Abstract The rheological properties of a starch suspensionare usually studied through two viscosity measurements-pasting behavior and flow behavior of the resulting starchpastes-performed separately with two different tools anddemanding rather high starch concentrations (6–10 wt %).This study focused on the feasibility of using a rheome-ter fitted with a starch stirrer cell to characterize, in asingle experiment, the starch suspension’s behavior duringand after pasting, all the while involving only low con-centrations (2–4 wt %), more representative of a real-foodcontext. A calibration of the starch stirrer cell in comparisonto the coaxial cylinders one was done using model flu-ids (Newtonian and shear-thinning). A link between torque,rotational speed, and rheological properties was determinedthrough two recalculated conversion factors (shear rate andshear stress). An operating diagram was then set indicat-ing the laminar flow and good sensitivity domain for this
A. Matignon · F. Ducept · J.-M. Sieffermann · C. Michon (�)AgroParisTech, UMR1145 Ingenierie Procedes Aliment,1 avenue des Olympiades, F-91300 Massy, Francee-mail: [email protected]
A. Matignon · F. Ducept · J.-M. Sieffermann · C. MichonINRA, UMR1145 Ingenierie Procedes Aliment,F-91300 Massy, France
A. Matignon · F. Ducept · J.-M. Sieffermann · C. MichonCNAM, UMR1145 Ingenierie Procedes Aliment,F-75002 Paris, France
A. MatignonFerrandi, L’ecole francaise de gastronomie, F-75006 Paris, France
P. Barey · M. Desprairies · S. MauduitCargill, Usine de Baupte, F-50500 Baupte, France
cell. The accuracy of those constants to starch suspensionsin the concentration range 2–4 wt % was demonstrated. Thepasting behaviors of 2 wt % starch suspensions were fol-lowed successfully at two selected shear rates (13.5 and135 s−1). The impact of the level of turbulence on the pro-files obtained was stressed, a result that is not limited tolow-concentration starch suspensions. Finally, the methoddeveloped was used to compare the pasting behaviors of 2wt % native and modified waxy maize starch suspensions.
Starch is used in a wide range of food. In lowconcentrations-2–10 wt % (water in excess)-it is mainlyused to thicken the texture of a product (Rao 1999). Numer-ous applications use starch in concentration lower than 5wt %: from neutral dairy dessert to baby milk or sauce(Thomas and Atwell 1999). The structure of those productsdepends highly on the swelling of starch. Nevertheless, theswelling behavior of low-concentrated starch suspensionscannot be easily measured, as a rapid sedimentation occursand the viscosity to be measured is low. The development ofaccurate measurement methods could be of great interest.
During a thermomechanical treatment in excess water,starch granules loose their native crystalline order abovea characteristic temperature known as the gelatinizationtemperature; they swell irreversibly and are either dis-persed or destroyed. Those changes can be followed throughviscosity measurements and define the pasting behavior
of starch. They depend on its intrinsic characteristics-botanical sources, composition, modifications—on the ther-momechanical treatment it underwent and on the suspen-sion’s characteristics (volume fraction, continuous phase)(Doublier 1990). At the end of the thermomechanical treat-ment, a starch paste/gel is obtained. Its rheological proper-ties mainly depend on the volume fraction and the state andcharacteristics—mostly their deformability—of the gran-ules in the suspension (Bagley and Christianson 1982;Doublier 1990; Rao 1999). The starch suspension rheologi-cal characteristics can be studied by viscosity measurementsduring the thermomechanical treatment (pasting behavior)and/or on the starch pastes/gels obtained at the end of thistreatment. Both types of measurements give different quali-tative information on the starch suspensions’ behaviors; theyare complementary. They are carried out using two differenttools.
Studying the pasting behavior of a starch suspensionis complex: native starch granules tend to sink to thebottom of the cup, which hinders the measures, and thepasting of starch induces a high differential of viscosity.Peculiar instruments were developed to monitor and com-pare the evolution of the viscosity of a starch suspensionduring a thermomechanical treatment. The reference toolsfor starch manufacturers and the food industry are theBrabender Visco-Amylo-Graph (BVA) and the Rapid ViscoAnalyser (RVA) (Be Miller and Whistler 2009; Thomasand Atwell 1999). Both of them are used for routine anal-yses. To limit sedimentation, BVA and RVA are equippedwith complex geometries composed of propellers. Thosegeometries induce complex flows and promote turbulentshear conditions (Loh 1992) that limit sedimentation butalso the obtaining of ‘true’ viscosity. BVA and RVA mea-sure the changes in consistency of a starch suspension underconstant stirring and a programmed heating and coolingcycle. The consistency is sometimes abusively called vis-cosity,it is expressed in Brabender Units (BU) and RapidVisco Units (RVU), respectively. Those instruments allowstudying starch suspensions during pasting in standardizedconditions used worldwide but are not sensitive enoughto measure low viscosities (Shi and BeMiller 2002). Theydemand at least a 5 wt% starch concentration which is repre-sentative of only part of the applications. Furthermore, theydo not allow interpreting the structure of the resulting starchpaste/gel because of the unknown measurements conditions.
In literature, many works use nonconventional geome-tries for rheological measurements. To obtain ‘true’ vis-cosity data, two methodologies are traditionally used. The‘mixer viscosimetry’ uses a dimensional analysis approach(Steffe 1996) and the Couette analogy a rheological sys-temic one (Estelle et al. 2011). They use the idea of ‘match-ing viscosity’ and, following their own methodology, definea proportionality constant between rotational speed and
shear rate (Choplin and Marchal 2007; Metzner and Otto1957; Rieger and Novak 1973). Both methodologies needto model shear-thinning fluids with power law equations.Hence, they could not be relevant in conditions where loworder of magnitude of shear rates can be measured. Thosemethods were successfully used to define proportionalityconstants between rotational speed and shear rate for BVAor RVA (Lai et al. 2000; Wood and Goff 1973). Lai et al.(2000) stated that RVA could be a good system to charac-terize the rheological properties of various non-Newtonianfluids. Nevertheless, they used high-viscosity fluids due tothe low sensitivity of this apparatus. Besides, to our knowl-edge, no other work using this kind of approach on the RVAor similar instruments was carried out since Lai’s work in2000. BVA and RVA are thus only used to measure thepasting behavior of a starch suspension containing at least5 wt% of starch.
To characterize a starch paste/gel, more fundamental vis-cosity measurements are used. They present the advantageof not depending on the instrument and the results are in SIunits. The measurements are based on the use of a rheome-ter fitted with coaxial cylinders or cone and plate geometries(Doublier 1990). The flow and viscoelastic behaviors ofthe paste/gel can be measured whatever their starch con-centrations. Still, the starch pastes/gels are in most of thecases obtained by means of procedures that are not alwaysstandardized (Abu-Jdayil et al. 2004; Chaudemanche andBudtova 2008; Doublier 1987; Tischer et al. 2006). Starchpasting behavior is then a black box despite its high impacton the characteristics on the final starch pastes/gels. As aresult, interpretation and comparison can be highly limited.To go through, samples can be prepared before their mea-surement in a viscoanalyser, like RVA or BVA (Funami et al.2005; Tarrega et al. 2005; Techawipharat et al. 2008). Thislater method allows linking knowledge about the pastingbehavior to the resulting starch paste rheological properties.Still, the limited sensitive range of the RVA or BVA machineremains (5–10 wt%). This method cannot be used for starchpastes/gels containing between 2 and 4 wt% of starch.
Nowadays, some companies set complex geometries forthe study of starch pasting using their rheometer. For exam-ple, TA instruments with the DHR Starch Pasting Cell (TAinstruments, USA) and Anton Paar with the starch stir-rer (Anton Paar, Austria). Their use is found in literature(Noisuwan et al. 2009; Oh et al. 2008; Perez-Gallardo et al.2012). They are used like RVA or BVA but do not pro-vide worldwide comparisons. Furthermore, no detail onthe ‘units’ of the resulting measurement or the measure-ment conditions is given. Apart from not having to buytwo instruments, their advantages are unclear and not stud-ied. Their proposed geometry is composed of vanes andpropellers which could theoretically permit to limit sedi-mentation to follow the pasting behavior but also to measure
Rheol Acta (2014) 53:255–267 257
the rheological characteristics of starch pastes/gels. Further-more, considering the high sensitivity of those machinesobtaining information on starch behavior but also on theresulting starch pastes/gels could be possible even for lowstarch percentages.
The objective of this work was to characterize witha starch stirrer cell the rheological behavior of low-concentrated starch suspensions during and after pasting.The study focused on starch concentrations in the range2–4 wt%. The complex geometry of the starch stirrer didnot a priori permit to establish a link between torque andstress or between rotational speed and shear rates. The studywas thus separated in two parts. (1) A calibration of thestarch stirrer in comparison with the coaxial cylinders wasset using model fluids (Newtonian and shear-thinning). Dueto the narrow range of shear rates (two decades maximum)measurable with the starch stirrer cell, only the beginningof the shear-thinning behavior could be observed. A fit bymeans of power law equations was not possible and didnot permit to use properly the Couette analogy method.An experimental methodology was then set. The resultsobtained using the starch stirrer were systematically com-pared to those obtained with coaxial cylinders taken asthe reference, and problems of measurements encounteredin laminar and turbulent flows were discussed and takeninto account. (2) This calibration was used to determinethe feasibility of using the starch cell to characterize theflow behavior of starch pastes/gels and their pasting behav-ior during a thermomechanical treatment. For the pastingbehavior, the impact of the measurement conditions on theobtained profiles was discussed.
Materials and methods
Fluids for the calibration of the starch stirrer cell
Four Newtonian Brookfield or Standard ISO-calibratedsilicone oils were used, with viscosity η as follows:(A) η = 500 mPa s at 25 ◦C; (B) η = 4.9 mPa s andρ = 914.0 kg m−3 at 25 ◦C; (C) η = 14.5 mPa s andρ = 848.4 kg m−3 at 25 ◦C; and (D) η = 100.9 mPa s andρ = 859.1 kg m−3 at 25 ◦C. The viscosities of standard sil-icone oils (C) and (D) were measured at 25, 40 ◦C and 40,60, and 80 ◦C, respectively. Their calibrated standard dataare detailed in Table 1.
Shear-thinning solutions were prepared with guar gum(Guar Meypro SEA, no. 9321 - Rhodia) and xanthan gum(Xanthan Rhodigel SEA, no. 0301002 - Rhodia). Differ-ent concentrations of 0.1 Mol NaCl aqueous solution/Guar(0.3, 0.4, 0.6, and 1 wt%) and 0.1 M NaCl aqueous solu-tion/Xanthan (0.02, 0.03, 0.04, 0.06 wt%) were prepared.They were chosen to achieve a wide range of viscosity (four
decades) and shear-thinning behavior (flowing index n ofthe power law equation between approx. 0.2 and 0.8). Thesolutions were prepared by dispersing the guar or xanthanpowder in 0.1 M NaCl aqueous solution and then heated at80 ◦C under stirring (750 rpm, 10 min) in a water bath at80 ◦C. They were kept at 4–5 ◦C for 24 h to attain a perfecthydration of the polymers with no air bubble left.
Starch suspensions preparation and characterization
A stabilized and cross-linked waxy maize starch (acetylatedadipate distarch) and a native waxy maize starch were pro-vided by Cargill (Baupte). They were both composed of atleast 99 % of amylopectin. All starch suspensions were pre-pared with the modified starch except the suspension usedfor the last experiment that was native starch.
The stabilized and cross-linked starch was chosen toobtain intact swelled granules after the thermomechanicaltreatment and limit starch solubility.
Every suspension underwent the same process: starchwas added to a 0.1 M NaCl aqueous solution, hydrated at50 ◦C under stirring (500 rpm, 30 min), and finally heatedfrom 50 ◦C to 80 ◦C under stirring
(500 rpm, 10 ◦C min−1)
in a water bath at 90 ◦C. The pastes were directly cooled ina 10 ◦C water bath. They reached 10 ◦C in 4 min. They werekept at 4–5 ◦C for 24 h. For modified starch, it was checkedby microscopy that the thermomechanical treatment did notalter the granules. The resulting starch pastes/gels could beconsidered as swollen gelled particles suspended in a liq-uid aqueous phase. When starch solubility can be neglected,as is the case for the modified starch, the volume fraction(φ (%)) of such a starch paste is defined as its concentra-tion, C (g dry matter / g of starch suspension), multipliedby the starch swelling capacity, Q (g g−1) (Bagley andChristianson 1982; Doublier 1990) (Eq. (1)).
φ = C.Q (1)
Particle size determination was performed at 20 ◦C usinga Malvern Master Sizer (Malvern Instruments, Ltd.) laserscattering analyser with a 300-mm Fourier cell (range0.05–879 μm) using 1.529 as refractive index and 0.1absorption for starch (Nayouf et al. 2003). Starch paste wasdispersed in the sample dispersion unit (1/100 ml water)and fed into the measuring cell. Volume distributions wereobtained using the Mie scattering theory. For each distribu-tion, the median volume diameter D (ν, 0.5) (μm)–50 %of particles are larger than it by definition–was noted. Thisvalue allowed defining a swelling ratio: (D/D0)
3 (with D0 =the median volume diameter of a raw starch suspension),which can be another way to represent the starch swellingcapacity (Q) (Nayouf et al. 2003).
For all the modified starch pastes, monomodal dis-tributions were observed (Fig. 1) and a D (ν, 0.5) of
258 Rheol Acta (2014) 53:255–267
Table 1 Estimation of theTaylor number (Ta) fordifferent standard oils
Standard oils T◦ (◦C) Density (kg m−3) Viscosity (Pa s) Nlim (s−1) Ta
(B) 25 914.0 4.9.10−3 0.3 2.4
(C) 40 849.7 46.0.10−3 3.2 2.5
60 837.5 20.0.10−3 1.3 2.3
(D) 25 848.4 14.5.10−3 0.8 2.0
40 838.7 8.41.10−3 0.5 2.1
60 825.5 4.7.10−3 0.3 2.5
80 812.6 3.7.10−3 0.3 2.4
34.5 +/- 0.3 μm was found. As for raw starch suspensions,a D0 (ν, 0.5) of 15.0 +/-0.1 μm was observed, the result-ing swelling ratio (D/D0)
3 was equal to 12.0. The volumefractions of the studied starch pastes were thus approxi-mately 24 % (2 wt%), 36 % (3 wt%) and 48 % (4 wt%). Forthe native starch pastes, broader distributions were obtained(Fig. 1) with smaller and larger granules correspondingprobably to disrupted granules but also swelled ghosts.
Rheometer and cells characteristics
Rheological measurements were performed using a MCR301 rheometer (Anton Paar, Austria) equipped with two dif-ferent measurement systems: a roughened coaxial cylinder(CC) (CC27/S) and a starch stirrer (SS) (ST24-2D/2V/2V-30/109) cells (Fig. 2). A volume of solutions of 19 and40 ml was used with these two systems, respectively. Thetemperature was controlled with a Peltier system for bothcells. When a measurement is carried out, the torque C(mN m) is measured as a function of the cell rotationalspeed N (min−1). The calculations of the shear stress σ (Pa)
0
4
8
12
16
Vo
lum
e (%
)
0 50 100 150Granule diameter (µm)
Fig. 1 Volume size distributions of 2 wt% waxy maize starch pastes—(black triangles) modified starch; (black rhombus) native starch—thermomechanically treated with the rheometer fitted with the starchstirrer cell (135 s−1)
(Eq. (2)) and the shear rate γ (s−1) (Eq. (3)) are done auto-matically by the software (Start Rheoplus, US 200) via twocell-dependant conversion factors (determined by the manu-facturer) CSS (Pa (mN m)−1) and CSR (min s−1). The shearstress/shear rate ratio gives the viscosity of the fluid η (Pa s)(Eq. (4)).
σ = CSS.C (2)
γ = CSR.N (3)
η = C.CSS
N.CSR(4)
The coaxial cylinders system is a standard ISO 3219 (gapsize δ ≤ 1.2, Fig. 2). Its cell gap is narrow enough to obtaina representative shear rate (Newtonian approximation) andshear stress as related to the middle of the shear gap(Steffe 1996). The given conversion factors CSR−CC =1.29 min s−1 and CSS−CC = 20.48 Pa (mN m)−1 werecomputed using the standard equations (Steffe 1996). Forthe starch stirrer system, the given conversion factors wereCSR−SS = 0.017 min s−1 and CSS−SS = 0.14 Pa (mNm)−1. However, since there is no standard equation to obtainthem, CSR−SS solely corresponded to a conversion of units:from per minute to per seconds (1/60), and CSS−SS wascalculated by viscosity equivalence with standard oil.
All the results will be shown using the shear stress, shearrate, and calculated viscosity. The coaxial cylinders systemwas defined as the reference.
Rheological measurements
The flow behavior of the fluids was measured at 25 ◦C. Anup shear scan was done by a stepwise logarithmic increase:from 0.05 to 500 s−1 in 10 min (coaxial cylinders) andfrom 3 to 300 rpm in 10 min (starch stirrer). Measurementswere performed most of the time in triplicates (at least induplicates).
The rheometer was also used to follow the evolution ofthe apparent viscosity of starch suspensions (2 wt%) duringthe following thermal cycle: 40–90 ◦C (5 ◦C min−1); 90 ◦C,5 min; 90–20 ◦C (5 ◦C min−1). Two rotational speeds wereused: 30 and 300 rpm. They included the rotational speedsseen in literature: 100 rpm (Noisuwan et al. 2007; Oh et al.
Rheol Acta (2014) 53:255–267 259
Fig. 2 Schematic representationand dimensions of (a) coaxialcylinders and (b) starch stirrermeasuring systems—(b′) focuson the starch stirrer geometry
14.46
13.33
40.02
e
i
r mm
r mm
L mm
===
er
ir
L
a – Coaxial Cylinders
1
2
13.15
12.00
11.00
30.00
er mm
r mm
r mm
L mm
====
2r
1r
b – Starch Stirrer
L
er
08.1==i
e
r
rδmm
rrRi 5.11
221 =
+=
b’ - Starch Stirrer geometry
2008) and 160 rpm (Perez-Gallardo et al. 2012). This lastrotational speed is the one generally used on an RVA. Tworepetitions were done at least for each thermal cycle.
Different parameters can provide information aboutstarch pasting characteristics. The most widely used inliterature are the swelling temperature (also called past-ing temperature; the temperature at which viscosity beginsto increase), the peak viscosity, the setback (the viscosityincrease during cooling), and the viscosity at the end of theprofile (Tecante and Doublier 1999; Techawipharat et al.2008).
Taylor number calculation
The evaluation of the Taylor number was done using Eq. (5)(Steffe 1996).
T a = 2.π.N.Ri.(Re − Ri)
ν.
√(Re − Ri)
Re
(5)
where ν (m2. s−1) is the kinematic viscosity of the fluid cal-culated from the dynamic Newtonian viscosity η (Pa .s). Theuse of a Ri equals to the average between the two internalradiuses was chosen (Fig. 2). For concentric cylinders sys-tems, a critical Taylor number Ta < 41.3 is usually definedto ensure laminar regime without Taylor vortices.
Results and discussion
Experimental calibration of the starch stirrer cell
Calculation of an equivalence factor between coaxialcylinders and starch stirrer cells with a Newtonian fluid
A rheological characterization of the standard oil, (A)η = 500.0 mPa s at 25 ◦C, was carried out using the coaxialcylinders and the starch stirrer measurement systems. Thecalculated viscosities were 510.0 and 45.0 mPa s, respec-tively, which was a strong divergence. The starch stirrergives a value 11 times smaller than the coaxial cylinders, fora Newtonian fluid: this points out the proposed conversionfactors did not allow obtaining correct viscosity values withthe starch stirrer.
The coaxial cylinders ensured a correct measure of stan-dard oil viscosity; it was set as the reference. The aim was
to obtain the same viscosity using the starch stirrer: ηCC =ηSS . The comparison of the torque C (mN m), measuredwith the two systems for a same rotational speed N (perminute),allowed defining an equivalence factor (Ef ) corre-sponding to the ratio needed between the conversion factorsof the starch stirrer (Eq. (6)) to obtain a viscosity equal tothe one measured with the coaxial cylinders.
Ef = CSS−SS
CSR−SS= 92.6 Pa.min.s−1(mN m)−1 (6)
Calculation of two conversion factors for the starch stirrerwith shear-thinning fluids
The next step was to see if two new conversion factorsfor the starch stirrer could allow obtaining shear rate andshear stress values equivalent to those obtained with coax-ial cylinders. The flow behavior of guar solutions from0.3 to 1.0 wt% was measured with the two systems andcompared (using their respective initial conversion factors)(Fig. 3). As expected, the viscosity level obtained with thestarch stirrer was much smaller than the one obtained withthe coaxial cylinders. Nevertheless, an identical shape ofcurves was observed. Hence, each curve obtained with thestarch stirrer was separately shifted in order to superim-pose perfectly with the corresponding coaxial cylinders one(Fig. 3). The two conversion factors were changed manually.
Shear Rate (s-1)10310210110010-110-2
Ap
par
ent
visc
osi
ty(P
a.s)
10-1
100
101
102
10-2
10-3
Fig. 3 Flow curves of guar solutions obtained with the coaxial cylin-ders (whole black), the starch stirrer (empty), and the starch stirrershifted using the optimized conversion factors (whole gray). Guar solu-tions (circles, 1.0 wt%; squares, 0.6 wt%; rhombus, 0.4 wt%; triangles,0.3 wt%)
260 Rheol Acta (2014) 53:255–267
Their ratio had to be equal to 92.6 Pa min s−1 (mN m)−1
as determined above (Eq. 6). Points of divergence wereobserved on the shifted curves of guar solutions at 0.3 and0.4 wt%. This effect was more pronounced for the 0.3 wt%one: it appeared at lower shear rates. They were attributedto modifications of the flow conditions (apparition ofTaylor vortices and turbulence). These not superimposingcurve parts were firstly not taken into account. A percentageof deviation between the two superimposed curves was cal-culated by means of all the points for a same shear rate. Theoptimal conversion factors were elected when the percent-age of deviation was minimized for each of the curves. FourCSR−SS /CSS−SS couples were obtained, corresponding tothe four solutions (Table 2). The percentages of deviationwere less than 3 % for all the solutions (Table 2). As theywere very similar, their average value was calculated; twoconversion factors were defined (Eqs. (7) and (8)).
CSR−SS = 0.450 ± 0.004 min.s−1 (7)
CSS−SS = 41.7 ± 0.4 Pa (mN m)−1 (8)
Using those average values of conversion factors (to shiftthe experimental flow curves obtained with the starch stirrercell) induced higher percentages of deviation for the guarsolutions at 0.6 and 1.0 wt% in comparison to coaxial cylin-ders curves. However, the percentages remained under 5% (Table 3), a reasonably good error level (Aıt-Kadi et al.2002).
In order to see if the two recalculated constants couldbe adapted on other shear-thinning fluids, the rheologicalbehavior of xanthan solutions at different concentrationswas measured with the two cells. This hydrocolloid waschosen because of its different shear-thinning behaviorcompared to guar, due to the higher rigidity of xanthanmacromolecular chains in 0.1 M NaCl aqueous solution.The flow curves were then shifted using the two averagedconversion factors (Eqs. (7) and (8)) determined with guarsolutions. The starch stirrer, coaxial cylinders and shiftedcurves are represented in Fig. 4. The shifted curves per-fectly superimposed with the coaxial cylinders ones, for thelower shear rates. Points of divergence were also observedabove critical shear rates; the value of which depends on the
Table 3 Estimation of the percentage of deviation between flowcurves obtained with the coaxial cylinders (CC) and the starch stirrershifted ones (SSnew) for all the studied fluids
Deviation = 1n×
n∑
i=1
Fluids (wt%)a ×( |ηCC−ηSS new|
ηCC× 100
)%
Macromolecular solutions
Guar
0.6 4.4 ± 0.6
1.0 3.9 ± 0.4
Xanthane
0.02 2.8 ± 1.0
0.03 3.6 ± 0.5
0.04 2.4 ± 0.5
0.06 2.8 ± 1.5
Starch suspensions
2 15.8 ± 0.5
3 4.5 ± 0.5
4 6.0 ± 0.5
aIt has been chosen to show here only one value through the threerepetitions done. The chosen one was in each case the one presentingthe “higher” percentage of deviations
viscosity level of the fluid. This effect was much more pro-nounced for low-viscosity solutions: the lower the viscosity,the smaller the shear rate for which it appeared (Fig. 4). Forshear rates lower than the critical divergence shear rate andfor all hydrocolloids concentrations, the deviation betweenthe two flow curves was less than 5 % as seen previously(Table 3). Hence, the averaged conversion factors calcu-lated with guar solutions were also appropriate for xanthansolution. They applied at low shear rates whatever the levelof viscosity (four decades) and for both tested hydrocol-loids. In their studies on RVA and BVA, respectively, using‘mixer viscosimetry method,’ Lai et al. (2000) found a shearrate constant of 0.33 min s−1 and Wood and Goff (1973)found a shear rate constant of 0.53 min s−1; those values arecomparable to ours.
Table 2 Estimation of theoptimized two conversionfactors for guar solutions atdifferent concentrations
Fig. 4 Flow curves of xanthan solutions obtained with the coaxialcylinders (whole black), the starch stirrer (empty), and the starch stir-rer shifted using the new conversion factors (whole gray). Xanthansolutions (circles, 0.06 wt%; squares, 0.04 wt%; rhombus, 0.03 wt%;triangles, 0.02 wt%)
The experimental method setup for the determinationof CSS−SS and CSR−SS permitted to define two new con-version factors suitable for both Newtonian fluids and theshear-thinning solutions in a rather wide range of viscosity.This result was consistent with the definition of a propor-tionality constant between rotational speed and shear rates.The complex geometry did not hinder establishing a linkbetween torque, rotational speed, and rheological propertiesfor the studied fluids.
Determination of the flow regime transition
The divergence between the starch stirrer and coaxial cylin-ders curves was surmised to correspond to a flow regimetransition that occurs for lower shear rates with the starchstirrer in comparison to coaxial cylinders (Figs. 3 and 4).
In order to evaluate the flow regime transition of thestarch stirrer, flow curves were determined for series ofNewtonian fluids in the range of viscosity 3.7 to 46.0 mPa. s(Table 1—standard oils (B), (C), and (D)). The limit pointof divergence of each curve was determined when the mea-sured viscosity deviated by more than 10 % from the New-tonian viscosity. Each shear rate (γ lim)/viscosity (ηNewt)
couple was collected and reported on Fig. 5a. A proportion-ality relationship between (γ lim) and (ηNewt) was found forNewtonian fluids (Eq. 9).
γ lim = 1, 662.ηNewt(R2 = 0.97) (9)
The Taylor number is the ratio of the centrifugal ‘forces’(or inertial ones) to the viscous forces and represents theapparition of flow instabilities (Steffe 1996). The pro-portionality relationship found between the experimentalpoints of divergence (Eq. 9) was in agreement with such aratio. Apparition of flow instabilities and turbulences couldbe stated. An experimental Taylor number was calculated
103
102
101
100
10-4 10-3 10-2 10-1
Turbulent flow
Laminar flowSensitivitylimit
( γγ γγlim
)
.
103
102
101
100
10-4 10-3 10-2 10-1
Apparent viscosity (Pa.s)
( γγ γγlim
)
.
a
bApparent viscosity (Pa.s)
Sh
ear
Rat
e
(s-
1 )S
hea
rR
ate
(
s-1 )
Sensitivitylimit
Turbulent flow
Laminar flow
Fig. 5 a Representation of the limit shear rate and viscosity val-ues using the starch stirrer cell for Newtonian fluids (black circles),shear-thinning fluids (cross), and starch suspensions (gray ovals). bRepresentation of the limit shear rate and viscosity values using thecoaxial cylinders for Newtonian fluids (black rhombus). Shear ratesensitivity limit versus viscosity (black zone); Domain of measurementin turbulent flow (gray zone); Domain of measurement in laminar flow(white zone)
using Eq. (5),for each Newtonian fluid, the experimentalNewtonian viscosity value (ηNewt), the measured limit rota-tional speed (Nlim), and a theoretical density were used(Table 1). Similar values between 2.0 and 2.6 were found(Table 1). They could represent the critical Taylor num-ber of our system. For concentric cylinders, the criticalTaylor number usually used to determine the appearanceof Taylor vortices is 41.3 (Steffe 1996). In comparison,the values obtained using the starch stirrer—about twentytimes lower—meant that the starch stirrer led to a quickerapparition of turbulence.
To check this hypothesis, the same method was used toevaluate the flow regime transition of the roughened coax-ial cylinders used in this study. Different Newtonian fluidswere used, and the limit points of divergence were collected.As described above, a proportionality relationship between(γ lim) and (ηNewt) was found (Fig. 5b). The obtained exper-imental critical Taylor numbers were between 22 and 28.Whatever the cell used, the divergence points obtained forNewtonian fluids could then be modelled. This result is
262 Rheol Acta (2014) 53:255–267
in good accordance with the hypothesis of a flow regimetransition occurring upon increasing shear rate. The coaxialcylinders’ experimental critical Taylor numbers were alsolower than 41.3 (Steffe 1996). This difference could beascribed to the roughened nature of the coaxial cylinders.Moreover, the use of Ri (average radius) did probably notpermit to reach a good representation of the measuring cellcharacteristics, i.e., the coaxial cylinders’ roughened surfacebut also the starch stirrer’s complex geometry. Those Taylornumbers should then not be taken as ‘true’ ones.
The points of divergence of each shear-thinning fluid(guar and xanthan solutions) were determined when thestarch stirrer curve deviated by more than 10 % from thecoaxial cylinders one. The shear rate (γ lim) and the corre-sponding measured viscosity (η lim) were determined andadded on Fig. 5a. Regime transitions measured for shear-thinning fluids were in good accordance with Newtonianones. The limit zone for flow modification was also suit-able for shear-thinning fluids. This result is in agreementwith the idea of ‘matching viscosity’ (Choplin and Marchal2007; Metzner and Otto 1957; Steffe 1996).
The determination of the flow regime transition and theout-of-sensitivity limit zone (black zone) of the apparatus(C = 1μN m) permitted to build an operating diagram giv-ing both the laminar flow and good sensitivity domains ofthe starch stirrer cell (Fig. 5a) and of the coaxial cylinders(Fig. 5b). Hence, Fig. 5 may be a good tool to properly usethe two geometries.
Rheological measurements of starch suspensionsusing the starch stirrer
Flow curves
The flow curves of the swelled-starch suspensions obtainedwith the starch stirrer were fitted using the two constantsfound previously. The fitted curves were compared to theflow curves obtained with the coaxial cylinders. Figure 6represents the flow curves obtained with both cells andthe shifted curves for three starch concentrations (2, 3and 4 wt%). The flow curves obtained with both cellsare well superimposed. The averaged conversion factorscalculated for guar solutions applied also to starch sus-pensions. However, divergences were also observed andcritical shear rates divergence could be determined. Whenreported in Fig. 5a, it is clear that they are similar to Newto-nian fluids ones. Hence, even if shear-thickening behaviorswere highlighted in literature for macromolecular solu-tions of starch (Dintzis 1996) or starch suspensions (Bagleyand Christianson 1982), the critical divergence shear ratesobtained here for starch suspensions were in good agree-ment with the limit of the laminar domain defined above forNewtonian fluids (Fig. 5a).
Shear Rate (s-1)10310210110010-110-2
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ty(P
a.s)
10-1
100
101
10-2
10-3 13.5 s -1 135 s -1
2 wt%
3 wt%
4 wt%
Fig. 6 Flow curves of modified starch pastes obtained with the coax-ial cylinders (whole black) and the starch stirrer shifted (whole gray).(squares, 4.0 wt%; rhombus, 3.0 wt%; triangles, 2.0 wt%)
The deviation percentages between the two cells werecalculated for the measurements done in laminar flow (shearrates lower than critical divergence shear rates). At 3 and4 wt% of starch, both cells permitted to obtain similar data(Fig. 6) with deviation percentages of maximum 3 and 6 %between each other (Table 3). At 2 wt% of starch, themeasurements obtained with the two cells were more dif-ferent with a maximum deviation percentage between themof 16 % (Table 3). In comparison with coaxial cylinders,the use of the starch stirrer cell led to higher viscositiesmeasured for the 2 wt% starch suspension and better mea-surement repeatability for the 4 wt% one. At low volumefractions (2 wt%), the starch stirrer limited sedimentation,mainly because of its peculiar geometry and the complexflows induced. At higher volume fractions (4 wt%), its largegap size eased the measurements (Barnes 2000). The pecu-liar geometry and the larger gap in the starch stirrer seemedbetter adapted than coaxial cylinders to the characterizationof the flow behavior of starch suspensions.
The 2 wt% starch suspensions showed a Newtonianbehavior (Fig. 6). Both 3 and 4 wt% suspensions showeda shear-thinning behavior which got more pronounced asthe concentration increased (Fig. 6). For a volume fractionof 24 % (2 wt% starch), swollen particles occupy such asmall volume that there is almost no contact between starchgranules: the flow behavior is Newtonian. As the concen-tration increases, the starch granules fill up the availablespace; there are more and more contacts between granules,resulting in a shear-thinning behavior. Those flow behaviorcharacteristics and viscosity levels are classically observedin literature for modified waxy maize starch suspensions(Nayouf et al. 2003). For the 4 wt% starch suspen-sion, a yield stress could be suspected: the viscosityslightly increases when the shear rate decreases (Fig. 6).
Rheol Acta (2014) 53:255–267 263
Nayouf et al. (2003) also observed a noticeable yield stressfor dispersions of volume fraction beyond 48 % (4 wt%).
Hence, the typical flow behaviors were observable usingthe starch stirrer. Nevertheless, the quick disappearance ofthe laminar regime (2 and 3 wt%) limited the range of shearrates that could be interpreted in terms of flow behavior. Forexample, only the Newtonian plateau was measured on the 3wt% starch suspension with this cell. However, a good rep-resentation of the viscosity levels and, in most cases, flowbehaviors of the suspensions was found. The use of suchgeometry and constants to characterize the flow behaviorsin SI units of starch suspensions was found to be consistentand adapted whatever the percentages of starch even if, forlow viscosities, early flow modifications hindered achievingcomplete flow behaviors.
Pasting behavior
The pasting behavior of the 2 wt% starch suspension attwo different shear rates was more accurately studied. Asstated by Loh (1992), in order to follow the pasting of starchduring a thermomechanical treatment, turbulent flow con-ditions are necessary at least at the beginning of the testto avoid sedimentation. The level of turbulences needed ishowever never described. Considering that the viscosity ofa raw starch suspension is the same as water, and usingFig. 5a, two shear rates of 13.5 and 135 s−1-correspondingto 30 and 300 rpm, respectively-were selected to followpasting behaviors. They had to favor turbulent flows and beout of the zone of limited sensitivity of the apparatus. Thisrange included those mostly used in literature regardless ofthe instrument used (Noisuwan et al. 2009; Perez-Gallardoet al. 2012; Techawipharat et al. 2008). Considering the2 wt% starch paste flow curves, 13.5 and 135 s−1 corre-sponded to two different levels of turbulence i.e. Ta ∼ 5 and50, respectively (Figs. 5a and 6). In consequence, the past-ing behavior of a 2 wt% starch suspension was measuredunder turbulence all along the thermomechanical treatment,whatever the shear rate.
The two profiles obtained along a 40–90–20 ◦C ther-mal cycle are represented in Fig. 7a and b. For both shearrates, the evolution of the viscosity during the treatmentwas measured. At first sight, the starch stirrer cell seemedto be appropriate to measure the pasting behavior of low-concentrated starch suspensions whatever the shear rates.Comparing Fig. 7a and b it appeared that levels of apparentviscosity were very different all along the treatment. At 135s−1, the apparent viscosity was higher than at 13.5 s−1: adecade higher at the beginning and half a decade higher atthe end of the heating treatment. A large and rapid increasewas observed from 67 to 70 ◦C (swelling temperature) forboth shear rates. This increase was much more pronounced
Ap
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10-2
10-3
10-1
Time (s)300025002000150010005000
10
20
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40
50
60
70
80
90
100T
emp
erature
(°C)
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a
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10-1
Time (s)300025002000150010005000
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80
90
100
Tem
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re(°C
)
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b
50 µm
Fig. 7 Apparent viscosity versus time and thermal cycle for a modi-fied starch suspension at 2 wt%. Shear rates: 13.5 s−1 (a) and 135 s−1
(b). a Image of the starch pastes/gels stained with iodine after the ther-momechanical treatment. Domain of measurement in turbulent flow(gray zone)
when a shear rate of 13.5 s−1 was used. When the temper-ature reached 75 ◦C, the apparent viscosity of the starchsuspension was maximum (peak viscosity) for both shearrates, but two very different behaviors were observed above.At 13.5 s−1, the apparent viscosity dropped drastically andreached a minimum at the end of the 90 ◦C plateau. At135 s−1, the apparent viscosity raised until the end ofthe 90 ◦C plateau. Then, the apparent viscosity started toincrease for both shear rates, albeit quicker for 13.5 s−1
than for 135 s−1 until 20 ◦C was reached (the set-back) to finally stabilize (end viscosity). In the main, theparameters—swelling temperature, peak viscosity, setback,end viscosity—providing information on the characteristicsof starch pasting were all observed on both profiles. How-ever, the two curves differed on two points: the level ofapparent viscosity during the whole measurements and theevolution of viscosity after the swelling of starch (67/70–90◦C). There may be two reasons for the lower level ofapparent viscosity measured at 13.5 s−1. On the one hand,this rate may induce a level of turbulent flow too low to keepall starch granules in suspension. On the other hand, 13.5s−1 and 135 s−1 induced two different levels of turbulence,responsible for different viscosity overestimations.
264 Rheol Acta (2014) 53:255–267
In order to see if both hypotheses were relevant, an eval-uation of the viscosity overestimation was launched. Flowcurves of 2 wt% suspensions were drawn during the cooling,after 1,300 s of a thermomechanical treatment at 135 s−1
and different temperatures: 90, 60, 40, and 20 ◦C (examplesin Fig. 8a). The objective of this experiment was to comparethe evolution of the Newtonian viscosity versus the evolu-tion of the apparent viscosity measured at 13.5 and 135 s−1.For each flow curve, the points (ηNewtonian/η13.5s−1) and(ηNewtonian/η135s−1) were collected (Examples in Fig. 8a).A correlation was found between the apparent viscositymeasured in nonlaminar conditions and the correspondingNewtonian one for 13.5 and 135 s−1 (Fig. 8b, Eqs. (10) and(11), respectively). This result is surprising: turbulence isoften described as chaos. The correlation found could thusbe contradictory with this description. The four points usedfor each correlation corresponded to the viscosity of a sim-ilar starch suspension measured at different temperatures.It can be hypothesized that the overestimation of viscosity
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ty(P
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10-1
100 101
10-2
10-3
102 103
Shear Rate (s-1)
a
135 s-113.5 s-1
ηηηηNewt Plateau
20°C
40°C
90°C
10-110-210-3
Apparent Viscosity (Pa.s)
10-3
10-2
ηη ηη New
tP
late
au (
Pa.
s)
b13.5 s-1 135 s-1
Fig. 8 Correlations between viscosities measured at 13.5 s−1 (graypoints) and 135 s−1 (black points) in turbulent flow conditions andNewtonian plateau viscosities of 2 wt% modified starch suspensionsflow curves. a Examples of the flow curves obtained and the col-lected points—Shear rate sensitive limit versus viscosity (black zone);Domain of measurement in turbulent flow (gray zone). b Correlationsbetween Newtonian viscosity measured in laminar flow conditions andapparent viscosity measured turbulent flow conditions
due to turbulent flows had close patterns for solutions ofsimilar natures (here a 2 wt% starch suspension) and vis-cosities. This result is thus only valid in those experimentalconditions; it is not believed that it can be generalized.
ηNewt = 3.53.η1.31γ=13.5s−1(R
2 = 0.99) (10)
ηNewt = 192.09.η2.65γ=135s−1(R
2 = 0.99) (11)
Still, this result meant that the cooling parts of the twoprofiles could be compared, after correcting the apparentviscosities using the Newtonian Plateau ones. Then, mak-ing the assumption that such correlations were still relevantduring swelling, it became possible to correct the apparentviscosities measured in nonlaminar conditions of Fig. 7aand b. The ‘new’ extrapolated viscosities were reported inFig. 9. The initial and final viscosity levels were then equalfor 13.5 and 135 s−1 which meant that possible sedimenta-tion of starch granules at 13.5 s−1 became negligible. Themeasured viscosity differences (Fig. 7a and b) were mainlydue to the measurements being performed in a nonlaminarregime and different levels of turbulence. However, compar-ing the two curves, the levels of viscosity during and justafter swelling (67/70–90 ◦C) were still very different.
The large drop in apparent viscosity observed at 13.5s−1 after swelling is generally attributed to the disruptionof granules. However, it was only observed on this profile(whereas higher levels of disruption would be expected at135 s−1) and the starch used in this study was modifiedin order to resist disruption. Measuring the distribution ofparticle sizes in the starch suspensions showed that starchgranule swelling stopped at 75 ◦C. Besides, microscopicobservation at the end of the thermal cycle showed onlyintact granules (Fig. 7a). Thus, the viscosity drop observedat 13.5 s−1 took place after starch swelling and was neitherdue to sedimentation nor to the disruption of the starch gran-ules. This observation was surmised to be a direct impact
Ap
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ty(P
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10-1
10-4
Time (s)300025002000150010005000
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70
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90
100
Tem
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)
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Fig. 9 Recalculated viscosity versus time during a thermal cyclefor a 2 wt% modified starch suspension. Shear rates: 13.5 s−1(graytriangles) and 135 s−1 (black triangles)
Rheol Acta (2014) 53:255–267 265
of the flow conditions: the measurement conditions at 13.5s−1 seemed to favor a particular structuring of the mediumunder shear in comparison to 135 s−1. During swelling,the presence of starch granules in different states—swelled,partly swelled, not swelled—thus presenting different rigid-ity levels and shapes, could promote a short-life structurethat would disappear when all the granules became swollenand soft. In literature, shear-thickening behaviors for starchsuspensions at the early stages of granule swelling werefound (Bagley and Christianson 1982) which is in goodagreement with our result. If confirmed, those measurementconditions could permit to highlight other characteristicsof starch granules such as their “rigidity” or their peculiarshape evolution during swelling.
Hence, measuring the pasting behavior of a 2 wt% starchsuspension was shown to be efficient using the starch stir-rer cell for a wide range of shear rates. However, the levelof turbulence induced by a given shear rate was provedto have a direct impact on the profiles. Different levelsof viscosity overestimation and different behaviors duringand after starch swelling were obtained. The methodologyused permitted to compare more accurately the two pro-files. Quantitative data was determined for the setbacks andends of the profile of the starch suspensions, and qualitativeinformation was highlighted for starch swelling in differentmeasurement conditions.
Comparison of the pasting behaviors of modifiedand native waxy maize starches
A comparison was launched between the rheological infor-mation obtained for 2 wt% modified and native waxy maizestarch suspensions. The profiles measured at 13.5 and 135s−1 are represented in Fig. 10.
Before swelling (67–70 ◦C), whatever the shear rate,both starches led to similar profiles: the apparent viscositiesmeasured were superimposed—raw starch granules almost
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)
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Native starch – 135 s-1
Native starch – 13.5 s-1
Modified starch – 135 s-1
Modified starch – 13.5 s-1
Fig. 10 Apparent viscosity versus time and thermal cycle for a starchsuspension at 2 wt% - (gray rhombus) native starch; (black lines)modified starch. Shear rates: (gray) 13.5 s−1; (black) 135 s−1
did not impact the viscosity of the medium. Then, duringand after swelling, four main differences were observed fornative starch in comparison to modified starch:
1. Whatever the shear rate, the increase of apparent viscos-ity appeared at higher temperatures and its amplitudewas larger. This result is in good accordance withthe fact that modified starch swelling temperature isreduced by stabilization and granule swelling reducedby reticulation.
2. The apparent viscosity drop recorded at 13.5 s−1 wassmaller. Usually, in literature, at percentages between5 and 10 wt%, native starch swelling is followed by alarge decrease of apparent viscosity ascribed to starchgranules disruption (Thomas and Atwell 1999). In thepresent work, starch granules disruption was confirmedthrough particle size determination (Fig. 1) and micro-scopic observations (data not shown) and can explainthe viscosity decrease recorded for native starch at 13.5s−1. However, the larger viscosity decrease showed formodified starch in this low concentration condition (2wt%) and low level of turbulences (13.5 s−1) con-firmed the hypothesis of a significant contribution ofthe softening of the completely swelled intact granules.
3. A more pronounced viscosity increase was recorded at135 s−1, it already started during the 90 ◦C tempera-ture plateau. This behavior was probably due to the highlevel of turbulences (135 s−1) and its particular effecton the contribution of entangled amylopectin chainsreleased in the solution by granules disruption.
4. Whatever the shear rate, the apparent viscosities wereapproximately a decade higher at the end. Usuallynative starch pastes/gels have lower apparent viscosi-ties at the end of the profiles than modified starchpastes (Thomas and Atwell 1999). For native starchsuspensions, the operating diagram setup (Fig. 5a) indi-cated that the apparent viscosities measured at 13.5s−1 at the end of the pasting and cooling were car-ried out in laminar flow while, at 135 s−1, they werecarried out at the beginning of the appearance of turbu-lences. Furthermore, the apparent viscosity measured at13.5 s−1 was higher than at 135 s−1 for native starchpastes/gels while the opposite was obtained for mod-ified starch suspensions. To compare more accuratelythose viscosities, the flow behaviors of the resultingpastes were measured. The 2 wt% native starch pasteshowed a shear-thinning behavior (result not shown)whereas the 2 wt% modified starch suspension wasNewtonian (Fig. 6). At 100 s−1, their apparent viscosi-ties were approx. 10−2 and 10−1 Pa s, respectively,which is in good agreement with the results obtained by(Nayouf et al. 2003) on a 2 wt% modified waxy maize
266 Rheol Acta (2014) 53:255–267
starch paste/gel and by (Dintzis 1996) on a 2 wt% waxymaize starch macromolecular solution, respectively.
Hence, to interpret native starch pasting profiles, the lowpercentages of starch used, the flow measurement condi-tions and granules disruption have to be taken into account.
Conclusion
In this study, the flow behaviors and pasting proper-ties of low-concentrated starch suspensions were measuredusing a rheometer fitted with a starch stirrer cell. Themethodology developed permitted to obtain, with this starchstirrer cell, flow curves in SI units by means of the determi-nation of two constant values suitable either for Newtonianstandard fluids, macromolecular solutions and suspensions.Still, the quick disappearance of the laminar conditions lim-its the characterization of the low-concentration solutions.Thus, an operating diagram was set to define the domainsof measurements of the starch cell. This diagram was shownto be a good tool to determine the regime flow during theperformed measurements.
It is the first time, to our knowledge, that the pastingbehavior of 2 wt% starch suspension is measured contin-uously during a thermomechanical treatment. Furthermore,the operating diagram set permitted to determine differentlevels of turbulence as a function of the viscosity valuesand of the shear rate. The turbulent conditions were shownto have a high impact on the measured pasting behaviorprofiles, which is a parameter never highlighted in litera-ture and even less taken into account for interpretation. Thedanger of comparing sole qualitative interpretations waspointed out and the need to crosslink parameter influencesas exhaustively as possible was shown to be efficient. Then,whatever the geometry, the level of turbulences induced bythe shearing should be identified and evaluated. The calcu-lation of an experimental Taylor number is a good methodto approximate the turbulence level. Then, the experimen-tal methodology to set up the protocol should include thefollowing steps:
1. Definition of the conversion factors of a complex geom-etry and validation of their accuracy on different flu-ids: Newtonian, shear-thinning—macromolecular solu-tions;
2. Verification of the conversion factors on the system ofinterests—here, starch pastes/gels;
3. Buildup of an operating diagram giving both thelaminar-to-turbulent flow regime transition and thegood sensitivity domains of the complex geometry;
4. Determination of experimental critical Taylor numbers;5. Use of the operating diagram and the critical Taylor
numbers to define the flow regime transition during
the measurements of the pasting behavior and the flowbehavior of low-concentration starch pastes/gels.
Finally, the starch stirrer cell geometry may be used in manyother laboratories. The methods developed here could helpa comparison between studies and to standardize the results.
Acknowledgments The authors thank Anne Marie Gibon (Tech-nical agent, AgroParisTech) for performing part of the calibrationexperiments.
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