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MINIMUM WETTING AND DISTRIBUTION RATES IN FALLING FILM EVAPORATORS K. R. MORISON , Q. A. G. WORTH and N. P. O’DEA University of Canterbury, Christchurch, New Zealand F alling lm evaporators are used extensively in the food industry for their ability to pro- cess heat sensitive liquids. A coherent liquid lm is required to maintain heat transfer efciency and minimize fouling. It is likely that most evaporator fouling occurs after lm breakdown as the substance within the evaporator dries out. The minimum ow rate required to maintain a lm is known as the minimum wetting rate which is dened as the minimum mass ow rate per unit circumference. In this work, minimum wetting rates were determined in a 1 m long, 48 mm internal diameter, vertical, stainless steel tube. Water and aqueous solutions of glycerol, alcohol and calcium chloride were used. These substances were chose n so as to give a wide range of proper ties such as viscosity (0.5– 39 mPa s), density (950– 141 0 kg m 23 ), surfac e tension (35– 90 mN m 21 ) and cont ac t angle (64– 98 8). In a separate set of experiments, the minimum ow rate required to distribute liquid and comple- tel y wet the top of indust rial evapo rat or tubes was meas ured using a range of suc ros e solutions. The tube wetting results obtained tted a dimensionless power law relationship well. Sur- face tension and contact angle had a strong inuence on the wetting rate but viscosity and density were found to have very little effect. The minimum ow rates for distribution were found to nea rly always exceed the min imu m wet ting rat es showin g that more att ention needs to be given to distributor design. Keywords: minimum wetting rate; falling lm evaporators; liquid distribution. INTRODUCTION Falling lm evaporators are used extensively in the food industry for their ability to process heat sensitive materials such as milk before spray drying and fruit and vegetable  juices. In these evaporators (Figure 1) the feed enters the top of the vessel, it is distributed so that it ows evenly down all the tubes as a lm, and the vapour and concentrate leave from the bottom. A complete lm should be main- tained inside the tubes at all times. This requires that the liquid is rst distributed to all the tubes to provide sufcient ow into each tube. The n the lm mus t be mainta ine d down the tubes. Film break down wil l decrease the ef - cie ncy of the pro ces s and may cause exc ess ive fouling (Paramalingam  et al ., 2000). The mi ni mum ow rate required to es ta bl is h or ma inta in a complete l m is known as the minimum wetting rate (normally designated G min ) which is dened as the mass ow rate per unit cir- cumfer enc e of the tube. Mini mum wet ting rat es can be measured for two distinct circumstances; in one case the liquid ow rate is increased until an initially dry surface is completely wetted while in the other the ow rate is reduced to the point of lm breakdown (Watanabe  et al., 1975). This research was concerned with the rst case of wetting a dry surface which requires a higher ow rate than the second. In particular the ow of isothermal vertical lms of aqueous solutions onto dry stainless steel with no or low heat ux was of interest. The paper of Hartley and Murgatroyd (1964) presents some of the earliest work done in the eld of lm break- down. They analysed the st abili ty of an existing dr y pat ch (Fi gur e 2) and det ermined the minimu m wet ting rate by using a theoretical force balance [equation (1)]. G min  ¼ 1:69  mr g 1=5 (s (1 cos u )) 3=5 (1) which can be expressed in the dimensionless form as G min m  ¼ 1:69  (s (1 cos u ))r 1=3 m 4=3 g 1=3 3=5 (2) where  s  is the surface tension,  u  is the contact angle,  m  i s the viscosity and r  is the density. Correspondence to : Dr K. R. Morison, University of Canterbury, Private Bag 4800, Christchurch, New Zealand. E-mail: ken.morison@canterbury.ac.nz 302 0960–3085/06/$30.00+0.00 # 2006 Institution of Chemical Engineers www.icheme.org/fbp Trans IChemE, Part C, December 2006 doi: 10.1205/fbp06031  Food and Biopr oducts Proce ssing , 84( C4) : 302– 310
Transcript

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MINIMUM WETTING AND DISTRIBUTION RATES

IN FALLING FILM EVAPORATORSK. R. MORISON, Q. A. G. WORTH and N. P. O’DEA

University of Canterbury, Christchurch, New Zealand 

Falling film evaporators are used extensively in the food industry for their ability to pro-cess heat sensitive liquids. A coherent liquid film is required to maintain heat transferefficiency and minimize fouling. It is likely that most evaporator fouling occurs after

film breakdown as the substance within the evaporator dries out. The minimum flow raterequired to maintain a film is known as the minimum wetting rate which is defined as theminimum mass flow rate per unit circumference. In this work, minimum wetting rates weredetermined in a 1 m long, 48 mm internal diameter, vertical, stainless steel tube. Water and

aqueous solutions of glycerol, alcohol and calcium chloride were used. These substanceswere chosen so as to give a wide range of properties such as viscosity (0.5– 39 mPa s), density(950– 1410 kg m23), surface tension (35– 90 mN m21) and contact angle (64– 988). In aseparate set of experiments, the minimum flow rate required to distribute liquid and comple-tely wet the top of industrial evaporator tubes was measured using a range of sucrosesolutions.

The tube wetting results obtained fitted a dimensionless power law relationship well. Sur-face tension and contact angle had a strong influence on the wetting rate but viscosity anddensity were found to have very little effect. The minimum flow rates for distribution werefound to nearly always exceed the minimum wetting rates showing that more attentionneeds to be given to distributor design.

Keywords: minimum wetting rate; falling film evaporators; liquid distribution.

INTRODUCTION

Falling film evaporators are used extensively in the foodindustry for their ability to process heat sensitive materialssuch as milk before spray drying and fruit and vegetable juices. In these evaporators (Figure 1) the feed enters thetop of the vessel, it is distributed so that it flows evenlydown all the tubes as a film, and the vapour and concentrateleave from the bottom. A complete film should be main-

tained inside the tubes at all times. This requires that theliquid is first distributed to all the tubes to provide sufficientflow into each tube. Then the film must be maintaineddown the tubes. Film breakdown will decrease the effi-ciency of the process and may cause excessive fouling(Paramalingam   et al., 2000). The minimum flow raterequired to establish or maintain a complete film isknown as the minimum wetting rate (normally designatedGmin) which is defined as the mass flow rate per unit cir-cumference of the tube. Minimum wetting rates can bemeasured for two distinct circumstances; in one case theliquid flow rate is increased until an initially dry surface

is completely wetted while in the other the flow rate isreduced to the point of film breakdown (Watanabe   et al.,1975). This research was concerned with the first case of wetting a dry surface which requires a higher flow ratethan the second. In particular the flow of isothermal verticalfilms of aqueous solutions onto dry stainless steel with noor low heat flux was of interest.

The paper of Hartley and Murgatroyd (1964) presentssome of the earliest work done in the field of film break-

down. They analysed the stability of an existing drypatch (Figure 2) and determined the minimum wettingrate by using a theoretical force balance [equation (1)].

Gmin ¼ 1:69  mr 

g

1=5

(s (1 cos u ))3=5 (1)

which can be expressed in the dimensionless form as

Gmin

m  ¼ 1:69

  (s (1 cos u ))r 1=3

m4=3g1=3

3=5

(2)

where  s  is the surface tension,  u  is the contact angle,  m  isthe viscosity and  r  is the density.

Correspondence to: Dr K. R. Morison, University of Canterbury, PrivateBag 4800, Christchurch, New Zealand.E-mail: [email protected]

302

0960–3085/06/$30.00+0.00# 2006 Institution of Chemical Engineers

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The work was extended by many others including Hokeand Chen (1992) who included terms for heat transfer butthey were concerned primarily with the heat flux requiredto disrupt an established film. However their clear state-ment of the force balance in the isothermal case is usefulhere even though the numerical results are almost identicalto equation (1). The forces acting on the vertical section of fluid above the stagnation point arise from momentum of the falling film, weight of the liquid and surface tensionwhich hold the fluid up. Expressed as force per unitwidth, the three terms can be added to yield:

r 3g2d 5min

15m2   þ1

4 r g

  d min

1 cos u 

2

(2u  sin2u ) þ s (cos u  1) ¼ 0 (3)

The film thickness,  d min, is related to the minimum wettingrate under steady laminar conditions by

Gmin ¼r 2gd 3min

3m  (4)

El-Genk and Saber (2001) provide a useful review of pre-vious work and developed analytical expressions for mini-mum wetting rates. They compared these with some of thedata of Munakata   et al. (1975) with satisfactory results.From the analytical results they obtained a simple empiricalexpression for the minimum wetting rate for a dry patchwhich can be written as equation (5).

Gmin ¼rms 3

g

0:20:67(1 cos u )0:623

þ 0:26(1 cos u )2:09

  (5)

Here  u  is the advancing contact angle.There is very little reported experimental work that

applies to the type of wetting of interest here (El-Genkaand Saber, 2001). Munakata  et al.  (1975) determined mini-mum wetting rates for falling films of aqueous glycerol

solutions flowing down the outside of stainless steel andglass tubes. They tested various distributors and for waterthey obtained minimum wetting rates on stainless steelfrom 0.065 to 0.124 kg m21 s21, showing an experimentalvariability of  +40% about the mean. Hobler and Czajka(1968) used aqueous glycerol solutions to wet stainlesssteel surfaces at various angles and obtained a minimumwetting rate of about 0.17 kg m21 s21. This was verymuch higher than the results of Munakata   et al.   (1975).Paramalingam et al.  (2000) reported the minimum wettingrate for 208C water on a vertical stainless steel plate to be0.222 kg m21 s21. No details of the distribution systemused were given. Morison and Tandon (2006) obtainedminimum wetting rates ranging from 0.16 kg m21 s21 for

water at 208C to 0.12 kg m2

1 s2

1 for water at 708C and0.22 kg m21 s21 for a 50% sucrose solution at 208C.They used a ceramic distributor with 36 holes near thebase through which liquid flowed before flowing downthe inside of a 47.6 mm internal diameter stainless steeltube. Their work showed that showed that viscosityaffected the wetting rate much less than predicted byequation (1).

In an industrial evaporator a distribution system isinstalled above the top tube sheet. A typical system consistsof a flat bottom container with holes (5–8 mm in diameter)that allows liquid to flow onto the flat tube sheet betweenthe evaporator tubes (Figure 3). One common design has

six distributor holes around every tube (as shown inFigure 3) while another has three. Some distributor plateshave vapour tubes that allow flashed vapour to escapedownwards into the tubes or upwards from the tube. Theeffectiveness of these is beyond the scope of the presentstudy.

No published reports of experimental or theoretical work have been found for wetting at the top edge of a verticaltube. Similarly no work has been found for the wetting of any edge such as a weir. One similar situation is thatknown as the ‘tea pot effect’ (Kistler and Scriven, 1994).This effect causes liquids (e.g., liquid tea) to cling to anedge and flow in the reverse direction. It is likely thatthis effect has phenomena in common with flow over an

edge, but theoretical analysis of the flow will not be con-sidered in this work.

Figure 1.  A falling film evaporator.

Figure 2.  Film breakdown (after Hartley and Murgatroyd, 1964).

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The flow rate,  Q, through a hole (diameter D  and area  A)in the distributor plate can be described by Toricelli’sequation

C d A  ffiffiffiffiffiffiffiffi2ghp    (6)

where h  is the height of liquid from the base of the hole tothe surface of the liquid and   C d   is a discharge coefficientthat is likely to vary with Reynolds number, plate thicknessand the radius of the edge of upstream entrance of the hole.For design purposes it is convenient to

 p (2gh) as at esti-

mate of velocity and thus an alternative Reynolds number Reh is defined:

Reh ¼ D

 ffiffiffiffiffiffiffiffi2gh

p   r 

m  (7)

Some of the physical properties required for this work had

been measured previously so were not measured here. Theviscosity and density of ethanol and water solutions aregiven by Yusa  et al.   (1977). The density and viscosity of water were obtained from Weast (1977). The surface ten-sions of the sucrose solutions were obtained from Schmidtet al.  (2000).

There were two main aims for this work. The first was toobtain data for minimum wetting rates of a vertical tube,using a selection of liquids with a sufficiently wide rangeof physical properties, so as to provide the basis for confir-mation or otherwise of the theoretical relationships. Thesecond aim was to determine the minimum flow rate(expressed as a wetting rate) that is required to achievefull liquid distribution into the top entrance of the evapor-ator tubes. The results from the two parts were then to becompared to determine whether distribution or tube wettingis a limiting factor in evaporator design.

METHODS AND MATERIALS

The solutions used for tube wetting experiments werewater at 608C, and aqueous solutions of 95% (by mass) gly-cerol at 608C, 30% ethanol at 258C, and 30% and 40% foodgrade calcium chloride at 258C. These were chosen to givea range of viscosity and contact angle while being reprodu-cible. For distribution experiments, water and aqueous sol-

utions of up to 66.5% sucrose between 258C and 308C wereused.

Three different apparatuses were used: a falling filmevaporator tube for the determination of tube wettingrates, a simple draining device for the determination of dis-charge coefficients for the design of distribution plates, anda model of the distribution system in an evaporator for the

examination of liquid distribution.

Physical Properties

The densities of solutions that could not be obtainedfrom literature were determined by the use of a densitybottle at 208C. Densities at other temperatures were calcu-lated by assuming that the specific gravity of the solutionwas constant. The viscosity of the 95% glycerol solutionwas measured using a Haake concentric cylinder visco-meter which had been calibrated using a standard oil. Theabsolute accuracy was better than  +5%.

The contact angle was measured using the apparatus

shown in Figure 4 which was housed in a humidified, temp-erature controlled air-bath. Solution was fed via a hypoder-mic needle into a hole in a 304 stainless steel plate. Asyringe pump (KDS100, KD Scientific, Hilliston, MA,USA) was used to inject a solution at a flow rate of 3 mL h–1 so that a slowly advancing drop formed withoutany size reduction from evaporation. The drop was backlitby reflecting light off white paper. As the drop formed (upto a diameter of about 10 mm) on the plate images werecaptured by a digital camera with a close-up lens. Thesize of the drop was determined by comparing it with theimage of a steel ball of known dimensions that was sus-pended above the drop. The shape of the drop was analysed

using axisymmetric drop shape analysis (Lahooti   et al.,1996). The equations were integrated using the Runge–Kutta– Fehlberg method and the parameters were solved

Figure 3.  Plan and elevation views of a typical distribution system.

Figure 4.  Apparatus for contact angle measurement.

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using Excel Solver. The contact angle was determined towithin  +18.Surface tension was measured either using a Fisher sur-

face tensiometer with a de Nouy ring or (for calcium chlo-ride solution) with a Wilhelmy plate suspended from anelectronic balance with a resolution of 0.1 mg. The forcereading relative to that for distilled water was used to cal-culate the surface tension. The methods were found to berepeatable to + 0.5 mN m21.

Falling Film Apparatus

The falling film apparatus (Figure 5) consisted of an

evaporator tube 1 m long with inner diameter 47.6 mminside an annular water jacket with an outer diameter of 72 mm. The evaporator tube and the other tubing in theapparatus were constructed from 304 stainless steel. Sev-eral different distributor designs were tested. The firstdesign was based on an annular gap between the distribu-tor and the inside wall of the evaporator tube and thesome distributors were made as overflowing weirs of plas-tic, glass and stainless steel. Next a ceramic annulus witha number of holes near the base [described by Morisonand Tandon (2006)] was used. The chosen distributor(Figure 6) was an unglazed ceramic annulus with thesame internal diameter as the evaporator tube. The sol-ution flowed from an external connection, up through a

perforated ring, and over the top of the distributor toform a coherent film on the ceramic before flowing into

the tube. A run was deemed acceptable only if a completefilm was flowing from the ceramic distributor onto the topedge of the stainless steel tube before complete tubewetting was achieved.

The evaporator tube was cleaned before every run exceptfor sequential runs with water. The preheater water bathwas set to a temperature to achieve the desired inlet temp-erature of 608C or 258C with an accuracy and stability of +0.18C. Heating was carried out by pumping the solutionsusing a gear pump (Series 120, Micropump Inc, Vancouver,WA, USA) through the feed preheating water bath, rota-meter, and the bypass line back to the feed tank. Waterwas circulated through the water jacket at the same temp-

erature to ensure there was no heat transfer. The gearpump speed was initially set to give a flow rate of about0.7 L min21 and the valves were changed to give flowinto the apparatus. The flow rate was then slowly increased,using a variable speed drive, by as little as 0.020 L min21

every 2 min, until the tube was observed to be completelywet. The flow rate was then determined by bucket and stop-watch by disconnecting the bypass line at a point that gaveno change in pumping head. The minimum flow raterequired to wet the tube was divided by the circumferenceto determine the minimum wetting rate. All of the experi-mental runs reported in this paper were conducted at atmos-pheric pressure.

Discharge Coefficient Apparatus

To enable appropriate calculation of hole sizes usingequation (6), experiments were carried out to determinethe discharge coefficient for water and sucrose solutionsthrough countersunk holes with diameters from 4 mm to8 mm in 5 mm thick acrylic sheet. A test cup was con-structed with a piece of acrylic containing a hole at thebase. The test liquid was pumped using a gear pump(Micropump GC, Vancouver, WA, USA) into the cup andthe flow rate and liquid heights (from the bottom of theplate) were measured. The viscosities and densities of thesucrose solutions were obtained from Weast (1977) and

temperature corrections were applied if required upto 308C.

Figure 6.  Liquid distributor used in the falling film evaporator.

Figure 5.   Falling film evaporator for determination of minimum wettingrates.

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Distribution Apparatus

A model of the top of a falling film evaporator was con-structed from 316 stainless steel (Figure 7). It comprised a10 mm tube sheet with 19 tubes, each 50.8 mm outsidediameter and 500 mm long that were welded in a triangularpitch of 60 mm (Figure 8). The top edge was ground to give

a radius of 1–2 mm. The tube arrangement was chosen toprovide a central tube that was unaffected by edge effectswith six tubes around the centre that were minimallyaffected by edge effects. The tubes were suspended overa collection tank. Various distributors were constructedfrom acrylic sheet and holes were drilled on the samepitch so that liquid would fall onto the tube sheet at apoint symmetrically between the tubes. A ‘pre-distributor’was fitted above the distributor to minimise flow disturb-ances on the distributor. The feed tank contained a coil of 

copper tubing through which tap water flowed to helpmaintain the temperature of the liquid.

Liquid was pumped from the feed tank, via a manualcontrol valve and rotameter, into the distribution system.The liquid then flowed down the tubes and through someinverted plastic bottles and tubing to allow manual flowmeasurement. The liquid then returned to the feed tank 

for recirculation.Four different distributors were constructed from 5 mm

acrylic sheet. Two (designated A) had three holes aroundeach evaporator tube and the other two (designated B)had six holes per tube, as shown in Figure 8. One of eachpair one was designed for liquids with viscosity similar towater (referred to as water) and the other was designedwith larger holes for liquids with a viscosity of about50 mPa s (referred to as sugar).

The diameters of the holes in the distributor plates werecalculated to give equal flow to each evaporator tube undertypical conditions. It was assumed that the flow from eachdistributor hole would flow to its nearest tubes. For holes

near the centre, the flow would be shared between threetubes giving one-third of the flow to each. For the Adesign distributor each central tube would be fed by threesuch distributor holes so the tube flow rate should havebeen the same as the distributor hole flow rate. Some of the outer holes would be shared between two tubes whileothers would feed only one tube. In Figure 8(a) the whiteholes should have a flow rate equal to the tube flow rate,while the cross-hatched and black holes should have flowrates of   2

3 and   1

3  respectively of the tube flow rate. For the

B design distributors [Figure 8(b)] each central tube isfed by six distributor holes so the tube flow rate is twicethe distributor hole flow rate. The flow rates through thewhite, cross-hatched and black holes should be   1

2,   1

3 and   1

6

respectively of the tube flow rate. The hole diameters areproportional to the square root of these ratios and aregiven in Table 1. All the holes were countersunk to adepth of about 1 mm on the top side. The side wall of thedistributor was 90 mm high, making this the maximumpossible liquid height in the distributor.

The pre-distribution system was designed after a seriesof trials with the aim of ensuring uniform distributionwith a minimum of momentum effects. Firstly (Figure 7)the single stream of liquid fell from the end of a 25 mm

Figure 7.  Apparatus for determination of minimum distribution rates.

Figure 8. Distributor designs A and B. White holes feed three tubes, cross-hatched holes feed two tubes and black holes feed one. The positions of the tubesare shown by the dashed circles.

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tube into a small 65 mm diameter container with holes onthe vertical wall about 30 mm up from the bottom; thisremoved the downward momentum of the liquid. Theliquid then flowed into a series of two large plastic bowls,the first with large holes in the base and the second withsmaller holes before landing onto the distributor plate. If the fluid had a viscosity less than 7 mPa s it also passedthrough an acrylic sheet with 4 mm holes drilled into itand with plastic mesh fixed onto either side to furtherreduce the momentum of the fluid. With this system thefluid was distributed horizontally to all parts of the distribu-tor plate with a minimum amount of momentum.

Before each run the tube sheet was cleaned with waterand dried using a hair drier. Often water was sufficientfor cleaning but if cleanliness was in doubt it was cleanedwith 2% sodium hydroxide solution followed, after a rinse,by 2% nitric acid and a further water rinse.

For each run the flow rate was slowly increased byadjusting the manual value until the top part of all of theseven internal tubes were completely wetted by a coherentfilm. At this point the distributor liquid height, liquid temp-erature and flow rates from the tubes were measured. Theminimum distribution rate was calculated as the averageof the mass flow rates down the seven inner tubes dividedby the tube circumference. This definition is analogous tothe minimum wetting rate for wetting within the tube.

RESULTS AND ANALYSES

Physical Properties

Table 2 lists the physical properties measured orobtained from literature (shown in italics).

Tube Wetting

The different distributor designs were tested before select-ing the design described above. The first design based on anannular gap between the evaporator tube and the distributor

was not effective as very small variations in the gap causednon-uniform distribution (Gmin   was 0.28 kg m21s21 forwater at 208C). Surface tension was seen to hold back 

liquid in distributors using a weir overflow (Gmin   was0.20 kg m21 s21). The ceramic distributor reported byMorison and Tandon (2006) described above proved unsatis-factory for viscous fluids. The overflowing ceramic distribu-tor became fully wetted on the inside ceramic surface andwould fully wet the top edge of the stainless tube at flowrates lower than that required to wet the entire tube. The wet-

ting rate obtained (0.104 kg m21 s21 for water) was lowerthan that obtained using the other distributor designs.

It took approximately 20 min to determine the minimumwetting rate for a particular condition. Initially the flow ratewas set well below the expected minimum wetting rate. Atthis low flow one single fat rivulet was often seen flowingdown the tube. When the flow rate was increased three orfour rivulets might form, then, as the flow rate wasincreased, the gaps between all but one of these wouldbecome wetted until finally there would be one dry patch,about 5– 10 mm below the top edge, similar to thatshown in Figure 2. The final stage of complete wettingoften occurred over a period of about 2 min with no further

increase in flow rate. Once a complete film was achieved inthe top section of the tube, the film never broke furtherdown the tube. The minimum wetting rates obtained forthe various fluids are reported in Table 2.

The data was analysed using the two dimensionlessgroups used in equation (2) and it was found that apower relationship [equation (8) and Figure 9] best fittedthe data ( R 2

¼ 0.995).

Gmin

m  ¼ 0:232

  (1 cos u )sr 1=3

m4=3g1=3

0:764

(8)

The effect of each parameter is more clearly shown by

equation (9)

Gmin ¼ 0:13((1 cos u )s )0:764r 0:255m0:018 (9)

Figure 9 shows that equations (2) and (5) are not a good pre-dictor of the experimental results. In an attempt to resolvethis discrepancy, the film thickness required to satisfy theforce balance given by equation (3) was calculated and com-pared with the steady laminar film thickness determined,using equation (4), from the experimental wetting rates.The correlation is shown in Figure 10 with a best fit lineforced to pass through the origin. The film thickness requiredby the force balance was always larger than for the calcu-

lated laminar film thickness. This indicated that the filmthickness at the stagnation point (Figure 2) is greater thanthe thickness for the same flow rate when complete wetting

Table 2.  Experimental film wetting results.

Temperature Concentration Density Viscosity Surface tension Contact Minimum wetting rateFluid   8C w/w kg m23 mPa s mN m21 angle 8   No. of runs kg m21 s21

Water 60   983.2 0.463 66.2   88 7 0.104 + 0.005Water 25   997.1 0.891 72.0   88   .10 0.104 + 0.005Glycerol/water 60 95% 1224 39 63.7 80 6 0.084 + 0.005Ethanol/water 25 30%   951.6 2.23   35.5 64.5 6 0.038 + 0.004CaCl2/water 25 30% 1300 3.36 87.3 97.6 1 0.156 + 0.005CaCl2/water 25 40% 1412 7.53 90.2 96.7 2 0.193 + 0.005

Values in italics were obtained from literature.

Table 1.  Hole sizes (mm) in the distributors.

Hole type Relative flow A-water A-sugar B-water B-sugar

White 1 6.0 8.0 4.5 6.4Grey 2/3 4.9 6.5 3.7 5.2Black 1/3 3.5 4.6 2.6 3.7

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is achieved. This seems reasonable as full wetting reducesthe surface tension term in the force balance to zero.

Discharge Coefficients

The discharge coefficient was measured for flow of liquids through a countersunk hole and related to the Rey-nolds number or the alternative estimate   Reh   defined byequation (7). The results are shown in Figure 11.

The relationship between   C d  and   Reh   was satisfactorilydescribed by the empirical equation

C d ¼ 1 2:44 Re0:36h   (10)

or based on  Re

C d ¼ 1 1:19 Re0:245 for  Re , 200 (11a)

C d ¼ 1 1:96 Re0:34 for  Re . 200 (11b)

Distribution

Distribution tests were carried out with aqueous sucrosesolutions from 0 to 66.5% sucrose by mass. It was observed(as shown in Figure 12) that in most cases the liquid formeda hydraulic jump on the tube sheet. Within the jump radiusthe liquid velocity was relatively high and the liquid flowedimmediately into the tube wetting the part of the circumfer-ence within the jump. Beyond the jump radius, the liquidrose to a height of about 3 mm and at low flow rates surfacetension effects held it on the tube sheet without flow intosome parts of the tube.

The tubes in the outer ring did not become fully wettedbefore the others and it seemed that some of the outer dis-tributor holes were a little too small. However there was no

evidence of any edge effects influencing the wetting of theseven inner tubes.

When all seven inner tubes in the tube sheet were fullywet, the range in flow rates through the seven tubes wastypically 10 –20% of the average of the seven. The Adesign (with three distributor holes per tube) tended tohave a greater range (up to 25%) than the B design (withsix holes per tube) which had a range of up to 17%. Itwas found that the A design gave much less consistentminimum distribution rates than the B design. Generally

Figure 9.   Experimental minimum wetting rates compared with equation(2) and predictions from equation (5).

Figure 10.   Comparison of film thicknesses calculated from the forcebalance and from experimental data.

Figure 11. Discharge coefficients for flow through a countersunk hole in a5 mm sheet.

Figure 12.   Flow from the A-sugar distributor with 57% sucrose solutionshowing hydraulic jumps and incomplete distribution into the tubes.

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the A design required a higher flow rate to achieve wettingand at concentrations above 60% failed to achieve wettingat distribution rates of about 0.3 kg m21 s21.

Two tests were carried out with a gap between thebottom of the distributor and the tube sheet of 69 mminstead of 40 mm as used in all other trials. For the Aand B designs the minimum distribution rates were 10%and 9% higher than for the 40 mm gap (shown as þ and in Figure 13). This difference is small and might not besignificant.

During initial tests it was found that pre-distribution wascritically important. In one final test only the first smallcontainer (Figure 7) was used for pre-distribution (abovethe distributor). The resulting distribution was visiblyinferior and the distribution rate for wetting was about10% higher (shown as an open circle in Figure 13). Therange of flow rates within the seven inner tubes wasmuch greater being 41% of the average.

Also shown in Figure 13 is a curve of the predicted mini-mum wetting rates that were calculated using the equation(8). Relevant properties of aqueous sucrose and an esti-mated contact angle of 888   were used. In nearly all casesthe minimum distribution rate was greater than the tubewetting rate.

DISCUSSION AND CONCLUSIONS

To obtain accurate minimum wetting rates in the fallingfilm tube it was found that the liquid distributor needed tohave superior wetting characteristics, and hence a lowerminimum wetting rate, than the falling film tube. It wassuspected that the main reason for the difference from pre-viously reported results is the inadequacy of the distributorsused in the earlier work.

The minimum wetting rates obtained in this work werelower than the studies mentioned above, except for thestudy of Munakata et al. (1975). However the repeatabilityof our results is better than the 1975 study.

Equation (9) shows that viscosity had very little influ-

ence on wetting rate. The exponent (20.018) was signi-ficantly lower than 0.2 used in equations (1) and (5) or

obtained from equations (3) and (4). Similarly the expo-nent of density is small and the effect of density on theminimum wetting rate was less than 11% over the fullrange of densities measured. The major influences onthe minimum wetting rate were surface tension and con-tact angle. Zisman (1964) showed that for a given surfacethere is normally a close (often linear) relationship

between surface tension and the cosine of the contactangle. Thus there is possibly only one independent vari-able (surface tension or contact angle) that has a majorinfluence on minimum wetting rate.

The empirical equation for wetting rate obtained hereindicates that the theory needs to be reconsidered. Itseems very likely that the weakness of the approach usedby others is the assumption that the film thickness at thestagnation point is the same as the steady laminar flowfilm thickness after complete wetting has been achieved.It is not obvious how one might develop of theoreticalrelationship between these two thicknesses, however itshould be possible to measure the thickness of the film at

the stagnation point and at the same point when the sameflow rate of liquid fully wets the tube.In the second part of the research, an equation was

obtained relating the discharge coefficient to Reynoldsnumber for flow through a countersunk hole in a thick plate. While the results were satisfactory for the selectionof hole sizes in distributor plates, the scatter in the resultsindicated that a single equation was not sufficient todescribe the flow for a range of holes sizes and fluid visc-osities. A more complex analysis was not required for thedesign of the distributors used in this work.

The distribution system for the distribution experimentswas designed such that it would model industrial systemsas closely as possible while at the same time allowing con-

sistent conditions. It became very clear during initial trialsthat any downwards momentum in fluid coming onto thedistributor plate resulted in variability in the flow ratesthrough the distributor holes, even when there was morethan 50 mm height of liquid in the distributor. As morepre-distribution devices were added, more consistent andlower distribution rates were obtained. The pre-distributionsystem used seemed to be effective in minimising momen-tum effects as seen by the reasonably consistent results thatwere obtained for the B-style distributor.

Visual inspection of the flow pattern on the tube sheet(Figure 12) indicated that the hydraulic jump radius influ-enced the minimum distribution rate. Full distribution

into the tubes was achieved within the jump radius,where the fluid velocity was higher, but at distancesbeyond the jump radius distribution was less effective.Attempts were made to relate the minimum distributionrates to the hydraulic jump radius but no clear quantitativerelationships were found.

The six-hole B design generally gave lower minimumdistribution rates than the three-hole A design. This isalmost certainly because a greater proportion of the topedge of the tubes is exposed to a region within the hydrau-lic jump and hence to a higher velocity.

The experimental results showed that the minimum dis-tribution rate was nearly always greater than the minimumtube wetting rate. Thus when designing evaporators, atten-

tion must be given to the distribution system and distri-bution rates, and not only to the tube wetting rates.

Figure 13.  Minimum distribution rates for distributor designs A and B,with curve showing predicted minimum tube wetting rates.

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REFERENCES

El-Genk, M.S. and Saber, H.H., 2001, Minimum thickness of a flowingdown liquid film on a vertical surface,   International Journal of Heat and Mass Transfer , 44: 2809–2825.

Hartley, D.E. and Murgatroyd, W., 1964, Criteria for the break-up of thinliquid layers flowing isothermally over solid surfaces,   International

 Journal of Heat and Mass Transfer , 7: 1003–1015.Hobler, T. and Czajka, J., 1968, Minimum wetting of a flat surface (in

Polish), Chemia Stosowana, 2B: 169–186.Hoke, B.C. and Chen, J.C., 1992, Thermo capillary breakdown of falling

film liquid films,   Ind Eng Chem Res, 31: 668–694.Kistler, S.F. and Scriven, L.E., 1994, The teapot effect: sheet-forming

flows with deflection, wetting and hysteresis,   J Fluid Mech, 263:19–62.

Lahooti, S., Del Rio, O.I., Neumann, A.W. and Cheng, P., 1996, Axisym-metric drop shape analysis, in Neumann, A.W. and Spelt, J.K. (eds),

 Applied Surface Thermodynamics   (Surfactant Science Series, 63),441–465 (Marcel Dekker Inc., New York, USA).

Morison, K.R. and Tandon, G., 2006, Minimum wetting rates for fallingfilms on stainless steel,   Developments in Chemical Engineering and 

 Mineral Processing, 14(1/2): 153–162.Munakata, T., Watanabe, H. and Miyashita, K., 1975, Minimum wetting

rate on wetted-wall column—correlation over wide range of liquid vis-

cosity, Journal of Chemical Engineering of Japan, 8: 440–444.

Paramalingam, S., Winchester, J. and Marsh C., 2000, On the fouling of falling film evaporators due to film breakup,  Trans IChemE, Part C,Food and Bioproducts Processing, 78: 79–84.

Schmidt, T., Christoph, D. and Senge, B., 2000, Surface tension behaviourof pure and technical sucrose solutions,   Zuckerindustrie, 125(3):175–180.

Watanabe, K., Munakata, T. and Matsuda, A., 1975, Minimum wettingrate on wetted-wall column in the absence of mass and heat transfer,

 Journal of Chemical Engineering of Japan, 8: 75–77.Weast, R.C. (ed.), 1977,  CRC Handbook of Chemistry and Physics, 58thedition (CRC Press, West Palm Beach, Florida, USA).

Yusa, M., Mathur, G.P. and Stager, R.A., 1977, Viscosity and compressionof ethanol-water mixtures for pressures up to 40000 psig,   Journal of Chemical and Engineering Data, 22(1): 32–25.

Zisman, W.A., 1964, Relation of contact angle to liquid and solid consti-tution, in Gould, R.F. (ed.),   Contact Angle, Wettability and Adhesion,1– 51 (ACS, Washington, DC, USA).

ACKNOWLEDGEMENT

The authors are grateful to Marcus Le Quesne for carrying out many of the distribution experiments.

The manuscript was received 4 May 2006 and accepted for publication

after revision 17 August 2006.

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