement run time, respec-tively. The MP20001, test on sub-sample aliquot CABRE3g(Fig. 11) is characterised by intense scattering of mean diam-eter values that show an increasing trend with increasing therun number (i.e. time). Intense scattering also occurs inD50,andD90 percentiles and in the sand, silt and clay size frac-tion data. The selected granulometric curves show a highervariability and a non systematic trend, compared to the cor-responding ones acquired at 5 s of measurement run time, asalso indicated by the corresponding modal values (Fig. 11d).For a constant total duration of the measurement precisiontest, increasing the measurement run time causes a decreaseof mean diameter data scattering and more linearly increas-ing trends of laser obscuration values (Fig. 12). We also ran aMP5 test on sub-sample aliquot CABRE3k by using the Cilas

930 laser diffraction particle size analyser. Results providedsignificantly smaller mean diameter values with respect tothose provided by the Mastersizer 2000, and these values sys-tematically decreased through time, as indicated by the verygood linear best fit (Fig. 13).

Plotting mean diameters of test MP20005 averaged everyfive measurement runs, indicates a progressive decrease ofvalues with time. In particular, such a decrease can be effec-tively fitted by an exponential curve, and the highest variationoccurs between the first two points (Fig. 14a). A similar trendcharacterises the corresponding modal values, despite higherscattering (Fig. 14b). A detail of laser obscuration data forthe first ten runs shows a very slight, almost linear increase,which reaches about 1% at the end of the test (Fig. 14c).The corresponding granulometric curves indicate that onlythe first and third runs provided coarser distributions, with amodal peak of about 510 µm, while the remaining eight ones

Solid Earth, 1, 25–48, 2010 www.solid-earth.net/1/25/2010/

F. Storti and F. Balsamo: Particle size distributions by laser diffraction 35

100

measure run number

a

0

100

200

300

400

500

0 20 40 60 80

Mean diameter (mm)

e

b

9

10

11

12

0 20 40 60 80 100 0 20 40 60 80 100

0

200

400

600

800

D10

D50

c

measure run number measure run number

0 20 40 60 80 1000

20

40

60

80

100

measure run number

d

Log Particle Size (mm)

Volume percentage

0.01 1 10 100 10000.1

2

4

6

0

Volu

me p

erc

enta

ge

clay sizesilt sizesand size

curve 1

curve 100

curve 90

curve 80

curve 70

curve 60

curve 40

curve 30

curve 20

curve 10

curve 50

Obscuration (%) Diameter (mm)

D90

8

Linear fit:

Y = 0.008490069007 * X + 10.48195152Residual sum of squares = 0.655079

Regression sum of squares = 6.00617R-squared = 0.901658

1 10 50 100300

340

380

420

460

500

Measurement run number

Mo

de

(m

m)

Regression sum of squares = 41648

R-squared = 0.225649

Linear fit:

Y = 0.7069838524 * X + 193.5241855

Average Y = 229.227

Residual sum of squares = 142922

Fig. 11.Results of the measurement precision test MP20001 performed on sub-sample aliquot CABRE3g by the Hydro 2000 MU dispersionunit. (a) Mean diameter value evolution with increasing the number of measurement runs. Data statistics are provided.(b) Laser obscurationvalue progression during the same test. Data statistics are provided.(c) Progression ofD10, D50, andD90 percentiles during the same test.(d) Granulometric curves representative of the particle size evolution. The corresponding modal values (same colour code) are illustrated inthe inset graph.(e)Distribution of the clay, silt and sand size fractions during the test.

are quite similar and have a modal peak of about 400 µm thatremains unchanged also after 50 and 100 runs (Fig. 14d). Inparticular, the third run curve provides the coarsest distribu-tion, and the correspondingD10, D50, andD90 percentilesand modal value are outliers with respect to the overall trendof the other data (Fig. 14e–g). This evidence questions thevalidity of the third run data.

Interpretation of the measurement precision test results

The measurement precision test provided contrasting resultsdepending on the rock type. Carbonate cataclastic brecciasare sensitive to the material recirculation time (i.e. the num-ber of measurement runs and/or the measurement run time),whereas eolian sand data remains almost unaltered throughtime. In particular, in carbonate cataclastic breccias a signifi-cant difference occurs between the first run and the following

ones, suggesting that only short recirculation times ensure asmall mechanical bias to particle size data from wet suspen-sion analyses.

6 Ultrasonication test

An ultrasonication test on eolian sand was performed on sub-sample aliquot SAND1d, using the maximum ultrasonicationprobe tip displacement (20 µm), 2500 rpm of pump speed,and 5 s of measurement run time (US205). Mean diametersremain almost constant in the first 26 runs, with an aver-age value of 270.8 µm, and then suddenly steps down to anaverage value of 262.3 µm in the remaining 73 runs of thetest. The average value over 100 runs is 264.5 µm (Fig. 15a).Laser obscuration values increase of about 12.5% during thetest (Fig. 15b). When only the first 10 granulometric curvesare compared, they show a virtually constant modal peak at

www.solid-earth.net/1/25/2010/ Solid Earth, 1, 25–48, 2010

36 F. Storti and F. Balsamo: Particle size distributions by laser diffraction

0 10 20 30 40 50

0

100

200

300

400

500 Linear Fit:

Y = -0.4961758944 * X + 206.8466653

Average Y = 194.194

Residual sum of squares = 8106.93

Regression sum of squares = 2563.46

R-squared = 0.24024

0 10 20 30 40 50

13

14

15

16

17

18

Obscura

tion (

%)

0 5 10 15 20 25

0

500 Linear Fit:

Y = -0.4750692308 * X + 176.2197

Average Y = 170.044

Residual sum of squares = 2613.06

Regression sum of squares = 293.398

R-squared = 0.100947

0 5 10 15 20 25

11

12

13

14

15

16

0 1 2 3 4 5 6 7 8 9 10 11 12 13

0

500 Linear Fit:

Y = -1.851313187 * X + 200.3955769

Average Y = 187.436

Residual sum of squares = 494.034

Regression sum of squares = 623.78

R-squared = 0.558035

0 1 2 3 4 5 6 7 8 9 10 1112 13

10

11

12

13

14

15

c

d

a

b f

e

measurement run time = 10s

Mean d

iam

ete

r (m

m)

measurement run time = 20s measurement run time = 40s

measure run number measure run number measure run number

Fig. 12.Results of measurement precision tests performed at different run times on sample CABRE3 by the Hydro 2000 MU dispersion unit.(a) Test MP200010 on sub-sample aliquot CABRE3h; mean diameter value evolution with increasing the number of measurement runs. Datastatistics are provided.(b) Laser obscuration value progression during the same test.(c) Test MP200020 on sub-sample aliquot CABRE3i;mean diameter value evolution with increasing the number of measurement runs. Data statistics are provided.(d) Laser obscuration valueprogression during the same test.(e) Test MP200040 on sub-sample aliquot CABRE3j; mean diameter value evolution with increasing thenumber of measurement runs. Data statistics are provided.(f) Laser obscuration value progression during the same test.

about 259 µm. The corresponding volume percentage dropsof about 1.75% from curve 7 onward (Fig. 15c). Modal val-ues remain almost constant for the entire test, about an aver-age value of 258.5 µm (Fig. 15d). Contrasting these 10 curvesfrom the ultrasonication test, against the first one from themeasurement precision test on sub-sample aliquot SAND1cindicates negligible differences (Fig. 15c).

Ultrasonication intensities of 2.5 µm, 5 µm, 10 µm, and20 µm of tip displacement were applied to the carbonate cat-aclastic breccia, using a pump speed of 2000 rpm and 5 s ofmeasurement run time. Results indicate that increasing theultrasound energy causes (i) a faster decrease of mean diam-eter values, which passes from linear to power law best fitcurves, (ii) higher increases of laser obscuration, and (iii) adecrease of average modal values up to 10 µm, which remainalmost constant when the maximum probe tip displacementis used (Fig. 16). Analysis of granulometric curves pertain-ing to the first 10 runs and to runs 50 and 100 in each testshows a progressively increasing difference between first runcurves and the remaining ones with increasing the ultrason-

ication probe tip displacement (Fig. 17). Moreover, shapedifferences among curves increase, particularly between testUS2.55 and the remaining ones, and the modal peak volumepercentage of the bulk of the curves in each test decreaseswith increasing ultrasonication intensity. Comparison of thefirst run curves from tests with and without ultrasonicationshows that the latter provide a significantly coarser particlesize distribution in the modal peak (Fig. 17e). The influ-ence of ultrasonication is also illustrated by the differencebetween first-run modal values and those averaged over thefirst 10 runs of the corresponding tests. The greater differ-ence occurs when no ultrasonication was used. The smallerdifference occurs at the minimum ultrasonication intensityand then it increases up to the US105 test.

Interpretation of the ultrasonication test results

Results from ultrasonication tests indicate negligible effectson eolian sand, particularly when only the first 10 to 20runs are considered, according to the measurement precision

Solid Earth, 1, 25–48, 2010 www.solid-earth.net/1/25/2010/

F. Storti and F. Balsamo: Particle size distributions by laser diffraction 37

0

100

200

300

400

500

0

measure number

10 20 30

174.63 mm

151.69 mm136.69 mm

132.60 mm

Me

an

dia

me

ter

(mm

)

Linear Fit:

Y = -1.413119021 * X + 166.5176782

Average Y = 144.614

Residual sum of squares = 355.134

Regression sum of squares = 4488.04

R-squared = 0.926673

Fig. 13.Results of a measurement precision tests performed on sub-sample aliquot CABRE3k by the Cilas 930 laser diffraction particlesize analyser; mean diameter value evolution with increasing thenumber of measurement runs. Data statistics are provided.

test evidence. On the other hand, in the carbonate cataclas-tic breccia sub-sample aliquots, ultrasonication has a muchgreater influence causing significant particle size reductionsafter few measurement runs, as indicated by the concomi-tant reduction of mean diameter and mode values, by the in-crease of laser obscuration, and by the increase of volumepercentages in the 0.5 µm to 100 µm segments of granulo-metric curves. Even after a single measurement run, ultra-sonication is able to shift fineward the modal peak value ofparticle size distributions by 60 to 80 µm.

7 Chemical test

In wet analyses, liquid dispersants can wet microfracturesand help cohesion loss, thus favouring disintegration of mi-crofractured particles. Fracture aperture thresholds for capil-larity permeability depend on the surface tension of the dis-persant liquid. Accordingly, dispersant liquids with low sur-face tensions are expected to enhance particle disintegrationin cataclastic materials, whereas this effect should be negli-gible for intact particles. To test this hypothesis, denaturatedethyl alcohol was used as dispersant liquid for data acqui-sition from eolian sand by performing a MP25005al, test onsub-sample aliquot SAND1e. Results are very consistent, asillustrated by the almost constant mean diameter values, bythe flat lying best fit line of mode values, and by the very sim-ilar granulometric curves in the first 10 runs, which providean extremely good overlap with the first curve from the sametest using decalcified tap water as dispersant liquid (Fig. 18).

The corresponding modal values show an initial decrease ofless than 5 µm, reaching a plateau value after 4 runs.

Two measurement precision test were performed onCABRE3p and CABRE3q sub-sample aliquots, using denat-urated ethyl alcohol and demineralised water, respectively(Fig. 19). The first test provided quite scattered mean diam-eter and mode values, both characterized by flat-lying bestfit lines, which are smaller than the corresponding ones ob-tained from demineralised water of about 70 µm and 53 µm,respectively. The increase of laser obscuration values isgreater for the dispersion in denaturated ethyl alcohol. Anal-ysis of granulometric curves pertaining to the first 10 runs in-dicates a higher variability for measurements acquired in de-naturated ethyl alcohol, of both curve shape and modal peakelevation (Fig. 19g, h). Such a higher variability is confirmedby the analysis of the corresponding modal values. Finally,comparison with the first run curve from the same test usingdecalcified tap water as dispersant liquid, indicates that gran-ulometric curves obtained from the denaturated ethyl alcoholsuspension have much greater differences with respect to thecorresponding ones acquired using demineralised water asdispersant liquid.

Interpretation of the chemical test results

Test results indicate that the use of denaturated ethyl alcoholhas a negligible influence on data acquisition in quartz eoliansand. Variations of mean diameter and mode values are lessthan 5 µm, which fall inside the variability associated withsub-sampling, even in well sorted sediments like dune sands.On the other hand, the same dispersant liquid causes a de-crease of about 75 µm of mean diameter values when car-bonate cataclastic breccia is analysed. The evidence that,when demineralised water is used, results are very similarto those from the corresponding test in decalcified tap waterrules out any significant bias produced by sub-sampling andsupports particle fragmentation during suspension recircula-tion. This is well illustrated by the systematic decrease ofmodal peak volumes and size, and by the corresponding in-crease of volume percentage values in the 0.5 µm to 110 µmsegments of granulometric curves in Fig. 19g. Higher varia-tions occurs after only two runs. It is worth noting that manyother dispersants could be used, as well as various pretreat-ments. However, performing detailed investigations on thisis out of our purposes in this paper.

8 Reprocessing test

The first run of the MP25005 test was selected for data re-processing following favourable behaviour in previous tests.Changing RI values from 1.4 to 1.8 causes negligible ef-fects in eolian quartz sand (sub-sample aliquot SAND1c),as illustrated in Fig. 20. The corresponding granulometriccurves almost perfectly overlap and percentiles and modal

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38 F. Storti and F. Balsamo: Particle size distributions by laser diffraction

Dia

mete

r (m

m)

D50

D90

0 4 8 100

200

400

600

800

62 50

100

0 4 8 1062 50

100

Dia

mete

r (m

m) Measurement number

D10

200

210

220

230

240

250M

ea

n d

iam

ete

r (m

m)

analysis time (s)

0 100 200 300 400 500

13.6

13.8

14

14.2

14.4

Measurement number

6 8 50

100

42

Measure n.

Obscura

tion (

%)

f

Log Particle Size (mm)

Volume percentage

0.01 1 10 100 10000.1

2

4

6

0

curve 1

curve 10

curve 9

curve 8

curve 7

curve 5

curve 4

curve 3

curve 2

curve 6

curve 50curve 100

2.5

3

3.5

4

4.5

a

b

e

d

350

370

380

390

400

410

Mo

de

(m

m)

analysis time (s)

0 100 200 300 400 500

360

0 2 4 6 8 10

320

360

400

440

480

520

Measurement run number

Mo

de

(m

m)

100

50

g

c

Fig. 14. Analysis of data from the test MP20005 on -sample aliquot CABRE3d (Fig. 9).(a) Mean diameter values averaged every fivemeasurement runs.(b) Average modal values corresponding to data in (a). In both cases, the best fits indicate an exponential decay.(c) Laserobscuration values recorded during the first 10 runs (black dots), compared with the values after 50 (red dot) and 100 (blue dot) measurementruns. (d) Granulometric curves computed for the first 10 runs, compared with the ones from the 50th and 100th run.(e) Progression ofD50 andD90 percentiles during the first 10 measurement runs. Data after 50 (red dot) and 100 (blue dot) runs are provided for comparison.(f) Progression ofD10 percentiles during the first 10 measurement runs. Data after 50 (red dot) and 100 (blue dot) runs are provided forcomparison.(g) Progression of modal values during the first 10 measurement runs (colour code as in (d)). Data after 50 (grey dot) and 100(black dot) runs are provided for comparison.

values show a very small variability. The same result was ob-tained when varying ABS values from 1.00 to 0.01 (Fig. 21).Changing RI in carbonate cataclastic breccia (first run of testMP20005 on sub-sample aliquot CABRE3d) causes somevariability in the corresponding grain size distributions, par-ticularly from RI = 1.4 to RI = 1.6 (Fig. 22). Analysis ofresiduals associated with best fit curves indicates that themost appropriate RI value is 1.6. Higher values, however,

do not significantly influence the computed particle size dis-tributions, as lower values do particularly for the volume per-centage of sizes lower than about 2 µm (Fig. 22b). The majoreffect of changing ABS values from 1.00 to 0.01 on CABREmaterial is to progressively shorten the tail of granulomet-ric curves, from about 0.25 µm (ABS = 1.00–0.50) to 0.6 µmwhen ABS = 0.01 (Fig. 23). For ABS lower than 1.00, de-creasing particle absorption causes an increase of percentile

Solid Earth, 1, 25–48, 2010 www.solid-earth.net/1/25/2010/

F. Storti and F. Balsamo: Particle size distributions by laser diffraction 39

0 20 40 60 80 100

0

100

200

300

400

500

24

25

26

27

28

29

30

31

32

33

34

35

36

37

Mean d

iam

ete

r (m

m)

measure number

Linear fit:

Y = -0.1183510451 * X + 270.4132088

Average Y = 264.496

Residual sum of squares = 586.783

Regression sum of squares = 1132.46

R-squared = 0.658698

0 20 40 60 80 100

measure number

Obscura

tion (

%)

a b

measure numberLog Particle Size (mm)

1 10 100 10000.1

c

Vo

lum

e p

erc

en

tag

e

4

12

16

0

8

Linear fit on the first 26 runs

Y = 0.0142817094 * X + 270.6178892

Average Y = 270.811R-squared = 0.00286513

Linear fit on the remaining 73 data

Y = -0.04511039121 * X + 263.9155502

Average Y = 262.246R-squared = 0.315638

0 20 40 60 80 100

250

260

270

280

curve 1

curve 10

curve 9

curve 8

curve 7

curve 5

curve 4

curve 3

curve 2

curve 6

curve 1 no US

Mo

de

(m

m)

Linear fit:

Y = -0.005597897341 * X + 258.790905

Average Y = 258.511

Residual sum of squares = 121.493

Regression sum of squares = 2.53355

R-squared = 0.0204275

d

Fig. 15. Results of the ultrasonication test US205 performed on sub-sample aliquot SAND1d by the Hydro 2000 MU dispersion unit.(a)Mean diameter value evolution with increasing the number of measurement runs. Data statistics are provided for the cumulative dataset, forthe first 26 runs, and for the remaining 73 runs, respectively.(b) Laser obscuration value progression during the same test.(c) Granulometriccurves computed for the first 10 runs, compared with the first curve from the test MP25005 on sub-sample aliquot SAND1c (Fig. 8).Progression of modal values with increasing the number of measurement runs. Data statistics are provided.

values and a decrease of modal values. Analysis of resid-uals associated with best fit curves indicates that the mostappropriate ABS value is 0.01. Finally, changing the RI val-ues of the dispersant liquid has negligible effects on eolianquartz sand, and an influence on CABRE material that iscomparable to what is produced by changing RI of carbonateparticles (Fig. 24).

Interpretation of reprocessing test results

Results of these tests indicate that in the case of the analyzedmaterials, the sensitivity of light scattering data reprocess-ing by the Mie theory is mainly governed by the particle sizerange, rather than by their optical properties. In fact, the verygood sorting of sample SAND1 results in a virtually insen-sitive behaviour to reprocessing, while the large spanning of

sizes in CABRE3 enhances the sensitivity of particles finerthat about 2 µm.

9 Discussion

Results illustrated above indicate that particles with differentstrength respond in a very different way to the same testingstrategy during particle size determination by laser diffrac-tion. Quartz eolian sand provided virtually identical particlesize distributions regardless of the adopted operating proce-dure. On the other hand, carbonate cataclastic breccia is verysensitive to operating procedures. Such a contrast indicatesthat the variability associated with the sample CABRE3 doesnot depend on instrumental bias, but instead it relates to thepeculiar fabric of cataclastic rocks derived from massive pro-toliths like platform carbonates.

www.solid-earth.net/1/25/2010/ Solid Earth, 1, 25–48, 2010

40 F. Storti and F. Balsamo: Particle size distributions by laser diffraction

c

0 20 40 60 80 100

0

500Power Law Fit

Y = pow(X,-0.1033986354) * 226.463531

Residual sum of squares = 1.15809

Regression sum of squares = 0.911613

R-squared = 0.440456

d

measure number

US = 5.0 mm

100

200

300

400

a0

100

200

300

400

500

0 20 40 60 80

Linear Fit:

Y = -0.1899744374 * X + 182.4314691

Average Y = 172.838

Residual sum of squares = 32919

Regression sum of squares = 3007.22

R-squared = 0.0837055

Mean d

iam

ete

r (m

m)

measure number

US = 2.5 mm

100measure number

Obscura

tion (

%)

0 20 40 60 80 10010

12

14

16

18 Power Law Fit:

Y = pow(X,0.04232472628) * 10.8680306

Residual sum of squares = 0.000679821

Regression sum of squares = 0.152746

R-squared = 0.995569

Sigma-hat-sq'd = 6.93695E-006

b

Mean d

iam

ete

r (m

m)

measure number0 20 40 60 80 100

10

12

14

16

18 Power Law Fit:

Y = pow(X,0.07027879979) * 10.6285407

Residual sum of squares = 0.00338771

Regression sum of squares = 0.421143

R-squared = 0.99202

e

Obscura

tion (

%)

measure number

g

0 20 40 60 80 100

Power Law Fit:

Y = pow(X,-0.1232596288) * 201.404938

Residual sum of squares = 1.06029

Regression sum of squares = 1.29546

R-squared = 0.549913

0

100

200

300

400

500

Mean d

iam

ete

r (m

m)

US = 10.0 mm

0

500

0 20 40 60 80 100

Power Law Fit:

Y = pow(X,-0.08921987851) * 191.7449856

Residual sum of squares = 2.00859

Regression sum of squares = 0.678741

R-squared = 0.252571

l

measure number

US = 20.0 mm

10

12

14

16

measure number

18

0 20 40 60 80 100

Power Law Fit:

Y = pow(X,0.06710359782) * 11.1765830

Residual sum of squares = 0.00377809

Regression sum of squares = 0.383948

R-squared = 0.990256

h

Obscura

tion (

%)

10

12

14

16

18

0 20 40 60 80 100

Power Law Fit

Y = pow(X,0.07053909631) * 12.43777868

Residual sum of squares = 0.0414187

Regression sum of squares = 0.424268

R-squared = 0.911059

m

measure number

Obscura

tion (

%)

100

200

300

400

Mean d

iam

ete

r (m

m)

200

300

400

500

600

0 20 40 60 80 100measure number

Mode (m

m)

n

Linear fit:

Y = -0.1322146715 * X + 348.4902909

Average Y = 341.813

Residual sum of squares = 149679

Regression sum of squares = 1456.58

R-squared = 0.00963755

200

300

400

500

600

0 20 40 60 80 100measure number

Mode (m

m)

i

200

300

400

500

600

0 20 40 60 80 100measure number

Mode (m

m)

f

200

300

400

500

600

0 20 40 60 80 100measure number

Mode (m

m)

Linear fit:

Y = -0.1255660546 * X + 358.9963158

Average Y = 352.655

Residual sum of squares = 61329.8

Regression sum of squares = 1313.77

R-squared = 0.0209722

Linear fit:

Y = -0.1172544734 * X + 370.2030109

Average Y = 364.282

Residual sum of squares = 36332.4

Regression sum of squares = 1145.6

R-squared = 0.0305673

Linear fit:

Y = -0.2282990159 * X + 353.2929703

Average Y = 341.764

Residual sum of squares = 45831.4

Regression sum of squares = 4342.94

R-squared = 0.0865569

Fig. 16. Ultrasonication tests on sample CABRE3 by the Hydro 2000 MU dispersion unit.(a) Ultrasonication test US2.55 performed onsub-sample aliquot CABRE3l; mean diameter value evolution with increasing the number of measurement runs.(b) Laser obscuration valueprogression during the same test.(c) Mode value progression during the same test.(d) Ultrasonication test US55 performed on sub-samplealiquot CABRE3m; mean diameter value evolution with increasing the number of measurement runs.(e)Laser obscuration value progressionduring the same test.(f) Mode value progression during the same test.(g) Ultrasonication test US105 performed on sub-sample aliquotCABRE3n; mean diameter value evolution with increasing the number of measurement runs.(h) Laser obscuration value progression duringthe same test.(i) Mode value progression during the same test.(l) Ultrasonication test US205 performed on sub-sample aliquot CABRE3o;mean diameter value evolution with increasing the number of measurement runs.(m) Laser obscuration value progression during the sametest.(n) Mode value progression during the same test. Data statistics are provided for all plots.

Solid Earth, 1, 25–48, 2010 www.solid-earth.net/1/25/2010/

F. Storti and F. Balsamo: Particle size distributions by laser diffraction 41

Log Particle Size (mm)

Volume percentage

1 10 100 10000.1

curve 50curve 100

curve 1

curve 10

curve 9

curve 8

curve 7

curve 5

curve 4

curve 3

curve 2

curve 6

2

4

6

0

d

US = 20 mm

Log Particle Size (mm)

Volume percentage

1 10 100 10000.1

curve 50curve 100

curve 1

curve 10

curve 9

curve 8

curve 7

curve 5

curve 4

curve 3

curve 2

curve 6

2

4

6

0

a

US = 2.5 mm

Log Particle Size (mm)

Volume percentage

1 10 100 10000.1

curve 50curve 100

curve 1

curve 10

curve 9

curve 8

curve 7

curve 5

curve 4

curve 3

curve 2

curve 6

2

4

6

0

b

US = 5 mm

Log Particle Size (mm)

Volume percentage

1 10 100 10000.1

curve 50curve 100

curve 1

curve 10

curve 9

curve 8

curve 7

curve 5

curve 4

curve 3

curve 2

curve 6

2

4

6

0

c

US = 10 mm

Volu

me p

erc

enta

ge

Log Particle Size (mm)

1 10 100 10000.1

e

noUS

460

500

420

380

340

300US2.5

US5

US10

US20

US = 20 mm

US = 10 mm

US = 5 mm

US = 2.5 mm

no US

Mo

de

(m

m)

0

2

4

6

Fig. 17. (a)Granulometric curves computed for the first 10 runs of test US2.55 performed on sub-sample aliquot CABRE3l, compared withthe ones from the 50th and 100th run.(b) Granulometric curves computed for the first 10 runs of test US55 performed on sub-sample aliquotCABRE3m, compared with the ones from the 50th and 100th run.(c) Granulometric curves computed for the first 10 runs of test US105performed on sub-sample aliquot CABRE3n, compared with the ones from the 50th and 100th run.(d) Granulometric curves computedfor the first 10 runs of test US205 performed on sub-sample aliquot CABRE3o, compared with the ones from the 50th and 100th run.(e)First run granulometric curves from the four tests listed above, compared with the first run curve from test MP20005 on sub-sample aliquotCABRE3d (Fig. 9). The inset graph shows the modal values of the same first run cuves (filled dots, same colour code) compared with modalvalues averaged over the first 10 runs of the corresponding tests (empty dots, same colour code).

www.solid-earth.net/1/25/2010/ Solid Earth, 1, 25–48, 2010

42 F. Storti and F. Balsamo: Particle size distributions by laser diffraction

1 2 3 4 5 6 7 8 9 10

250

260

270

Measurement run number

Mode (m

m)

c

a

Mean d

iam

ete

r (m

m)

measurement run number measurement run number

Obscura

tion (

%)

b

0 20 40 60 80 100measurement run number

Mode (m

m)

0 20 40 60 80 100

0

100

200

300

400

500

Linear Fit:

Y = 0.0009950435043 * X + 267.9889503

Average Y = 268.039

Residual sum of squares = 121.964

Regression sum of squares = 0.082501

R-squared = 0.000675978

Sigma-hat-sq'd = 1.24454

0 20 40 60 80 100

10

11

12

13

14

250

260

270

280

290

300

Linear fit:

Y = 0.002526540654 * X + 257.6840297

Average Y = 257.812

Residual sum of squares = 96.7848

Regression sum of squares = 0.531897

R-squared = 0.00546563

Average Y = 258.715

e

Log Particle Size (mm)

1 10 100 10000.1

Vo

lum

e p

erc

en

tag

e

4

12

16

0

8

curve 1

curve 10

curve 9

curve 8

curve 7

curve 5

curve 4

curve 3

curve 2

curve 6

curve 1 tap

water2

6

10

14

18

d

Fig. 18. Results of the chemical test MP25005al performed on sub-sample aliquot SAND1e by the Hydro 2000 MU dispersion unit, usingdenaturated ethyl alcohol as dispersant liquid.(a) Mean diameter value evolution with increasing the number of measurement runs. Datastatistics is provided.(b) Laser obscuration value progression during the same test.(c) Progression of modal values with increasing thenumber of measurement runs. Data statistics are provided.(d) Granulometric curves computed for the first 10 runs, compared with the firstcurve from the test MP25005 on sub-sample aliquot SAND1c (Fig. 8).(e)Modal values corresponding to the curves in (d).

In fact, in this case particles are produced by multiple frac-turing, rolling and grinding of material within fault zones(e.g. Borg et al., 1960; Storti et al., 2003; Sammis and BenZion, 2008). Particle size depends on the relative strengthdistribution along cleavage and microfracture sets as a func-tion of the applied stress (e.g. Sammis et al., 1987). Ac-cordingly, the mechanical behaviour of these carbonate cat-aclastic particles can be compared to that of sedimentaryparticles made of cohesive aggregate grains. Conversely,multiple collisions of quartz particles during eolian trans-port along coastal dunes ensures effective exploiting of pre-existing flaws. The resulting rounded particles are strongenough for being not significantly influenced by mechanicalsolicitations in laser diffraction particle size analysers.

It follows that determining the appropriate operating pro-cedure bears a fundamental importance for heavily mi-crofractured materials, while it has secondary effect whenhigh strength particles are analysed. In the latter case, onlypump speed can influence the final results by not ensuringeffective particle recirculation in the dispersion unit. How-ever, given the high strength of this material, pump speed val-

ues close or higher than half of maximum speed (e.g. 2000–3000 rpm) can be used without expecting any significant me-chanical bias. On the other hand, operating procedures asless invasive as possible are required when analysing fragilegranular materials. In this case, finding the proper analyti-cal workflow benefits of some general guidelines for broadsample categories, followed by further specific refinements.Moreover, selecting an effective instrumentation plays a fun-damental role to determine particle size distributions of frag-ile materials. According to our tests, peristaltic pumpingduring sample recirculation introduces a systematic bias tothe final results and, consequently, laser diffraction analy-sers adopting this technical solution are inappropriate. Onthe other hand, centrifugal pumping provides a much moreflexible and effective solution for analysing fragile materials.Between the two Malvern dispersion units we used, the largevolume Hydro 2000 MU ensured effective sample recircu-lation at lower pump speed values compared to the Hydro2000 S.

Solid Earth, 1, 25–48, 2010 www.solid-earth.net/1/25/2010/

F. Storti and F. Balsamo: Particle size distributions by laser diffraction 43

ab

measurement run number

Mean diameter (mm) Obscuration (%)

measurement run number0 20 40 60 80 100

0

100

200

300

400

500

Linear Fit:

Y = 0.05530309631 * X + 126.6512636

Average Y = 129.444

Residual sum of squares = 89516.2

Regression sum of squares = 254.844

R-squared = 0.00283882

Power Law Fit:

Y = pow(X,0.0162270493) * 10.95206667

Residual sum of squares = 0.00243261

Regression sum of squares = 0.0224523

R-squared = 0.902245

d

measurement run number

Mean diameter (mm) Obscuration (%)

measurement run number0 20 40 60 80 100

0

100

200

300

400

500

0 20 40 60 80 100

Linear Fit:

Y = 0.1002275308 * X + 195.6247497

Average Y = 200.686

Residual sum of squares = 37227.6

Regression sum of squares = 837.046

R-squared = 0.0219901

10

11

12

13

14

e

0 20 40 60 80 100

13

14

15

16

17

measurement run number

Power Law Fit:

Y = pow(X,0.01951090091) * 10.5557782

Residual sum of squares = 0.00244476

Regression sum of squares = 0.032459

R-squared = 0.929957

Mode (mm)

0 20 40 60 80 100

0

100

200

300

400

500

Linear fit:

Equation Y = -0.02004089409 * X + 331.61

Average Y = 330.608

Residual sum of squares = 172028

Regression sum of squares = 33.4664

R-squared = 0.000194503

c

Mode (mm)

0 20 40 60 80 100

0

100

200

300

400

500

measurement run number

f

Linear fit:

Equation Y = 0.03191116112 * X + 382.176

Average Y = 383.788

Residual sum of squares = 39417.4

Regression sum of squares = 84.8517

R-squared = 0.00214802

denaturated ethylicalcohol

demineralised water

Log Particle Size (mm)

Volume percentage

1 10 100 10000.1

2

4

6

0

Log Particle Size (mm)

Volume percentage

1 10 100 10000.1

2

4

6

0

curve 1 tap

water

curve 1

curve 10

curve 9

curve 8

curve 7

curve 5

curve 4

curve 3

curve 2

curve 6

g

0 2 4 6 8 10250

300

350

400

450

Mode (m

m)

Measurement run number

h

Fig. 19. Results of chemical tests performed on sample CABRE3e by the Hydro 2000 MU dispersion unit.(a) Test MP20005al performedon sub-sample aliquot CABRE3p using denaturated ethyl alcohol as dispersant liquid; mean diameter value evolution with increasing thenumber of measurement runs. Data statistics are provided.(b) Laser obscuration value progression during the same test. Data statisticsare provided. (c) Progression of modal values with increasing the number of measurement runs. Data statistics are provided.(d) TestMP20005dw performed on sub-sample aliquot CABRE3q using demineralised water as dispersant liquid; mean diameter value evolutionwith increasing the number of measurement runs. Data statistics are provided.(e) Laser obscuration value progression during the same test.Data statistics are provided.(f) Progression of modal values with increasing the number of measurement runs. Data statistics are provided.(g) Granulometric curves computed for the first 10 runs in (a), compared with the first curve from the test MP20005 on sub-sample aliquotCABRE3d (Fig. 9).(h) Granulometric curves computed for the first 10 runs in (d), compared with the first curve from the test MP20005 onsub-sample aliquot CABRE3d (Fig. 9). The inset graph show the comparison between modal values corresponding to the curves in (g) (filleddots) and in (h) (empty dots).

www.solid-earth.net/1/25/2010/ Solid Earth, 1, 25–48, 2010

44 F. Storti and F. Balsamo: Particle size distributions by laser diffraction

a

Log Particle Size (mm)

Volume percentage

1 10 100 10000.1

RI = 1.4

RI = 1.8

RI = 1.7

RI = 1.6

RI = 1.5

6

12

18

01 4 8 12 16 20 24 28 32 36 40 44 48 52

4000

3000

2000

1000

0

1 4 8 12 16 20 24 28 32 36 40 44 48 52

4000

3000

2000

1000

0

Detector number

Detector number

Lig

ht energ

yLig

ht energ

y

1 4 8 12 16 20 24 28 32 36 40 44 48 52

4000

3000

2000

1000

0

1 4 8 12 16 20 24 28 32 36 40 44 48 52

4000

3000

2000

1000

0

Detector number

Detector number

Lig

ht energ

yLig

ht energ

y

1.4

366

367

368

370

1.5 1.6 1.7 1.8

Refractive index365

1.4

261

262

263

265

1.5 1.6 1.7 1.8

Refractive index260

1 4 8 12 16 20 24 28 32 36 40 44 48 52

4000

3000

2000

1000

0

Detector number

Lig

ht energ

y

1.4

262

263

264

265

1.5 1.6 1.7 1.8Refractive index

261

2601.4

189

190

1.5 1.6 1.7 1.8

D90

(mm

)

Mode

(mm

)

b

c d

e f

16

14

10

8

4

2

188

187

186

185

Refractive index

369 264

D10

(mm

)

D50

(mm

)

Fig. 20. Reprocessing of the first run data from test MP25005 on sub-sample aliquot SAND1c (Fig. 8).(a) Light scattering data (blackcurve) and corresponding best fits for variable RI values of quartz from 1.4 to 1.8 (colour code in (b)), constant ABS values of quartz = 0.1,and constant RI values of decalcified tap water = 1.33.(b) Granulometric curves computed from reprocessed data in (a).(c) D10 percentilesfor data in the 5 curves illustrated in (b).(d) D50 percentiles for data in the 5 curves illustrated in (b).(e) D90 percentiles for data in the 5curves illustrated in (b).(f) Modal values for data in the 5 curves illustrated in (b). It is worth noting that changing RI of quartz producesnegligible changes in the reprocessed data.

Finally, it is worth noting that, despite the effectivenessof statistical parameters like mean diameter, percentiles, andothers, they cannot replace the use of granulometric curvesfor comparing results from different tests. This because verysimilar average values can relate to very different granulo-metric curves (e.g. Selley, 2000).

10 Conclusions

Particle size distributions significantly contribute to the de-scription of many geological processes including sedimenta-tion, rock fragmentation and soil formation. Modern laserdiffraction particle size analysers ensure fast data acquisitionover a wide size range, coupled with the appropriate flexibil-

ity for analysing very different granular materials. This flex-ibility, however, can produce severely biased results wheninappropriate analytical operating procedures are used, par-ticularly on fragile materials. We analysed both high strength(eolian quartz sand) and low strength (carbonate cataclas-tic breccia) essentially monomineralic materials to test theimpact of different analytical operating procedures involvingparticle dispersion into a liquid, on the obtained particle sizedistributions. Our results can be summarised by the follow-ing points:

1. centrifugal pumping the particle-liquid dilute disper-sion at the most appropriate pump speed is cru-cial in wet analyses of granular material to prevent(i) dramatic underestimating coarser particles when

Solid Earth, 1, 25–48, 2010 www.solid-earth.net/1/25/2010/

F. Storti and F. Balsamo: Particle size distributions by laser diffraction 45

a

Log Particle Size (mm)

Volume percentage

1 10 100 10000.1

6

12

18

01 4 8 12 16 20 24 28 32 36 40 44 48 52

4000

3000

2000

1000

0

1 4 8 12 16 20 24 28 32 36 40 44 48 52

4000

3000

2000

1000

0

Detector number

Detector number

Lig

ht energ

yLig

ht energ

y

1 4 8 12 16 20 24 28 32 36 40 44 48 52

4000

3000

2000

1000

0

1 4 8 12 16 20 24 28 32 36 40 44 48 52

4000

3000

2000

1000

0

Detector number

Detector number

Lig

ht energ

yLig

ht energ

y

366

367

369

370

365

259

260

262

263

2581 4 8 12 16 20 24 28 32 36 40 44 48 52

4000

3000

2000

1000

0

Detector number

Lig

ht energ

y

262

263

264

265

261

260

189

190

D90

(mm

)

Mode

(mm

)

b

c d

e f

16

14

10

8

4

2

188

187

186

185

368 261

ABI = 1.00

ABI = 0.01

ABI = 0.05

ABI = 0.10

ABI = 0.50

1.0 0.5 0.1 0.05 0.01

Particle absorption

1.0 0.5 0.1 0.05 0.01

Particle absorption

D10

(mm

)

D50

(mm

)

1.0 0.5 0.1 0.05 0.01

Particle absorption

1.0 0.5 0.1 0.05 0.01

Particle absorption

Fig. 21.Reprocessing of the first run data from test MP25005 on sub-sample aliquot SAND1c (Fig. 8).(a) Light scattering data (black curve)and corresponding best fits for constant RI values of quartz = 1.5, variable ABS values of quartz from 0.01 to 1.00 (colour code in (b)), andconstant RI values of decalcified tap water = 1.33.(b) Granulometric curves computed from reprocessed data in (a).(c) D10 percentiles fordata in the 5 curves illustrated in (b).(d) D50 percentiles for data in the 5 curves illustrated in (b).(e)D90 percentiles for data in the 5 curvesillustrated in (b).(f) Modal values for data in the 5 curves illustrated in (b). It is worth noting that changing also ABS of quartz producesnegligible changes in the reprocessed data.

ineffective pumping and stirring allow particle sedimen-tation; (ii) overestimating coarser particles when in-effective pumping and stirring allow transient particlestagnation within the measurement cell; (iii) underes-timating coarser particles when fast pumping and stir-ring produce significant particle size reduction in lowstrength material during measurement running;

2. high strength material is not significantly influenced bythe adopted instrumentation and standard operating pro-cedure, provided that effective sample recirculation isobtained in the dispersion unit;

3. adding ultrasonication in wet analyses of low strengthmaterial systematically causes mechanical particle size

reduction during measurement that, however, is less ef-fective than that caused by fast pumping and stirringduring sample recirculation and mainly produces veryfine particles by polishing of the larger ones;

4. in low strength material, the number of averaged mea-surement runs has to be carefully determined by statis-tical data analysis of large datasets in order to ensurerobust outputs and minimize mechanical biasing of par-ticle size during recirculation in the dispersion unit;

5. Selecting appropriate optical properties for the analysedsample material and dispersant liquid, respectively, isparticularly important for fine and very fine particles, ascoarser particles are less affected by this parameter.

www.solid-earth.net/1/25/2010/ Solid Earth, 1, 25–48, 2010

46 F. Storti and F. Balsamo: Particle size distributions by laser diffraction

a

Log Particle Size (mm)

Volume percentage

1 10 100 10000.1

RI = 1.4

RI = 1.8

RI = 1.7

RI = 1.6

RI = 1.5

2

4

6

01 4 8 12 16 20 24 28 32 36 40 44 48 52

200

150

100

50

0

1 4 8 12 16 20 24 28 32 36 40 44 48 52

200

150

100

50

0

Detector number

Detector number

Lig

ht

en

erg

yL

igh

t e

ne

rgy

1 4 8 12 16 20 24 28 32 36 40 44 48 52

200

150

100

50

0

1 4 8 12 16 20 24 28 32 36 40 44 48 52

200

150

100

50

0

Detector number

Detector number

Lig

ht

en

erg

yL

igh

t e

ne

rgy

1.4

720

725

730

735

1.5 1.6 1.7 1.8

Refractive index715

1.4

490

495

500

505

1.5 1.6 1.7 1.8

Refractive index485

1 4 8 12 16 20 24 28 32 36 40 44 48 52

200

150

100

50

0

Detector number

Lig

ht

en

erg

y

1.4

220

230

240

250

1.5 1.6 1.7 1.8Refractive index

210

2001.4

1

2

3

4

5

1.5 1.6 1.7 1.8

D90

(mm

)

Mo

de

(mm

)

b

c d

e f

Refractive index

D10

(mm

)

D50

(mm

)

Fig. 22. Reprocessing of the first run data from test MP20005 on sub-sample aliquot CABRE3d (Fig. 9).(a) Light scattering data (blackcurve) and corresponding best fits for variable RI values of calcium carbonate from 1.4 to 1.8 (colour code in (b)), constant ABS values ofcalcium carbonate = 0.1, and constant RI values of decalcified tap water = 1.33.(b) Granulometric curves computed from reprocessed datain (a). (c) D10 percentiles for data in the 5 curves illustrated in (b).(d) D50 percentiles for data in the 5 curves illustrated in (b).(e) D90percentiles for data in the 5 curves illustrated in (b).(f) Modal values for data in the 5 curves illustrated in (b).

We propose a workflow as a guideline for addressing par-ticle size determinations by laser diffraction granulometry.Application of this procedure is typically flexible due to thegreat variability of analysed materials and the common needof several iterations before reaching the most statistically ro-bust results. Systematic support of laser diffraction granu-lometric data by preliminary test results performed to selectthe adopted operating procedure is necessary. The lack ofinformation on this can contribute to misleading data inter-pretation and data comparison.

Acknowledgements.We are grateful to R. M. Joeckel, J. Mason,and A. Young for their helpful reviews of the submitted manuscript.Constructive criticism and advice from T. Blenkinsop and S. Blotton an early version of the manuscript were very useful for signif-icantly improving it. Funding for this work was provided by the“Roma Tre” University Laboratory Upgrade Programme, grantsto F. Storti, and by the Italian MIUR (Ministero dell’Istruzione,dell’Universita e della Ricerca). L. Aldega, C. Giampaolo andS. Lo Mastro kindly provided the composition of the Privernosand by X-ray diffraction. We are grateful to Malvern InstrumentsLtd. (particularly to B. Floure, P. Kippax and A. Virden) and toAlfatest s.r.l. (particularly to M. Congia and V. Polchi) for theirtechnical support and advice.

Edited by: R. M. Joeckel

Solid Earth, 1, 25–48, 2010 www.solid-earth.net/1/25/2010/

F. Storti and F. Balsamo: Particle size distributions by laser diffraction 47

a

Log Particle Size (mm)

Volume percentage

1 10 100 10000.1

ABI = 1.00

ABI = 0.01

ABI = 0.05

ABI = 0.10

ABI = 0.50

2

4

6

01 4 8 12 16 20 24 28 32 36 40 44 48 52

200

150

100

50

0

1 4 8 12 16 20 24 28 32 36 40 44 48 52

200

150

100

50

0

Detector number

Detector number

Lig

ht

en

erg

yL

igh

t e

ne

rgy

1 4 8 12 16 20 24 28 32 36 40 44 48 52

200

150

100

50

0

1 4 8 12 16 20 24 28 32 36 40 44 48 52

200

150

100

50

0

Detector number

Detector number

Lig

ht

en

erg

yL

igh

t e

ne

rgy

720

730

735

745

715

488

492

496

500

4851 4 8 12 16 20 24 28 32 36 40 44 48 52

200

150

100

50

0

Detector number

Lig

ht

en

erg

y

240

250

260

270

230

2201.0

3

4

5

6

0.5 0.1 0.05 0.01

D9

0(m

m)

Mo

de

(mm

)

b

d

e f

Particle absorption

D1

0(m

m)

c

1.0 0.5 0.1 0.05 0.01Particle absorption

1.0 0.5 0.1 0.05 0.01

Particle absorption

1.0 0.5 0.1 0.05 0.01

Particle absorption

725

740

D5

0(m

m)

Fig. 23. Reprocessing of the first run data from test MP20005 on sub-sample aliquot CABRE3d (Fig. 9).(a) Light scattering data (blackcurve) and corresponding best fits for constant RI values of calcium carbonate = 1.6, variable ABS values of calcium carbonate from 0.01 to1.00 (colour code in (b)), and constant RI values of decalcified tap water = 1.33.(b) Granulometric curves computed from reprocessed datain (a). (c) D10 percentiles for data in the 5 curves illustrated in (b).(d) D50 percentiles for data in the 5 curves illustrated in (b).(e) D90percentiles for data in the 5 curves illustrated in (b).(f) Modal values for data in the 5 curves illustrated in (b).

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48 F. Storti and F. Balsamo: Particle size distributions by laser diffraction

Log Particle Size (mm)

Log Particle Size (mm)

Volume percentage

1 10 100 10000.1

dispersant RI = 1.33

dispersant RI = 1.45

dispersant RI = 1.42

dispersant RI = 1.39

dispersant RI = 1.36

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Volume percentage

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