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Modellingofshearratedistributionintwoplanetarymixturesforstudyingdevelopmentofcakebatterstructure.JFoodEng

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Journal of Food Engineering 105 (2011) 343–350

Contents lists available at ScienceDirect

Journal of Food Engineering

journal homepage: www.elsevier .com/ locate / j foodeng

Modelling of shear rate distribution in two planetary mixtures for studyingdevelopment of cake batter structure

A.K.S. Chesterton a, G.D. Moggridge a, P.A. Sadd b, D.I. Wilson a,⇑a Department of Chemical Engineering & Biotechnology, New Museums Site, Cambridge CB2 3RA, UKb Premier Foods, High Wycombe, Buckinghamshire HP12 3QR, UK

a r t i c l e i n f o

Article history:Received 23 November 2010Received in revised form 14 February 2011Accepted 20 February 2011Available online 24 February 2011

Keywords:KenwoodHobartPlanetary mixerShear rate

0260-8774/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.jfoodeng.2011.02.044

⇑ Corresponding author. Tel.: +44 1223 334 791; faE-mail address: Ian_wilson@cheng.cam.ac.uk (D.I.

a b s t r a c t

The shear rate experienced by a fluid near the wall of a planetary mixer when agitated by a wire whisktool has been estimated using a simple geometrical analysis. The bowl and whisk geometries were mea-sured for a Kenwood KM250 and a Hobart N50 mixer which are in widespread use in domestic and lab-oratory installations. The shear rate is shown to be a maximum at the bowl wall. This value is relativelyuniform over a large fraction of the wall height, except for a small volume near the base and the regionabove the maximum width of the mixer. The shear rate profile is sensitive to the vertical positioning ofthe agitator within the bowl. For standard manufacturer speed settings, the range of maximum shearrates was estimated to be 100-500 s�1 in the Hobart and 20–100 s�1 in the Kenwood.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Mixing is a key step in many manufacturing processes as this isused both to combine ingredients and to generate microstructure.Understanding the impact of processes such as mixing on productstructure is essential for process improvement and the effect canbe quantified by determining rheological properties (Cullen andO’Donnell, 2009). Industrial processing can involve a wide rangeof shear regimes (Table 1): it is therefore important to know themagnitude and range of shear rates experienced by the materialduring mixing for (i) relating results from different types of mixer(e.g. in comparing results from different laboratories), (ii) scalingup from laboratory to factory scales, and (iii) determining the rel-evant range of shear rates for rheological measurement.

Planetary mixers are often used in domestic, laboratory andindustrial applications to prepare food and other soft solid materi-als. To our knowledge the shear rates developed in these deviceshave not been quantified. Rotational and beater tip speeds arereported but these are not direct indicators of shear rate. We reportan approximate method for calculating representative shearrates generated in two widely-used laboratory mixers (namely aKenwood KM250 and a Hobart N50 mixer).

Our particular interest lies in the preparation of cake batters,where planetary mixers are widely used to combine solid and li-quid ingredients to form a liquid matrix and then to incorporateair by vigorous mixing. In a companion paper (Chesterton et al.,

ll rights reserved.

x: +44 1223 331 796.Wilson).

2011) the information on shear rates is used to inform an investi-gation of the development of structure in aerated cake batters.

1.1. Planetary mixing

Planetary mixers are batch devices which use a characteristicwhisking motion created by two simultaneous rotations. Thisarrangement allows the entire mixed volume to receive a vigorousbeating action and ensures efficient mixing whilst minimising agi-tator diameter, and avoiding high specific power consumption andtemperature rises (Niranjan et al., 1994). Planetary mixing is pop-ular in many industrial applications, particularly within the phar-maceutical and food industries, as it is a reliable and robust wayof homogeneously mixing solid–liquid systems (Hiseman et al.,2002). It is also commonly used in laboratory studies and domesticapplications, as the volume of material can be varied readily andthe progress of mixing monitored visually. Bakeries often use plan-etary type vertical mixers for the preparation of sponge batters.Many development or test bakeries use this type of machine to de-velop a product even though a continuous machine might be usedfor production purposes (Cauvain and Cyster, 1996).

Scaling up mixing processes from small scale batch studies tolarger devices with different geometries remains a major challengein mixing and powder technology (Delaplace et al., 2007). Classicalmeasures of mixing performance such as modified power numbersand Reynolds numbers have been reported (e.g. Delaplace et al.,2005) but the difficulty lies in linking mechanical action tomicro-scale attributes such as distribution of components (e.g. insolids mixing) or development of microstructure in the materials

Nomenclature

A point on whisk perimeter of maximum diameterB attachment axis of rotationC centre of bowlD arbitrary point on whisk perimeterHA height of maximum radius on whisk tool, mmHh height of Hobart mixer bowl, mmHk height of Kenwood mixer bowl, mmr radius of rotation of attachment shaft about the bowl

centre, mmR radius of rotation of attachment shaft about its own

axis, mmt time, sVD velocity of point D, m s�1

x, y Cartesian co-ordinates, Fig. 3z height within the bowl, mm

Xr rotational speed of the shaft about the bowl centre,rad s�1

XR rotational speed of the whisk about its shaft, rad s�1

hr angle created over time due to the revolution of theattachment shaft about bowl centre

hR angle created over time due to the revolution of theattachment about its own axis

d gap between the whisk and wall, m_cw estimated peak shear rate experienced at the bowl wall,

s�1

Subscriptsk Kenwood mixerh Hobart mixer

Table 1Typical food processes and their associated shear regimes.a

b Source: Stern and Cmolik (1976).a Source: adapted from Steffe (1996).

344 A.K.S. Chesterton et al. / Journal of Food Engineering 105 (2011) 343–350

employed in the food and pharmaceutical sectors. In the area ofcake batters, although planetary mixers have been used for manyyears and it is known that the batter structure develops during ex-tended mixing, published information on their operating charac-teristics is limited (Cauvain and Cyster, 1996).

Some studies of the flow patterns in planetary mixers have beenreported, for a range of materials. Clifford et al. (2004) investigatedliquid mixing in a simplified planetary mixer by visualisation ofdye placed near the surface of a stirred vat of transparent liquid(golden syrup or glycerol). They observed complex, three dimen-sional flow patterns. Similarly complex patterns were observedfor granular materials by Hiseman et al. (2002), who studied theflow of dry and wet (5–14 wt.% water) lactose powders in a plane-tary mixer using positron emission particle tracking (PEPT). Theyreported two flow regions, independent of agitator speed and levelof fill: (i) a well-mixed central region characterised by rapid mo-tion, and (ii) quasi-stagnant wall layers which were periodicallydisturbed by the passage of the mixer blade. The PEPT tracer parti-cles transferred regularly between the two regions, implying that,averaged over time, all the material experienced similar shear his-tories. For both liquids and solids, it is clear that simulation ofthese shear histories would require extensive computational effort.

Linking material distribution and structure development duringmixing is not straightforward for many food and pharmaceuticalmaterials as these are frequently soft-solids (Coussot, 2005) whosestructures and rheological behaviour can be stress or strain-ratedependent. Correlating the shear experienced during mixing withsubsequent product properties has been attempted for granulationof pharmaceutical products (Schmidt and Kleinebudde, 1999;Visavarungroj and Remon, 1991) by comparing planetary mixers(representing low shear devices) to different designs of highershear mixers. In such studies the shear regime was describedqualitatively as ‘low’ and ‘high’, and quantitative information was

only presented to differentiate the product properties. Knowledgeof the range of shear rates experienced by a material during mixingis critical to understanding how its microstructure is developedduring processing; to be meaningful, rheological data must becollected over the shear rate range appropriate for the problemin question (Steffe, 1996), which may vary widely in industrial pro-cesses. Given the complexity of planetary mixers, a reliable spatialdistribution of shear rates and therefore shear history of even aNewtonian fluid is unlikely to be readily calculable, but knowledgeof the range of shear rates – and particularly the maximum value –experienced during processing would be useful for comparingmachines and methods.

To our knowledge the estimation of shear regimes duringmixing has not been attempted previously for standard planetarymixers. Steffe (1996) reported (Table 1) the shear rate range 101–103 s�1 for mixing and stirring without detail of the calculationor geometries involved. Delaplace et al. (2005) studied a planetarydevice geometrically different to those considered here – a sub-merged, rotating impeller – and correlated the rheological proper-ties over the shear range 0–500 s�1, but again without justification.

The aim of this work is to characterise the maximum apparentshear rate experienced by a liquid in commonly used laboratorydesigns of planetary mixers. Particular attention was given to mix-er speeds used in the preparation of cake batters. Extensional shearrates were not estimated.

2. Materials and methods

2.1. Equipment

Two planetary mixers with similar mixing capacities and fittedwith balloon-whisk agitators were studied: a Kenwood KM250(Kenwood UK Ltd., Havant) and a Hobart N50-110 (Hobart UK, Lon-don). Both whisk attachments were fabricated from stainless steelwire, around 2 mm in diameter, arranged in loops equidistantlypositioned around the agitator axis to create an open structure(Fig. 1). The Hobart whisk was used as supplied, with 11 wireloops, and able to produce cakes with similar volume to industri-ally baked cakes. The Kenwood whisk was modified; the originaltool was supplied with 5 wire loops, and 5 more were added insidethe whisk, leaving the agitator profile unaffected. The addition ofextra loops improved the volume of cakes produced from battersprepared with this mixer (data not shown), giving volumes compa-rable to those produced by the Hobart.

Table 2 summarises the settings and range of speeds availablefor each mixer. The rotational speed of a point on the whisk

Fig. 1. Photographs of (a) Kenwood and (b) Hobart planetary mixer balloon-whisk agitator tools.

Table 2Rotation and revolution rates for each mixer speed setting.

Setting Kenwood HobartRotation a Xr/rpm

Revolutionb

XR/rpmRotationc Xr/rpm

Revolutiona

XR/rpm

Min 32 105 – –1 53 175 61 2002 66 220 125 4103 84 280 259 8494 99 330 – –5 128 425 – –6 154 515 – –Max 165 550 – –

a Calculated.b Measured.c Provided by manufacturer.

A.K.S. Chesterton et al. / Journal of Food Engineering 105 (2011) 343–350 345

perimeter (planetary motion, XR) for the Kenwood mixer wasmeasured using a tachometer and the rotational speed of thewhisk shaft (orbital motion, Xr) was calculated from the gearingratio (10/3). The orbital rotational speed, Xr, for the Hobart devicewas provided by the manufacturer and the planetary rotationalspeed, XR, calculated from the gearing ratio (59/18). For cakebatter production two speeds of rotation are required, one forthe homogenisation of ingredients (slow speed), and one for theincorporation of air (fast speed). For these studies the optimum slowspeeds were speed setting 1 on each mixer (Table 2); and for thefast speeds, the maximum speed for the Kenwood and speed setting3 for the Hobart were used. All speeds were investigated, withattention given to those used in preparing batter for cake baking.

The bowl and whisk profiles (Fig. 2) were measured by tracing acast, moulded to the inside of the bowl and outside of the whiskperimeter, respectively. The cast was fashioned from a length of10 mm wide fusible metal alloy, which could be manipulated read-ily at room temperature. This cast was then traced onto 5 mmgraph paper. The profiles were generated by plotting the measure-ments at 5 mm vertical intervals for the majority of the profile,with the bottom 5 mm measured in 1 mm intervals, and interpola-tion between the points. AutoCAD 2000 software (Autodesk, Inc.)

was used to plot the bowl and whisk profiles and used to measurethe minimum gap distances by use of the software’s circle tool andradius calculator.

2.2. Visualising the whisking pattern

The visualisation methods used for each mixer to confirm thecalculated whisk trajectories were determined by the individualmixer geometries. Upon removal of the mixing bowl, the Hobartmixer whisked in normal operation with a clearance of several mil-limetres between the attachment and mixer base. A flat sheet ofpaper was inserted into this gap, and a pen attached vertically tothe whisk perimeter (at Rh = 60 mm) which traced the whiskedpattern. The trace was scanned, the colours adjusted to greyscale,and the levels adjusted for contrast.

The Kenwood mixer operated with the attachment tip sub-merged in a recess in the mixer base such that the above methodcould not be used. The Kenwood mixer did, however, operate inthe ‘lifted’ position as efficiently as in the ‘down’ position (a traitnot shown by the Hobart). The characteristic whisking actionwas followed in the lifted position by using time-lapse photogra-phy following a small LED attached to the whisk perimeter. Thebattery operated LED was attached to the perimeter atRk = 47.5 mm by use of adhesive putty and adhesive tape, and thebattery fixed to the attachment shaft. The mixer was set into itslifted position, and the camera held in place by a clamp stand. Aseries of time-lapse photographs were taken over 15 s, in the ab-sence of any light source other than the LED.

3. Analysis of wall shear rate

The profiles of the two mixers are shown in Fig. 2. Althoughthey feature similar bowl volumes, the whisk dimensions differnoticeably. The planetary action common to both has been ana-lysed by a simple geometrical model for a point, D, on the whiskperimeter, as shown in plan view in Fig. 3. The planetary motioninvolves two opposing rotations. Firstly the whisk shaft (B) rotatesanticlockwise about the bowl centre (C), tracing a circle with radiusr. Simultaneously, the whisk itself rotates clockwise about its shaft,

Rk

Hk

. A

B C

rk

60 mm

z

HA

RhHh

C B

. A

rh

60 mm

z

HA

Fig. 2. Bowl and whisk profiles: (a) Kenwood (Hk = 155 mm, HA = 70 mm,Rk = 48.5 mm, rk = 28 mm) and (b) Hobart (Hh = 170 mm, HA = 90 mm, Rh = 64.5 mm,rh = 30 mm). C denotes the orbital axis of rotation about the bowl, B the axis ofrotation of the revolving whisk and A is the point of maximum diameter on thewhisk profile, located at height HA.

Fig. 3. Plan view of agitator motion. C is the bowl centre and orbital axis, defined asthe origin (see also Fig. 2). B is the whisk axis (Fig. 2) which revolves anti-clockwiseabout point C. D is any point on the agitator perimeter, which revolves about B in aclockwise direction.

346 A.K.S. Chesterton et al. / Journal of Food Engineering 105 (2011) 343–350

tracing a circle with radius R. The trajectory of point D is describedby (Hiseman, 1995).

x ¼ r cosð2ptXrÞ þ R cosð2ptXR � 2ptXrÞ ð1aÞy ¼ r sinð2ptXrÞ � R sinð2ptXR � 2ptXrÞ ð1bÞ

where Xr is the whisk shaft rotational speed about the bowl centre,XR is the rotational speed of the whisk about its shaft, and t is time.

The ratio XR/Xr remains constant for each speed setting, dependenton the device gear ratio.

The whisk radius, R, varies with height, resulting in a range ofmotion patterns and velocities within the bowl. The trajectory cal-culated for the Kenwood device at Rk = 37.5 mm (i.e. near the max-imum, point A, Fig. 2) is illustrated in Fig. 4. The locus describes aseries of 10 loops due to the gearing ratio (10/3) after which thepattern repeats itself. This result matches experimental observa-tions exactly. Image Fig. 4d) was obtained by attaching an LED tothe whisk at Rk = 37.5 mm and photographing the moving devicein a darkened room with a 15 s extended exposure time.

The gearing ratio for the Hobart device (59/18) results in a 59loop repeating pattern, as shown in Fig. 5. This calculated pattern(Fig. 5a) also matches the experimental result (Fig. 5b), acquiredby tracing the trajectory by use of a pen adhered vertically to thewhisk perimeter.

Fig. 6 shows the calculated trajectories for 20 mm intervals be-tween vertical heights z = 10–90 mm for each mixer. At the base(R = 0, data not reported) the whisk tip traces a circle as there isno contribution from XR. As the whisk diameter, R, increases fromz = 0 with height, the contribution from XR becomes more pro-nounced causing larger loops in the trajectory. The loops intersectmore often as the height above the base increases. The pattern atz = 70 mm corresponds to the maximum diameter of the Kenwoodattachment (Rk = 48.5 mm) after which the diameter reduces, andsimilar trajectories to those observed at smaller diameters repeat.The Hobart whisk maximum diameter is located at z = 90 mm(Rh = 64.5 mm). These trajectories, which resemble Lissajous fig-ures, are similar to those reported for PEPT studies by Hisemanet al. (2002) and Laurent (2005).

The whisk perimeter experiences a non-constant velocity whentracing the described patterns. The local linear speed can be ob-tained from differentiation of Eq. (1) with respect to time, whichyields:

VD ¼ 2pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðXR �XrÞ2R2 þX2

r r2 � 2XrðXR �XrÞrR cosð2pXRtÞq

ð2Þ

where VD is the velocity of a point on the whisk perimeter, r and Rare the corresponding radii at that height. The lowest velocity oc-curs when the rotations (planetary and orbital) oppose one anotherdirectly, which occurs when the point under consideration is closestto the bowl wall. The velocity is at a maximum as the point passesthe centre of the bowl. For the Kenwood mixer, at maximum radius(R = 48.5 mm), the velocity at the wall is 0.28 m s�1 for speed set-ting 1 and 1.45 m s�1 for the maximum speed. For the Hobart mixerthe corresponding speeds are 0.51 m s�1 and 2.18 m s�1 atR = 48.5 mm for settings 1 and 3, respectively. Generally the speedof the whisk at the wall is higher for the Hobart machine at compa-rable R values. Although the whisk speed is lowest at closest prox-imity to the bowl wall, the gap between the whisk and wall, d, isalso at a minimum at this point. The apparent shear rate, _cw, calcu-lated via

_cw ¼VD

dð3Þ

is expected to be greatest at this point. The assumption that shearrate is maximum at the bowl wall is justified later. This shear rateis used to characterise the mixer action.

The estimated wall shear rate distributions are presented inFig. 7. The shear rate distribution is not uniform with height, beingdependent on the whisk speed and gap dimensions, which bothvary with height. There is a significantly wide range of shear ratesin the region between the base (z = 0) and z � 20 mm, but abovez = 20 mm the shear rate is quite uniform, at �30 s�1 for theKenwood and �110 s�1 for the Hobart at speed setting 1 (Fig. 7a),until z > 80 mm. Whether the mixer and agitator geometries were

Fig. 4. Trajectories calculated for a point on the circumference of the Kenwood whisk attachment at Rk = 47.5 mm and Xr = 165 rpm after (a) 0.2 s, (b) 0.4 s, and (c) 1.1 s.Numbers indicate the order of loops traced. (d) Time-lapse photograph collected over 15 s of a small LED attached to the whisk perimeter. Axes scales in mm.

-100

-50

0

50

100

-100 -50 0 50 100

(a ( ) b)

Fig. 5. Hobart mixer trajectory: (a) Plan view of the calculated trajectory for a point on the agitator perimeter at R = 60.0 mm showing a cycle of 59 loops. Axis dimensions inmm. (b) Trace of corresponding point obtained by attaching a pen to the whisk perimeter.

A.K.S. Chesterton et al. / Journal of Food Engineering 105 (2011) 343–350 347

designed or evolved with experience to deliver this even distribu-tion is not known, but the result explains why these devices haveproven to deliver robust performance.

The form of the wall shear rate distributions do not alter withrotational speed (Fig. 7b). The wall shear rate values experiencedat most heights of the mixer are �100 s�1 for the Kenwood at its

maximum speed and �500 s�1 for the Hobart at speed setting 3.Specific attention is given to these speeds (1, 3, max) due to theirrelevance to cake baking, where speed setting 1 is used by bothmixers to homogenise the ingredients, and speed setting 3(Hobart) and maximum speed (Kenwood) to aerate the batter.These values lie comfortably within the range reported for mixing

-100

-50

0

50

100

-100

-50

0

50

1000

10

20

30

40

50

60

70

80

90

x / mmy / mm

z / m

m

-100

-50

0

50

100

-100

-50

0

50

1000

10

20

30

40

50

60

70

80

90

x / mmy / mm

z / m

m

(a ( ) b)

R = 27 mm

R = 39 mm

R = 45.3 mm

R = 48.5 mm

R = 46 mm

R = 24.3 mm

R = 45 mm

R = 56.5 mm

R = 62.8 mm

R = 64.5 mm

Fig. 6. Trajectories of five points on the whisk perimeter for (a) Kenwood and (b) Hobart devices at z = 10, 30, 50, 70 and 90 mm (corresponding R values marked). Thelocation of largest R is shown for each mixer; Rk = 48.5 mm and Rh = 64.5 mm.

Fig. 7. Estimated wall shear rate at (a) speed setting 1, and (b) maximum speed, for Kenwood (solid grey symbols) and Hobart (open black symbols) mixers with balloonwhisk attachment. Interpolated lines between data points are added to guide the eye. One noticeable outlier exists for the Hobart mixer, at z = 25 mm: this is a measurementartefact. Horizontal lines show fill levels when the bowl is filled with the homogenised ingredients (slurry) and aerated batter (foam) for the Kenwood mixer (grey) and theHobart mixer (black). Clearance at base = 2 mm.

348 A.K.S. Chesterton et al. / Journal of Food Engineering 105 (2011) 343–350

operations in Table 1. The shear rates estimated for all otheravailable speed settings can be found in summary in Table 3.

The shear rates imposed by the two devices are different; theHobart gives approximately four times higher shear rates thanthe Kenwood at speed setting 1, and five times greater at themaximum speed. This is due to (i) the differences in tool width,the Hobart’s being generally larger, and (ii) the gap size betweenthe whisk and bowl, which is generally smaller in the Hobart

machine – although both approach 2 mm near the base of thebowl. The Hobart device consistently imposes substantially highershear rates on the material being mixed in the peak shear zonethan the Kenwood.

Fig. 7 also shows the measured fill levels for the homogenisedingredients (labelled slurry) and aerated batter (labelled foam)stages of cake batter production, when the batch volume is �1 L.When this batter level is not exceeded (which is the case with

Fig. 8. Calculated wall shear rate profiles for the Kenwood mixer for differentvalues of whisk-bowl clearance, at the maximum rotational speed. Horizontal linesindicate fill level for slurry (dotted line) and for aerated batter (dashed line).

Fig. 9. Variation in shear rate for one revolution (one rotation of the whisk aboutaxis B (Fig. 1) calculated for a point on the Hobart whisk perimeter (D, Fig. 1) atz = 60 mm. The peak shear rate is located at the origin (0 rad), at which point D is atits closest to the bowl wall. Conditions: clearance 2 mm, maximum speed.

A.K.S. Chesterton et al. / Journal of Food Engineering 105 (2011) 343–350 349

the experiments reported in the companion paper), the lower shearrates associated with the top of the bowl are not relevant. Theshear rate, however, also decreases below z = 20 mm approachingzero and then rises dramatically at the whisk tip. The volume ofmixed material associated with this region of higher shear rate isrelatively small, at 12 ml for the Kenwood mixer and 4 ml for theHobart. Since the volume involved is small and the gap size is ofthe order of 2 mm or less, it is assumed these shear rates willnot be experienced by the majority of the material at any giventime.

The calculated shear rate distribution presented in Fig. 7 is sen-sitive to the height of the whisk attachment relative to the bowl,which can be modified by changing the vertical position of thewhisk within the bowl (for the Kenwood only; the Hobart whisklocation could not be altered). The effect of varying the clearanceon the magnitude and distribution of wall shear rates was investi-gated and the results are summarised in Fig. 8. Values of 2 mm (theminimum practicable for this bowl design, and that for whichFigs. 6 and 7 were derived), 3, 5, 10 and 14 mm were considered.The Figure shows that the shear rate distribution is most uniformover the volume of interest at a clearance of 5 mm. A clearanceof 5 mm was therefore employed when studying batter properties.

These estimates of the shear rate at the wall make severalassumptions. Firstly, it is assumed that the maximum shear rateoccurs at the wall, because the smallest distance between movingparts is located there. As the whisk approaches the wall, its speeddecreases but the gap size also decreases. Calculation of the changein shear rate when the whisk approaches and then leaves the bowlwall is a complicated exercise in 3D geometry, but analyses can beattempted for points near the top of the bowl (where the wall andwhisk are approximately vertical). Calculations of this quasi 2D re-gion (Fig. 9) confirm that the apparent shear rate is a maximumwhen the whisk perimeter is closest to the bowl wall, and de-creases as the tool moves away. The minimum shear rate is foundat the bowl centre, which then rises at the next wall apogee. Theextent of change in shear rate on approach to the bowl wall varieswith rotational speed and bowl height but the maximum does notshift from the wall position.

Secondly, the whole charge of material is assumed to be subjectto the estimated wall shear rate for some fraction of its time in themixer. Hiseman et al. (2002) found that tracer particles regularlytransfer between the wall and bulk regions, when studying granu-lation using positron emission particle tracking (PEPT). The resi-dence time of material in the wall zone has not been calculated,but a perfect mixing argument would suggest that this would berelated to the volume of the wall region relative to the filled vol-ume of the bowl (around 30%). Tracer studies would be neededto confirm this.

In these studies the majority of material was subject to a uni-form peak shear rate during mixing, namely 30 s�1 during homog-enisation (lower speed) and 100 s�1 during aeration (high speed)for the Kenwood mixer, and �100 s�1 during homogenisationand �500 s�1 during aeration for the Hobart mixer. Only a small

Table 3Average maximum wall shear rate for 1 L volume charge. Values are reported for eachmixer speed setting.

Setting Kenwood _cw/s�1 Hobart _cw/s�1

Min �20 –1 �30 100–1202 35–40 210–2503 40–50 450–5004 50–70 –5 70–90 –6 80–120 –Max 90–120 –

fraction of the material experienced higher shear rates (at thebase), corresponding to a maximum of 1.2% of the charge in thehigh speed case.

4. Conclusions

The geometrical model of the motion within a planetary mixerreported by Hiseman et al. (2002) has been employed to estimatethe wall shear rate generated in planetary mixers. Experimentalvisualisations of the whisk motion confirmed the validity of thetrajectory model. The peak shear rate was assumed to occur atthe bowl wall, where the whisk speed is lowest but the gap be-tween whisk and bowl wall is at a minimum. This assumptionhas been confirmed for the case where the bowl wall is vertical,

350 A.K.S. Chesterton et al. / Journal of Food Engineering 105 (2011) 343–350

but its validity is not certain near the base where the curvature isgreater (and the 3D analysis was not performed). The latter regionrepresents a relatively small volume if the bowl is filled to a heightof 50 mm or greater: the latter value is suggested as a minimal le-vel of fill for the devices employed here.

The distributions of shear rate with height obtained for twocommonly used laboratory scale devices, namely a KenwoodKM250 and a Hobart N60 mixer, were found have a similar form.The shear rates imposed at the wall were near uniform for themajority of the wetted bowl region, despite the whisk speed andwall gap both being a function of height within the bowl. The rangein shear rates achievable with the Kenwood was 20–100 s�1, whilethe corresponding range for the Hobart was 100–500 s�1.

Acknowledgements

A Food Processing Faraday studentship for AKSC is gratefullyacknowledged, as is funding and technical support from PremierFoods.

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