the rate-independence of the mixing of wheat flour dough to peak dough development

Journal of Cereal Science 27 (1998) 167–177

The Rate-Independence of the Mixing of Wheat FlourDough to Peak Dough Development

R. S. Anderssen∗, P. W. Gras† and F. MacRitchie†§

∗CSIRO Mathematical and Information Sciences, GPO Box 664, Canberra, ACT 2601, Australia†Grain Quality Research Laboratory, CSIRO Plant Industry, PO Box 7, North Ryde, NSW 2113,

Australia

Received 28 May 1997

ABSTRACTWhen examining quantitatively the material properties of wheat flour dough, the need arises tomodel the mixing of the dough in terms of some constitutive relationship which simulates the changingrheology of the dough during the mixing. In formulating a mathematical model of the mixing onekey issue is the extent to which the mixing of the dough displays, at least with respect to certainmixers, rate-independent characteristics. Evidence is presented to support the hypothesis that, atleast to first order, the evolving rheology, resulting from the mixing of a wheat flour dough in aMixographTM, (but not necessarily in some other recording or commercial mixers), has a clear rate-independent character. When mixed on a variable speed 35 gm MixographTM, flour water dough ofconstant moisture content, prepared from seven flours of widely differing protein contents, showedstatistically significant differences in the number of mixer revolutions required to reach peak doughdevelopment and in their resistance at peak dough development. For each of the flours, the numberof revolutions was essentially constant at the five different speeds examined, whereas the resistanceincreased gradually (and steadily) as the mixer speed increased. 1998 Academic Press Limited

Keywords: hysteresis, peak dough development, mixing, MixographTM, rate-independence, rheology,wheat flour dough, work input.

been published on quantitative models which char-INTRODUCTIONacterize ‘how the rheology of the dough changes

Most quantitative examinations of the rheology of during mixing’.wheat flour dough focus on the properties of the To construct such models of the evolving rhe-fully developed dough1–4. Except for the analysis ology, one must work within a framework thatand interpretation of the qualitative features of

allows for such evolution as an essential part ofmixing curves5, as determined by instruments suchthe modelling. One possibility is the introductionas MixographsTM and FarinographsTM, little hasof hysteresis concepts into the modelling6. Theapplication of such concepts will be quite complexunless some appropriate simplifying assumptionscan be invoked about the nature of the mixing of : PDD=peak dough development;

N (PDD)rev =the number of revolutions of the mixer to the dough, such as rate-independence.

achieve peak dough development; R(PDD)=the resistance Since the evolving rheology of a dough can beof the dough at peak dough development; R(max)=the interpreted as a memory process, there is a needmaximum resistance in an extension test; Ext=the to confirm the extent to which the mixing ofelongation at rupture in an extension test; RPM=

the dough can be viewed as a rate-independentrevolutions per minute.process. This is the goal of the present paper.§Permanent Address: Department of Grains Science and Industry,

Kansas State University, Manhattan KS 66506, USA Before turning to an examination of the new

0733–5210/98/020167+11 $25.00/0/jc970160 1998 Academic Press Limited

R. S. Anderssen et al.168

experimental evidence, it is first necessary to review various stages of hydration, development, peakthe nature of the evolving rheology of wheat flour dough development and breakdown that occurdough during mixing as well as the earlier and during the mixing. Consequently, if one wishes tocircumstantial evidence for the rate-independent determine the current rheological properties of anature of the mixing of wheat flour dough. given material, then one is limited to experiments

that do not change that rheology as a result of: the results and conclusions in this paper are basedthe measurements. For example, oscillatory shear

on experiments performed on a MixographTM, where themeasurements are ideally performed on materials

mixing action, as performed on the dough, is clearly one ofwhen the material is in a state for which suchelongation-and-rupture. Consequently, it does not followmeasurements will cause only an insignificantthat the conclusions reached in this paper will necessarilychange in its rheology. In fact, because their actionapply to all types of mixers, especially when the actionpartially mimics the mixing, the application ofperformed on the dough is unambiguously different fromoscillatory shear measurements to an under-de-elongation-and-rupture.veloped wheat flour dough could yield incorrectresults about its rheology at the time it wassampled; especially if sampled at a time when theThe evolving (developmental) rheology of wheatrheology of the dough is changing rapidly as aflour doughfunction of the mixing. Even the application of

To model (conceptually, physically and/or math- standard rheological measurements to developedematically) the evolving rheology of a material due wheat flour dough must be performed with dueto the action of external forces (such as the elasto- care1 so that the results obtained truly reflect theplastic behaviour of a steel sample subjected to nature of the rheology under examination.repetitive loading in a fatigue test, or the visco- Often, in industrial situations, it is sufficient toelastic behaviour of a wheat flour dough during study the rheology of a material once it has attainedmixing), it is first necessary to identify and un- a stable steady-state, since it is only this informationderstand: that is required for decision-making purposes. It

is for this reason that the rheology of wheat flour(a) the chemical and physical processes (mech-dough is tacitly assumed to be the rheology of theanisms) that determine and control the rhe-developed dough, though there are exceptions9.ology of a material in its various phasesNevertheless, there is a clear need to distinguish(states) (such as solid, liquid, viscoelastic,between situations where it is appropriate to worketc); andwith the rheology of the material in a quasi-stable(b) the nature of the mechanisms through whichsteady-state and when it is not. For example, withinthe rheology of the material changes inthe context of metal fatigue10, the need for suchresponse to the various classes of externaldifferentiation has been acknowledged ever sinceforces that can be applied (such as an in-the work of Bauschinger7, already discussed above.crease in temperature or the mechanical

This leads naturally to the idea that, in part,action of mixing).the current need for clear differentiation arises

Consequently, the evolving rheology of a ma- because the mathematical modelling of such ex-terial will be determined not only by its current periments lacks the sophistication necessary toconfiguration, but also by the nature, size and model comprehensively the true nature of rheo-duration of the forces to which it is being subjected. logical processes involved; in particular, to modelFor example, in many applications, steel behaves, the interaction between the mixer (or experimentalover short periods, like an elastic solid. Over longer apparatus) and the material being mixed inperiods, when fatigue is a prime consideration, terms of the material’s changing rheology. Theit behaves like an elasto-plastic material. This advantage associated with building such modelsdifference was demonstrated by showing that the would include:stress–strain behaviour of steel, obtained from a

(a) the removal of the need for the differ-monotonic tension or compression test, was notentiation; andnecessarily the same as that obtained during re-

(b) the construction of a more natural frame-petive loading7,8.work in which to simulate the processesFor wheat flour dough, the situation is more

complex. Its rheology is quite different at the occurring in the dough during mixing.

Rate-independence of dough development 169

However, the difficulty with such an approach dependent of this variety of mixing scenarios,which is characteristic of a rate-independence in-is the much greater complexity that it introduces

into the mathematical modelling that must be terpretation. This does not imply that it is im-possible to mix dough unsuccessfully. Dough,undertaken6. In such an undertaking, the first step

is the identification of key assumptions that can which has been mixed for too long a period,is known to have poor gas retention properties.be invoked about the nature of the mixing of the

dough, such as rate-independence. However, the evidence is there that, with littletraining (except for the normal trial-and-error ex-perience), a wide spectrum of people, on a regular

The earlier and circumstantial evidence for rate- basis, mix dough under a variety of circumstancesindependence with ‘success’, and that this fact is telling one

something pertinent about the mixing of wheatThough the question of the rate-independence offlour dough.the mixing of wheat flour dough does not appear

When viewed from the framework of the dy-to have been investigated directly, there is con-namics occurring within the dough, the mixingsiderable circumstantial evidence. Initially, how-process, whatever the mechanism being used, isever, it is necessary to clarify the meaning of thequite stochastic (random but statistically pre-term rate-independence. The first step is the for-dictable) in nature. The fact that the end result ismulation of a notional model for the mixing pro-more or less independent of such stochastic activitycess. Within the present context, an input–outputis again indicative of a rate-independent process.(stimulus–response) model is appropriate, where

These observations lead to the idea that doughthe evolving rheology of the dough correspondsis mixed (i.e. reaches full development) once theto the output (response) of the mixing process,mixing device has imparted sufficient energy towhile the mixing mechanism (action) corresponds(i.e. performed sufficient work on) the dough.to the input (stimulus). With respect to such a

model, one can introduce the following definitionfor rate-independence. Mixing intensity and work input investigations: with respect to a specified stimulus, the

The effect of the speed of mixing has been ex-corresponding response of a process is said to be rate-amined5,13–17. Kilborn and Tipples14 showed that,independent, if the response is independent of the speedto achieve the proper development of a dough,with which the stimulus is applied.two basic requirements must be satisfied:

Consequently, to assess the rate-independence ofthe mixing of wheat flour dough, one has simply mixing intensity (impeller speed) must be above a mini-to examine the extent to which various properties mum critical level that varies with both flour and mixer;of the dough, such as the time to full development and the work [which is] imparted to the dough must beand baking characteristics, are independent of the greater than a minimum critical amount dependent onspeed with which the mixing is performed. the flour used.Note. More formal definitions of rate-in-dependence11,12 could have been used, but they To prove the point about mixing intensity, theare inappropriate here. authors presented graphs of various baking char-

acteristics of the dough as a function of the speedof mixing (cf. Figures 6, 8 and 10 in Kilborn andThe intuitive evidence Tipples14). They all indicate the existence of thethreshold, but, more importantly, they also show,There are a number of general observations that

can be made about the mixing of wheat flour except for the graph of minimum time to de-velopment, that, after the threshold is exceeded,dough which, though normally taken for granted,

are indicative of rate-independent behaviour. the baking characteristics examined (cf. loaf vol-ume, crumb colour and crumb texture) are clearlyThey relate to the fact that, in the home, bakeries

and cake shops, dough is ‘successfully’ mixed to independent of the mixing speed. Furthermore, ifthe graph of minimum time to development ismake good quality products with different types

of mixers that vary in how they manipulate the replotted as a graph of the minimum number ofrevolutions of the mixer to achieve development,dough and in the speed with which they operate.

The end result appears to be more or less in- then it also, after the threshold is exceeded, be-


comes a plot that is essentially independent of the curring. It is much higher in the plots publishedby Kilborn and Tipples14 than the results presentedmixing speed. Clearly, time can be a misleading

indicator for specifying the development of a in this paper for the MixographTM.Though important and indicative in their owndough, if all factors are not taken into account.

A more appropriate indicator is the number of right, the above results can only be viewed asqualitative confirmation of the rate-independentrevolutions of a mixer as this is, to a first order

approximation, a fairly direct measure of the en- nature of the mixing of a wheat flour dough, sincemost of the measures used (such as loaf volume)ergy imparted to (or the work performed on) a

dough by a mixer. are themselves secondary (qualitative) rather thanprimary (quantitative) measures.In addition, in their analysis of the rate of work-

input to the dough by a mixer, Kilborn andTipples14, figure 15, present graphs, for various

Independent indirect evidencework-input levels, of the dependence, on mixingspeed, of loaf volume for the resulting developed The work of Skeggs and Kingswood17, which in-dough. Though the graphs are not as convincing cludes a fairly comprehensive summary of earlieras those discussed above, they nevertheless research, examined the effect of various mixingidentify, for the higher work-input levels, a situ- speeds and work inputs on the properties of theation consistent with a behaviour that is more or dough and its baking characteristics for four floursless independent of the speed of the mixing. with different protein content. The conclusions are

A more convincing confirmation of the latter consistent with a rate-independence hypothesis.point can be found in Oliver and Allen5 who However, as the goal of their research was a pilotestablished that, with respect to optimal loaf vol- scale study of mechanical dough development, itume; can only be viewed as indirect evidence.

Independent evidence can be found in the paper‘the work requirement to this point [optimal loaf by Jin et al.18 in which, among other things, thevolume] was independent of mixing speeds.’ effect of screw speed on the physical properties

and microstructure of corn meal extrudates isIn addition, their various graphs show clearly examined. Their figures 2 and 3 show, for the

that, for a number of factors (though not all; physical characteristics considered, a behavioure.g. extensibility), the behaviour is more or less that is fairly independent of screw speed, especiallyindependent of the speed of mixing. In particular, when compared with other factors such as fibrethe curved line for the development time in Oliver content.and Allen5, figure 2, becomes horizontal, if thedevelopment time is transformed to the number

MATERIALS AND METHODSof revolutions of the mixer to reach peak doughdevelopment. InstrumentationAs already indicated above, this represents anexample of where plotting in the wrong units can A standard 35-gram MixographTM was modified

to measure its ‘elongation-and-rupture’ mixinghide key information. In fact, because the mixingtime, to peak dough development, will change action in much greater detail by (a) adding a Hall-

effect sensor to monitor the time of revolution offrom one mixer to another whenever the speed ofthe mixer changes, one needs a measure that is the mixer’s head, and (b) replacing the spring by

a strain gauge to measure the resistance to theindependent of the mixing speed, such as thenumber of revolutions of the mixer. mixing electronically every 2·5 ms. For such meas-

urements, the arm of the MixographTM was con-The various studies of the work input re-quirements in the Chorleywood Bread Process give strained to remain at its mid-scale position. The

torque exerted by the dough on the mixer bowlresults that are consistent with a rate-indpendenceinterpretation, as long as the mixing speed is above was measured with a cantilever-type transducer

(Model K4 of Applied Measurements Pty Ltd,a critical threshold. This leads naturally to theconclusion that the mixing of wheat flour dough Sydney) which was mounted 20 cm from the centre

of rotation of the bowl.will be rate-dependent below the threshold. How-ever, it appears that the value of the threshold All doughs were prepared with 35 g of flour and

21 mL of water.depends heavily on the nature of the mixing oc-


Table I Analytical data for the flours tested

Flour Protein (%) Moisture (%) Starch damage (%) Source

Baker’s flour 13·3 13·3 5·9 Commercial Flour (Defiance Ltd)Biscuit (cookie) flour 11·0 13·3 4·0 Commercial Flour (Arnotts Ltd)acv Amery 11·7 9·9 6·2 cBRI Australia Ltdcv Osprey 16·9 11·9 6·2 BRI Australia Ltdcv Sunbri 16·0 11·6 6·6 BRI Australia Ltdcv Yanac 9·9 10·9 6·5 BRI Australia Ltdbbl Sun 224B 17·0 12·1 6·5 BRI Australia Ltd

a cv=cultivarb bl=advanced breeders linec BRI=Bread Research Institute

Extension tests were performed using doughs moves any ambiguity associated with themeaning of ‘mixing time’.mixed to peak dough development (PDD) (with

the ratio of flour to water being 100:60) on a (iv) An investigation of the dependence, on2-g Mixograph, and stretched at 1 cm/sec on a mixing speed, of other parameters as-prototype extension tester developed at CSIRO sociated with the mixing of dough, suchPlant Industry, Canberra, Australia19. as the resistance (R(PDD)) of the dough at

The seven flours tested are listed in Table I PDD as traditionally measured from aalong with their percentage protein and moisture Mixogram of the dough. A discussion ofcontent as well as the percentage starch damage, the standard methods, which are appliedwhich were determined by BRI Australia Ltd. to estimate the ‘time to’ (‘position of’)

peak dough development (PDD) as wellas the resistance (R(PDD)) at PDD, is given

EXPERIMENTAL in Gras et al.21

(v) An examination of the time of eachFor a study of the feasibility and merit of modellingrevolution of the mixer as a function ofthe evolving rheology of dough in terms of thethe number of revolutions since the start‘elongation-and-rupture’ mixing action of theof the mixing.MixographTM, the first step is to collect appropriate

data about the nature of the input-output process The results from an earlier feasibility study areunder examination. Initially, the goal has been to reported in Anderssen et al.22 where identicalstudy the action of the MixographTM in terms of samples of water, salt and flour (cv. Sunco) werethe Mixograms it produces for various flours. This mixed at three independent speeds. To obtain anhas involved: accurate characterisation of the N (PDD)

rev at each ofthe three speeds, a number of samples were mixed(i) The formulation of a mathematicalat each of the speeds. In essence, this gave amodel for the motion of the Mixo-direct measure of the extent of variability in thegraphTM during mixing. Details aboutdetermination of the N (PDD)

rev , as the resulting rep-the relative motion between the movinglicates (i.e. independent repeated measurements)and fixed pins in a MixographTM, whenof the N (PDD)

rev , at each speed, define a histogram forit contains no dough, have been pub-the determination of the average value of thelished by Buchholz20.N (PDD)

rev for each of the given speeds. In this paper(ii) The modification of a standard 35-gramthe results of a much more comprehensive studyMixographTM (as outlined above), in orderwith seven flours, selected to cover a range of flourto monitor the mixing electronically.types, are reported (cf. Table I).(iii) The decision to define and measure ‘mix-

In the current study, the full development ofing time’ as the ‘number (N (PDD)rev ) of re-

the dough (i.e. PDD as determined from a Mixo-volutions (of the mixer) to achieve PDD’gramTM) was taken as the property to examine(after the commencement of the mixing).

As already mentioned above, this re- the validity of the rate-independence hypothesis.


Table II Number of rotations to peak dough development as a function of mixing speed

Flour Average number of revolutions Slopes of linear regressions

Aver(rev)5 Aver(rev)

4 Aver(rev)3 Slope(rev)

5 Slope(rev)4 Slope(rev)

3

Amery 336·8 332·1 328·8 −0·57 −0·40 —0·24Bakers 245·3 242·3 243·6 −0·16 —0·16 −0·10Biscuit 206·5 206·5 207·6 0·05 0·10 −0·04Osprey 154·3 153·1 152·8 −0·14 −0·08 −0·13Sun 224B 284·0 281·0 278·3 −0·39 −0·31 −0·11Sunbri 258·3 255·1 258·9 −0·48 −0·42 −0·28Yanac 220·8 220·4 220·3 −0·08 −0·11 −0·29

Though this choice is not unique, it can be justified The advantages of performing replicates in acomparative experiment (that characterizes theon the following grounds:

(a) it is widely accepted as a measure that reflects situation under examination in that the value ofthe N (PDD)

rev is being compared for different floursa key property in the mixing of a dough;(b) it identifies a crucial stage in the mixing with for different mixing speeds) has been discussed in

some detail by Chatfield23. In fact, he states:respect to the commercial and industrial usesof a dough;

‘A fundamental principle of such experiments is that it(c) there are well established correlates betweenis essential to carry out more than one test on eachthe full development of dough (e.g. PDD)treatment [Mixograph experiment with one flourand its baking properties16;at one speed] in order to estimate the size of the(d) objective procedures exist for determiningexperimental error and hence to get some idea of thethe onset of PDD from a mixogram (cf. Grasprecision of the estimates of the treatment effects.’et al.21).

However, as indicated above, unlike previous In some situations, where one cannot directlypractice, the ‘time’ was measured as ‘the number perform replicates, one can still perform ‘repeatedof revolutions’ (of the mixer) to attain PDD; i.e. measurements’ (in a statistical sense) (e.g. cor-N (PDD)

rev . related measurements on a single individual overIn performing a confirmatory experiment of the a period of time), and then apply appropriate

type outlined above, it is necessary not only to statistical techniques to obtain an idea about theobtain estimates of the N (PDD)

rev as a function of precision of the treatment effects (cf. Diggle etmixing speed, but also to quantify the nature of al.24). However, such considerations are outsidethe variation of the N (PDD)

rev estimates at the different the scope of the present discussion.mixing speeds examined. This was achieved byperforming replicates (up to 20) on each flour for

RESULTS AND DISCUSSIONeach of the speeds examined. The amount ofscatter in the data confirms why replicates were For the seven flours listed in Table I, the valuenecessary. Not only do the values of N (PDD)

rev show a of N (PDD)rev and R(PDD), for five different mixing speeds,

clear scatter about a well-defined mean for each are plotted in Figures 1 and 2, respectively, whereflour and each speed, they also contained the the flours are ordered in terms of the ascendingoccasional outlier due to some accidental mal- values of N (PDD)

rev and R(PDD). The average N (PDD)rev and

function of the experimental equipment (e.g. a R(PDD) of each set of (trimmed) replicates of N (PDD)revmechanical malfunction in the operation of the and R(PDD), for each flour and each speed, along

strain-gauge due to a loose screw). These oc- with the corresponding standard deviations, arecasional outliers (which occurred stochastically shown (with straight lines joining the averages forwith an average rate of about one every 50 to 100 each flour). For the j highest mixing speeds ( j=5,experiments) have been removed from the data 4, 3), for each of the seven flours, letpresented below. This was achieved by simplyremoving the smallest and largest values from each

Aver(rev)j =

1j

R5

k=6-jN (PDD)

rev (RPMk), Aver(R)j =

1j

R5

k=6-jR(PDD) (RPMk),set of replicates.


120

390

14060

Mixer speed (RPM)

Rev

olu

tion

s to

PD

D

340

290

240

190

100 11070 80 90

Amery

Sun224B

SunbriBakers

Yanac

Biscuit

Osprey

Figure 1 The average values, along with standard deviations, of 19 replicates of the number of revolutions of the mixer toachieve PDD for the seven flours listed in Table I, for five different mixing speeds.

where RPMk denotes the speed, in revolutions per is sufficient scatter in the data shown inFigures 1 and 2 to indicate that, if only oneminute, and Slope (rev)

j and Slope(R)j denote the slopes

of the least-squares straight line fits to the various experiment has been performed for eachspeed (for each flour), one might, in somereplicates of N (PDD)

(revj and R(PDD) for the j highestmixing speeds, respectively. The values of Aver(rev)

j cases, have obtained a misleading pictureabout the dependence of N (PDD)

rev and R(PDD) onand Slope(rev)j (Aver(R)

j , and Slope(R)j ) are listed in

Tables II and III. mixer speed.(2) For each flour, the N (PDD)

rev values, as a functionAn examination of these Figures and Tablesindicates that: of the four highest mixing speeds, are reas-

onably constant. This is supported quite(1) For each flour and each speed, there is a strongly by the values of Aver(rev)

j andSlope(rev)

j listed in Table II. On the onereasonable, though not excessive, scatter inthe N (PDD)

rev and R(PDD) values. This confirms hand, for each flour, the values of Aver(rev)j ,

as a function of j, have a variation of lessthe need to perform replicates in order toassess the variability in the data, and thereby than 36. On the other hand, all the slopes

are quite small and not all of the sameremove the uncertainty that arises whenreplicates are not performed. In fact, there sign.


120

5.0

2.060

Mixer speed (RPM)

Res

ista

nce

at

PD

D (

N)

4.5

3.5

3.0

2.5

100 11070 80 90

Amery

Sun224BSunbri

Bakers

Yanac

Biscuit

Osprey

4.0

Figure 2 The average values, along with standard deviations, of 19 replicates of the resistance of the dough to the mixingat PDD for the seven flours listed in Table I, for five different mixing speeds.

Table III Peak resistance as a function of mixing speed

Flour Peak resistance (Newtons) Slopes of linear regressions

Aver(R)5 Aver(R)

4 Aver(R)3 Slope(R)

5 Slope(R)4 Aver(R)

3

Amery 2·80 2·90 3·00 0·0151 0·0153 0·0144Bakers 3·60 3·73 3·87 0·0185 0·0165 0·0072Biscuit 2·99 3·05 3·17 0·0116 0·0148 0·0077Osprey 4·46 4·56 4·65 0·0137 0·0117 0·0082Sun 224B 4·00 4·12 4·27 0·0208 0·0223 0·0181Sunbri 4·07 4·17 4·30 0·0176 0·0180 0·0139Yanac 2·68 2·75 2·92 0·0163 0·0222 0·0154

(3) For each flour, the R(PDD) values appear to the values of Aver(R)j and Slope(R)

j listed inTable III. On the one hand, for each flour,be plateauing to a constant value at the

highest mixing speeds. This is supported by the values of Aver(R)j , as a function of j, have


Table IV The ordering of the flours with respect to various properties

1/Ext # Revolutions Peak resistance % Protein R(max)

(Mixograph) (Mixograph)

Amery Amery Osprey Sun 224B SunbriSunbri Sun 224B Sun 224B Osprey Sun 224BOsprey Sunbri Sunbri Sunbri OspreySun 224B Bakers Bakers Bakers AmeryBakers Yanac Biscuit Amery BakersYanac Biscuit Amery Biscuit YanacBiscuit Osprey Yanac Yanac Biscuit

development is not well understood (Frazier etTable V Averages of R(max) and Ext recorded on the CSIROextension tester al.13), the present work represents an opportunity

to examine the variability of R(max) and Ext for theseFlour R(max) Ext seven flours and their correlation with the in-

formation presented in Figures 1 and 2. BecauseAmery 535 1299Bakers 301 1383 the mixing action of the 2 gm MixographTM is theBiscuit 463 1703 same as that of the 35 gm MixographTM the samplesOsprey 622 1326 for the extension testing were prepared on theSun 224B 866 1367

2 gm mixer. The averages R(max) and Ext of theseSunbri 867 1291values tabulated in Table V, show that there is aYanac 321 1404statistical significant correlation between theR(PDD) and R(max) values (with correlation coefficientr=0·64), but that the correlation between the

a variation of less than 10. On the other N (PDD)

rev and Ext values is not so strong and is negativehand, all the slopes are quite small and, with correlation coefficient r=−0·33).though they do not change sign, they allshow a clear tendency to decrease as themixing speeds increase. CONCLUSIONS

(4) For the three mixer speeds greater thanAs already stressed in the Caveat at the end of85 rpm, the N (PDD)

rev and R(PDD) values, for eachthe Introduction, the results and conclusions inflour, show less variability than for the fullthis paper are based on experiments performedset of five mixer speeds. It is likely that, foron a MixographTM, where the mixing action, asthe two speeds below 85 rpm, one is seeing aperformed on the dough, is clearly one of elong-ramification of the threshold effect examinedation-and-rupture. Consequently, it does not fol-by Kilborn and Tipples (1972)14.low that the conclusions reached in this paper will(5) The ordering of the seven flours in Figuresnecessarily apply to all types of mixers, especially1 and 2 clearly indicate that, except forwhen the action performed on the dough is un-Amery and Osprey which drastically reverseambiguously different from an elongation-and-positions, there is a good correlation betweenrupture action. The above results give strong em-the N (PDD)

rev and R(PDD) values for the flourspirical support to the hypothesis that, at least toexamined. The reversal in the relative po-first order, the evolving rheology of wheat floursitions of Amery and Osprey, shown in Tabledough, as encapsulated in measurements of peakIV, could be due to factors not examined indough development, has a clear rate-independentthis paper such as the relative water content.character, when mixed in a MixographTM at reas-In addition, replicated extension tests were per- onably high speeds.formed on each dough using the CSIRO’s Ex- Various implications of this fact include:tension Tester, to determine, for each of the seven

flours, the corresponding R(max) and Ext values. (a) The number of revolutions N (PDD)rev to achieve

PDD, when mixed in a MixographTM, rep-Because the nature of how the resistance to ex-tension of a dough depends on the stage of its resents a more realistic and robust identifier


of a dough than any indicator that depends accumulated elastic energy to the baking char-acteristics of the dough. Gras et al. (unpublishedon the mixing speed, since the value ofobservations) have examined the extent to whichN (PDD)

rev thereby determined is independent ofPDD, which is known to correlate well with thethe mixing process in a MixographTM.baking performance for breads, correlates with the(b) Testing dough on a MixographTM allows oneelasticity of, and the accumulated elastic energyto decouple the rheology of the dough fromin, the dough. In fact, there is a natural trade-offthe speed at which it has been mixed and,that determines the extent to which elastic energythereby, to simplify the construction of acan be accumulated by the dough as a result ofmodel of the mixing process. For example,its mixing. On the one hand, the increasing elast-in situations where the dough property oficity is reflected in an initial increase in the re-interest and its measurement depend on thesistance of the dough to the mixing, as the glutenspeed of mixing, it will be necessary to takematrix forms. On the other hand, if the dough isthis explicitly into account in the con-overmixed, the matrix is partially destroyed withstruction of a mathematical modelling of thea loss of elastic energy. Clearly, the nature of thismixing process.trade-off will depend on the type of mixer used(c) The data presented above only confirm the(as indirectly mentioned above in (c)).hypothesis for mixing on a MixographTM.

One is, however, tempted to conclude thatthe hypothesis extends naturally to mixing Acknowledgementson other devices such as a FarinographTM.

The authors wish to thank Ms S. Partridge for herHowever, because it is known that thereexpert assistance, the CSIRO Plant Industry and theis not always a strong correlation betweenCSIRO Mathematics and Information Sciences forproperties estimated for the same doughtheir financial support, and Dr R. A. Appels and Drwhen mixed on the MixographTM and theM. A. Cameron for their continuing encouragementFarinographTM (cf. Gupta et al.25), such aand support.generalisation of the above hypothesis can

only be viewed as tentative at this stage.REFERENCESIn fact, any simple measure, which one wishes

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