Nonlinear, time-dependent shear flow behaviour, and shear-induced effects in wheat flour dough rheology

Journal of Cereal Science 49 (2009) 262–271

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Nonlinear, time-dependent shear flow behaviour, and shear-induced effects in wheat flour dough rheology Jacques Lefebvre 1, * INRA, UR1268 Biopolyme`res Interactions Assemblages, F-44300 Nantes, France

a r t i c l e i n f o

a b s t r a c t

Article history: Received 17 December 2007 Received in revised form 15 October 2008 Accepted 23 October 2008

Retardation test, step-shear rate experiments, low-amplitude and large-amplitude dynamic measurements have been combined to study the nonlinear and time-dependent viscosity of dough and shearinduced effects of flow on dough structure. Despite large quantitative differences in linear viscoelastic constants, doughs from different flours or with different water contents display the same type of flow behaviour. Shear-induced structural changes cause flow to shift from a high viscosity steady-state regime to a low viscosity one. The process, irreversible, is responsible for the time-dependent character of dough viscosity and seems to be controlled by the mechanical energy absorbed. Nevertheless, the two steadystate viscosities follow the same shear-thinning flow curve, fitted by a Cross equation with an exponent close to 1; the Newtonian plateau is approached at very low shear rate values. Viscosity data obtained on different doughs yield a unique flow master curve in reduced coordinates. Shear-induced structural changes cause also the linear viscoelastic plateau modulus of dough to decrease; this progressive weakening of the network structure is irreversible and seems governed by the accumulated strain. These characteristics of dough rheology are discussed with reference to the behaviour of concentrated suspensions. Ó 2008 Elsevier Ltd. All rights reserved.

Keywords: Dough Nonlinear rheology Flow behaviour Shear-induced effects

1. Introduction Common opinion holds that the rheological properties of dough play a key role in flour functionality and baking quality. During mixing, shaping, fermentation and oven rise, dough is submitted to stress and to deformation, so that the rheological properties of dough are directly involved in its functional behaviour during these steps of the baking process. Although the link is much less clear and is perhaps indirect (Bloksma, 1990a,b), the rheological characteristics of dough seem also important as to the quality of the final product. Thus, it appears that dough rheology is one of the main factors governing the overall baking performance. On the other hand, the rheological behaviour of dough, as that of any material, is the mechanical expression of its structure (i.e. the spatial arrangement of the structural elements and their interactions). Therefore, its investigation provides an insight into the structure at the spatial scales corresponding to the time scale of the rheological experiments, tools to study the connections of structure with composition, and to understand how it is affected by biochemical and technological processes.

* Tel.: þ33 2 40 67 50 40; fax: þ33 2 40 67 50 43. E-mail address: [email protected] 1 Now retired. 0733-5210/$ – see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcs.2008.10.010

However, our views on these problems rest upon limited experimental bases, often of an indirect nature (such as statistical correlations), and on results that are not devoid of ambiguity if not actually unexploitable on rheological grounds. The largest body of results comes in effect from the application of empirical tests. When proper rheological techniques are used, the results are seldom analysed in order to extract rheologically relevant parameters; moreover the data are generally obtained only over restricted ranges of strain, strain rate, stress, and time, and those are not necessarily the relevant ones as regards the baking process step considered (Bloksma, 1990b; Dobraszczyk and Morgenstern, 2003). Indeed, we are still lacking a comprehensive characterisation of dough rheological behaviour, which would be in the abstract the prerequisite for any study of the relationships between dough rheology and baking performance or dough structure. Among the reasons for this situation, the main one is certainly that dough does not lend itself to easy and quick rheological study, by the very fact of the complexity of its rheological behaviour, but also because of the limited play we can have on this behaviour by acting on wellidentified control factors in a reasoned way. The complexity of dough rheology is principally due to that of its flow behaviour (Lefebvre, 2006). Flow behaviour of dough, in shear and in extensional deformations, is obviously important as regards mixing and sheeting. Moreover, the strain hardening effect, i.e. an increase with strain of the extensional viscosity at fixed strain rate

J. Lefebvre / Journal of Cereal Science 49 (2009) 262–271

Nomenclature

h2

f m n

hþ(t)

t tm tp: t* E G0 , G00 GoN Jc(t) Jr(t) ðJeo Þr LMS P/L ROS S U(t) W

h h0 h1

damage factor Cross equation exponent spread parameter of the high frequency loss peak (LMS) time time at the peak of hþ(t) time at the (pseudo-)plateau of hþ(t) creep time at the onset of time-dependent flow accumulated Hencky strain (ROS) storage modulus and loss modulus (LMS) viscoelastic plateau modulus (LMS) compliance function (creep) recoverable compliance function (creep recovery) steady-state value of the recoverable compliance function (quasi-)linear viscoelastic spectrum (go ¼ 0.1%) Alveograph parameter application of repeated sinusoidal strain oscillations (103  go  2) creep duration mechanical energy absorbed by unit volume of the sample Alveograph parameter steady shear viscosity Newtonian plateau viscosity viscosity value in the initial steady flow regime (creep test)

hþ m hþ p g, g(t) gc(t) gm gp gr(t) go g* (gf)N (gr)N:

g_ , g_ ðtÞ g_ c g_ 1 g_ 2 s, s(t) sc so u u1 G

in uni- or bi-extensional flow, has been pointed out as crucial for the stabilisation of the gas bubbles and gas retention (Dobraszczyk and Roberts, 1994; Dobraszczyk et al., 2003; Kokelaar et al., 1996; van Vliet et al., 1992). However, available data on dough viscosity, whatever the deformation mode, are actually limited; moreover they do not necessarily represent steady flow values. In effect, direct measurement of dough viscosity using viscometric techniques comes up against experimental difficulties, which are in last analysis inherent to the rheological behaviour of the material. In rotational viscometry, it has been repeatedly observed that steady-state flow could not be reached in the experimentally accessible range of shear rates (Bagley et al., 1998; Bloksma and Nieman, 1975; Phan-Thien et al., 1997); dough samples are ejected out of the gap or they fracture well before stress reaches an equilibrium value. The transient stress response of dough upon the application of a steady shear rate is often implicitly treated as a viscous response, without evidence given. On the contrary, since dough is a viscoelastic material displaying a high level of retarded elasticity with very long terminal relaxation time (Lefebvre, 2006), retarded elasticity is more likely to dominate up to long times or to large values of strain during transient viscometric experiments or shear rate sweep tests. The same remark applies to the results of these types of experiments when performed in extensional modes on dough; in this case, besides, the ranges of deformation and deformation rate that are accessible in practice are still narrower than in shear. On the other hand, attempts to extract steady-state viscosity values from transient response data by application of linear or nonlinear viscoelasticity models (Bagley et al., 1988, 1998; Dus and Kokini, 1990; Launay, 1990; Phan-Thien et al., 1997) or from that of semi-empirical rules (Bagley et al., 1998), circumvent the problem. In addition, the models used did not allow for thixotropy. That dough exhibits some form of thixotropy was observed in several studies (Berland and Launay, 1995; Smith et al.,

263

viscosity value in the final steady flow regime (creep test) transient shear viscosity function (step-shear rate tests) peak value of hþ(t) viscosity at the (pseudo-)plateau of hþ(t) shear strain, shear strain function creep strain function (creep test) strain at the peak of hþ(t) strain at the (pseudo-)plateau of hþ(t) recoverable creep strain function (creep recovery) strain amplitude (oscillatory tests) creep strain at the onset of time-dependent flow value of the total non-recoverable strain corresponding to ðJeo Þr value of the total recoverable strain corresponding to ðJeo Þr shear rate, shear rate function critical shear rate (Cross equation) shear rate value in the first steady flow regime (creep test) shear rate value in the final steady flow regime (creep test) shear stress, shear stress function creep stress stress amplitude (oscillatory tests) angular frequency central frequency of the high frequency loss peak (LMS) accumulated strain (ROS)

1970). However, since these studies were based on dynamic measurements, the reported reversible and irreversible effects of strain amplitude could have resulted from network structure modifications affecting the delayed elastic response rather than from time-dependent flow properties (thixotropy). In a recent paper (Lefebvre, 2006), I focused on steady-state flow, studied with the help of the retardation test. The timedependent flow behaviour of dough was unambiguously demonstrated, but it was not investigated. Besides, the work was restricted to a single commercial flour and to a single value of dough hydration. The purpose of the present article is to widen the scope of the previous paper on the different aspects of dough shear flow behaviour. The same general approach will be applied to doughs from different flours and at different water contents, in order to introduce variability in dough properties, the aim being to verify the generality of our previous conclusions, but not to study varietal or water content effects per se. The time-dependence of dough flow behaviour, which was simply observed in the previous paper, will be now examined more in detail by combining retardation and viscometric tests. The nature of the time-dependence of dough viscosity will be examined, and the governing mechanical factors will be considered. Data obtained in previous studies (Lefebvre, 2006; Lefebvre et al., 2004) are revisited and compared to a large body of original results. 2. Materials and methods 2.1. Flours Doughs obtained with six different flours were studied: one commercial flour (‘‘CNS’’), one flour from a French cultivar (‘‘Caphorn’’), and the flours from four experimental strains of the OlympicXGabo line (‘‘Gabo’’).

264

J. Lefebvre / Journal of Cereal Science 49 (2009) 262–271

The ‘‘CNS’’ flour contained 10.5% protein and 0.56% ash (db); its Chopin Alveograph parameters were W ¼ 194 J and P/L ¼ 0.56. Caphorn flour contained 10.32% protein and 0.46% ash (db); its Chopin Alveograph parameters were W ¼ 309 J and P/L ¼ 1.77, very different from those of CNS in spite of a comparable protein content. The Gabo lines differed in HMW glutenin subunits compositions (Barro et al., 1997; Lawrence et al., 1988). They comprised the control OlympicXGabo line 1/17 þ 18/5 þ 10 (‘‘Gabo control’’), the double-deleted line -/17 þ 18/– (‘‘Gabo 00’’), and the two transgenic lines 1/17 þ 18/– (‘‘Gabo Ax1’’) and -/17 þ 18/5- (‘‘Gabo Dx5’’), obtained from the double-deleted one by reintroducing the genes 1Ax1 and 1Dx5, respectively. The Gabo flour samples were kindly provided by Long Ashton plant breeding station. Their compositions were given in Lefebvre et al. (2004). They displayed extremely different mixing characteristics (Popineau et al., 2001). 2.2. Dough mixing All doughs were prepared by mixing flour with distilled water at 20  C using a 2 g Mixograph rotating at 88 rpm. CNS doughs and Gabo doughs were mixed to the peak at 46.1% and 50% hydration (total water/dough w/w), respectively. In the case of Caphorn, mixing time was 10 min and three hydration values were used: 42.7%, 46.2%, and 49.4%. A new dough sample was mixed for each rheological experiment. 2.3. Rheometers The different rheological experiments were carried out using three rheometers: two stress-controlled instruments (TA Instruments AR2000, and Rheometric SR2000) and a strain-controlled instrument (TA Instruments Rheometrics series ARES-LS). The SR rheometer was used to study doughs of the Gabo lines. The results on the CNS doughs were obtained with the AR rheometer. The study of the Caphorn doughs combined results obtained with the AR and with the ARES instruments. All the experiments with the SR rheometer were performed in cone–plate geometry (2.5 cm-diameter/5.7 -angle Teflon cone). Most of the measurements with the ARES and AR rheometers were performed with cone–plate geometries (2.5 cm-diameter/5.7 angle Teflon cone, and 2 cm diameter/4 -angle steel cone, respectively). For some of the experiments with these instruments, we used plate–plate geometries (2.5 cm Teflon and 2 cm steel plate, respectively; gap was set to 0.5 or to 1 mm). CP geometry has the great advantage over PP geometry that the sample is in principle uniformly sheared in the gap, whereas shear is not uniform between parallel plates. To insure that the sample undergoes the same mechanical history in all of its points is particularly important when studying materials with time-dependent flow properties or exhibiting a yield stress. This is why we preferred as a rule CP geometries. Wall slip is an important issue and a recurrent concern in dough shear rheology literature. In most papers, sanded cones or serrated plates were used to avoid slippage, even when performing just small amplitude oscillatory measurements. Of course, the risk of slippage due to some kind of syneresis is greater in long-lasting experiments at high strain values, in particular during the creep or step-shear rate experiments performed in our work. However, although we used tools with smooth surfaces, we found almost always that the samples were still adhering firmly to the surfaces (steel or Teflon) at the end of the experiments (after mixing doughs were sticking to the pins and the bowl of the Mixograph as well). The few exceptions were observed after shearing to extremely high strains, and they were visibly due to sample fracture. In addition, according to the classical

procedure used to check for the absence of wall slip, we carried out a few experimental sequences using PP geometries, with two different gap values, in comparison with the corresponding experiences carried out with CP. Allowing for the experimental error, the results were the same. This agreement is a good indication that wall slip did not occur during our experiments. Besides, it shows that the presence of starch granules was not affecting CP measurements, although the size of starch granules (w20 mm) is not much smaller than the cone truncation gaps (which were either 50 mm or 100 mm). 2.4. Rheological experiments All experiments were done at 20  C. Dough was transferred to the rheometer immediately after mixing. After the gap was set, the sample was covered with fluid silicon oil to avoid drying, and it was left to rest during 1 h before rheological measurements were started. A new dough preparation was used for each rheological test sequence. 2.4.1. Small amplitude dynamic measurements The first step in all test sequences consisted in recording the linear mechanical spectrum (LMS) of the sample d a rheological expression of its unperturbed structure. The dynamic measurements were performed at go ¼ 0.1 % strain amplitude over the 0.06  u  100 rad/s frequency range; the viscoelastic behaviour of dough in the harmonic regime is practically linear at this strain amplitude (Lefebvre, 2006). This initial step was followed by an experiment in transient regime in order to study the long term/large strain behaviour of dough. The transient regime test was either a retardation test (creep and recovery), or a viscometric test, or a large-amplitude oscillation test sequence. The LMS was also recorded after the transient regime tests, so as to monitor their effect on the structure of the sample. The LMS’s were analysed by fitting the Cole–Cole model to the complex compliance functions (Lefebvre et al., 2000), yielding the viscoelastic plateau modulus GoN, and the central frequency u1 and spread parameter n1 of the high frequency loss peak. For Caphorn dough at 46.2% hydration, the mean value and the relative standard error (57 repetitions) were: for GoN, 2.19 kPa and 1.5%; for u1, 0.022 rad/s and 4.8%; and for n1, 0.283 and 0.2%. Thus, we can consider that, albeit it has been observed that dough preparation reproducibility could be a problem in some deformation modes (Bagley et al., 1998), it is acceptable for phenomenological studies in rotational shear (Phan-Thien et al., 1997; Phan-Thien and SafariArdi, 1998). 2.4.2. Retardation tests The retardation tests were carried out with the AR instrument, except in the case of the doughs from the Gabo lines, for which the SR rheometer was used. Creep stress sc varied in the 0.3–350 Pa (CNS), 2–150 Pa (Gabo strains), 20–920 Pa (Caphorn, 42.7% hydration), 5–600 Pa (Caphorn, 46.2% hydration), and 5–160 Pa (Caphorn, 49.4% hydration) ranges. In the case of the Gabo strains, creep stress was maintained during S ¼ 3 h systematically. This was also the creep duration S for most of the experiments on CNS dough; a few were carried on for longer times, up to 12 h. In the case of the Caphorn doughs, S was varied more systematically, in the range 2–50 h, depending on the time necessary to reach the final steady state at the different applied stress values. For all dough samples, creep recovery was recorded during 12 h, a lapse of time long enough for a steady-state value ðJeo Þr of the recoverable compliance to be reached in all cases. The retardation test was followed by the repetition of the initial frequency sweep in small amplitude dynamic measurements.

J. Lefebvre / Journal of Cereal Science 49 (2009) 262–271

2.4.3. Viscometric tests Step-shear rate tests were performed with the AR instrument on CNS doughs, and with both the AR and ARES instruments on Caphorn doughs. After the initial mechanical spectrum of the sample was recorded, a constant shear rate value g_ ¼ g_ 1 in the range 104–0.06 s1 was applied and maintained during the time necessary to approach a stress plateau, although a true constant stress value (which would correspond to steady shear flow regime) was never observed. In a few experiments on Caphorn doughs, this first step-shear rate test was followed by a second shear rate step g_ ¼ g_ 2 . 2.4.4. Repeated oscillation tests In order to study the irreversibility of structure modifications induced by mechanical excitation, 46.2% hydration Caphorn dough samples were submitted to repeated sinusoidal oscillations of variable amplitudes (ROS) at two frequencies, 6.28  102 and 6.28  103 rad/s, using the ARES rheometer. Two types of ROS sequences were applied: - Sequence 1 (continuous): LMS1–ROS1–LMS2–ROS2 . – LMS5, without interruption between the steps. Each ROS step comprised 16 cycles performed at the same strain amplitude go in the 103–2 range. Amplitudes were changed at random from one ROS step to the following one, and from one test sequence to the other. Each sequence comprised 4 ROS steps. - Sequence 2 (discontinuous): LMS1–ROS1–12 h rest–LMS2– ROS2–LMS3. In this case, the two ROS were identical, with 16 cycles each and go ¼ 1.

265

ðJeo Þr after a recovery time w3 h. Flow contribution ht to the creep strain gc(t) ¼ scJc(t) dominated over the recoverable (elastic) contribution gr(t) ¼ scJr(t) as soon as gc(t) reaches moderate values (w0.5 for sc ¼ 200 Pa, to take an example). Dough viscosity was very dependent on sc, showing that dough flow behaviour is highly shear-thinning. Time-dependent flow was observed above a stress value 200
3. Results and discussion

- Does the onset of time-dependent shear flow viscosity actually require a critical stress, or a critical strain, value to be exceeded? - When time-dependence shows up, would the system eventually reach steady flow if S were increased? To answer both questions, we have carried out retardation tests over larger extended creep stress and creep time ranges on Caphorn dough. The following exposition will be based on the study of 46.2% hydration doughs, but similar results were obtained at the two other hydration values of Caphorn doughs. In ‘‘short’’ creep experiments (3  S  12 h), 46.2% hydration Caphorn dough displayed the classical creep behaviour up to creep stress sc ¼ 200 Pa. Creep curves showed the linear terminal region characterising steady flow, whereas the recoverable compliance Jr(t) recorded during the recovery step of the test reached a plateau

Creep compliance J(t), recoverable compliance Jr(t) (m2/N)

Retardation tests performed over a large enough creep stress range of values provide probably the best way to approach the flow behaviour of highly viscoelastic materials with long terminal relaxation times and large viscosity values. For each value of the creep stress, steady-state viscosity h and shear rate g_ are easily determined from the terminal part of the creep curve, provided the stress has been maintained for a time long enough for steady flow to be reached. In a previous paper (Lefebvre et al., 2004), this approach was applied to doughs of the Gabo lines; apparent steady flow was reached in all cases. In the experimental conditions of the study of CNS dough (Lefebvre, 2006), apparent steady flow was reached when sc  200 Pa (final creep strain  w5), but timedependent viscosity was observed at larger stress values. However, in both studies the maximum values of sc and of S remained relatively limited. Thus, two questions were left open:

a 10-1

10-3

10-5 0 100

2 104

4 104

Time t (104 s)

b

2

Creep compliance J(t), recoverable compliance Jr(t) (10-2 N/m2)

3.1. The two flow regimes of dough

1

0

0

1

2

Time t (105 s) Fig. 1. The retardation behaviour of Caphorn dough (46.2% hydration) showing the transition between two apparent steady-state flow regimes during creep. Symbols: creep compliance; line: recoverable compliance (recovery curve). (a) Under relatively high creep stress value (280 Pa) maintained during 3 h. (b) Demonstration that a similar creep behaviour is observed also under low creep stress (20 Pa), provided stress is applied during a time long enough (46 h in this example).

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J. Lefebvre / Journal of Cereal Science 49 (2009) 262–271

steady-state flow regimes, characterised by the viscosity values h1 and h2, respectively, separated by a region of the creep curve where flow viscosity is time-dependent, as exemplified by the creep curves of Fig. 1. This is confirmed by considering the variation of the shear rate during creep. Fig. 2a demonstrates indeed that for sc ¼ 280 Pa, a final shear rate plateau ðg_ 2 z0:032 s1 Þ is reached, but also that it is preceded by a first one ðg_ 1 z5  104 s1 Þ extending approximately over the 1400–3400 s creep time range; we shall call it the ‘‘first steady-state flow regime’’. The viscosity values corresponding to these two regimes are h2 ¼ 9  103 Pa s and h1 ¼ 5.4  105 Pa s, respectively. Although they are less well characterised than for sc ¼ 280 Pa, two steady-state regions are also seen in the case of the 20 Pa creep test (Fig. 2b), with g_ 1 z6:6  107 s1 (h1 ¼ 3.0  107 Pa s) and g_ 2 z1:6  106 s1 (h2 ¼ 1.3  107 Pa s), respectively. One can notice that in this case h1 and h2 are close to each other; we observed that the difference between them decreases as the creep stress decreases. An inflection with upward curvature of creep curves of doughs, occurring above some creep shear stress value, though observed in very different stress and time ranges as compared to our results, has been observed a long time ago by Bloksma (1962). On the other hand, it is observed in general for concentrated suspensions; it is often considered in this case to result from shear-induced solid to liquid transition and it is classically related to the existence of a yield stress. However, recent studies (Coussot et al., 2002, 2006; Uhlherr et al., 2005) show that the transition from the elasticitydominated deformation to the terminal steady flow-dominated creep regimes of concentrated suspensions and pastes is actually

Strain rate (s-1)

a

100

10-1

10-2

10-3

10-4 0 100

4 103

8 103

b

10-5

Strain rate (s-1)

Time t

10-6

(103

1.2 104

s)

Jr(t) = const

complex and bears to a large extent similarity with our observations on dough. The terminal steady-state flow appears indeed to be preceded by a creep irreversible deformation phase corresponding to that we called the ‘‘first steady-state flow regime’’. Uhlherr et al. (2005) showed that ‘‘continuous flow exists at stresses well below the (conventional) yield stress’’, but they preferred to classify it as ‘‘creeping flow’’ rather than as ‘‘viscous flow’’, considering the very low shear rates (107–105 s1); on the other hand, while they observed ‘‘that there exists neither a critical stress nor a critical shear rate for causing the catastrophic flow (i.e. what we call the second or final steady flow regime)’’ of their materials, they considered that the onset of terminal flow occurs when the accumulated strain reaches a certain critical value, although they showed that the critical strain does increase with creep stress in most cases. There is a good parallel with our findings on dough. However, in the following section we shall show that h1 and h2 follow the same curve when plotted against the shear rate; therefore, we think that there is no reason to consider the first irreversible deformation regime as a specific process differing from usual ‘‘viscous flow’’. Coussot et al. (2002) observed that below a certain value of the creep stress, applied after pre-shearing, concentrated suspensions of bentonite displayed an initial flow phase, followed by a sudden dramatic decrease of the shear rate to values of the order of magnitude of the instrument sensitivity threshold (103–104 s1). Because no final steady state was apparently reached, they considered that the shear rate fall corresponded to an actual flow stoppage, the system reverting to solid state. For creep stress values larger than the critical one, the suspensions exhibited timedependent viscosity, decreasing continuously towards a constant value in steady-state flow regime (constant shear rate). In a subsequent paper (Coussot et al., 2006), the authors generalised these findings to other ‘‘soft-jammed’’ pasty systems. They considered that in the ‘‘solid regime’’ (below the creep stress critical value) the systems could not exhibit stable flow. The irreversible deformation, increasing with creep time and not recovered after stress release, observed in the ‘‘solid regime’’ was interpreted as the result of an aging process reminiscent of that of glasses, the system structure rearranging progressively when it is submitted to stress. The authors suggested that flow characteristics are governed by a competition between structure restoration (during aging) and rejuvenation due to flow. Depending on which of these two processes dominates, either flow stoppage or steady flow is observed and the change in behaviour occurs at a definite non-zero shear rate value. Our results seem to differ radically from those of Coussot et al. in that we never observed flow stoppage; however, this is perhaps due to the fact that it was not possible for practical reasons to perform creep experiments on dough under low enough stress values. The complex flow behaviour of dough is not necessarily related to the high volume fraction of starch granules only. It could result as well, at least to some extent, from shear-induced effects in the highly viscoelastic matrix (the gluten) in which the particles are embedded. Even systems much simpler than concentrated suspensions or pastes can exhibit complex flow behaviour in creep, as for example has been shown in a recent study (Schweizer, 2007) on a highly entangled monodisperse polystyrene solution. 3.2. A unique flow curve for flour–water doughs

10

-7

2

6

10

14

18

Time t (104 s) Fig. 2. Variation of the strain rate during the creep of a 46.2% hydrated Caphorn dough. The plots show the existence of two steady-state flow regimes (see text). Symbols: data; the continuous line segments materialise the ordinates of the two steady-state shear regimes. (a) Creep stress: 280 Pa and (b) creep stress: 20 Pa.

Plotting h1 and h2 against the corresponding shear rate values for 46.2% hydration Caphorn doughs (Fig. 3) shows that both steady flow viscosities follow the same flow curve if we allow for the experimental noise which affects the data. The flow curve of Fig. 3, at first sight, is of the classical shear-thinning type. An initial Newtonian viscosity plateau h0 is approached at low shear rates,

J. Lefebvre / Journal of Cereal Science 49 (2009) 262–271

5

3 -7

-5

-3

-1

log(dγ/dt) (s-1) Fig. 3. The flow curve of 46.2% hydrated Caphorn dough. The data relative to the terminal steady flow regime (h2, filled triangles) and to the ‘‘first steady flow’’ regime (h1, empty circles) have been fitted by equation (1) with m ¼ 1 (line). The fit (R2 ¼ 0.98) gives h0 ¼ 1.61  107 Pa s and g_ c ¼ 2:0  105 s1 .

and a power law variation of the viscosity is observed above g_ > w3  104 s1 . The simplified Cross equation (1) satisfactorily fitted the data.

h¼ 

ho

1 þ ðg_ =g_ c Þm



recoverable (reversible, or ‘‘elastic’’) part manifests the viscoelastic nature of the material. Let us now compare the contributions of the recoverable strain (gr)N ¼ sc(Joe )r and of the non-recoverable strain (gf)N ¼ g(S)  sc(Joe )r, to the total strain g(S) ¼ scJ(S) reached at the end of the creep step of the retardation test. Fig. 4 shows that the (gr)N data of all doughs fall on a single curve when plotted against g(S), and the same for the (gf)N data, one more illustration of the fact that all the doughs shared the same rheological behaviour. Moreover, the few data available on a gluten sample, taken from a previous paper (Lefebvre et al., 2003), fall on the same curves as those of the doughs; this intriguing result probably reflects that dough rheological behaviour is governed principally by gluten rheology in the nonlinear domain, as it is in the linear one (Lefebvre, 2006), but it requires more solid experimental evidence. Fig. 4 reveals several remarkable features of dough behaviour. Up to g(S) w 0.1, (gr)N and (gf)N contribute almost equally to g(S) and they are proportional to the final creep strain. Above g(S) w 0.1, proportionality is lost; besides, the two curves diverge as g(S) increases: (gf)N keeps on of course to increase, whereas (gr)N tends towards a plateau ((gr)N w 0.61) which is reached at g(S) w 8. The (gr)N plateau extends up to at least (gf)N z g(S) ¼ 103, the upper creep strain value reached in our study; thus, dough appears to keep or to recover an elastic character even after it has undergone large flow strains during creep, although the behaviour of the elastic contribution shows a drastic change above g(S) w 0.1.

(1)

However, the value of the exponent (m ¼ 0.96) was very close to the theoretical maximum value (m ¼ 1) admissible for stable flow; typical shear-thinning materials, such as concentrated polymer solutions, exhibit m values in the range 0.6–0.8. In fact, fixing m ¼ 1 in Eq. (1) yields a 2-parameter fit which cannot be distinguished from the 3-parameter one, because of the scatter of the experimental data (Fig. 3). In our previous work (Lefebvre, 2006), we obtained a very similar flow curve in the case of CNS dough, and we checked that the value of h0 resulting from the fit of Eq. (1) was consistent with the Newtonian viscosity value of dough calculated from the stress modulus function obtained by performing stress relaxation tests in the linear viscoelasticity domain. Thus, we are allowed to consider that the initial plateau of dough flow curve is not an artefact and that it corresponds actually to an initial Newtonian plateau. Therefore, the fact that m w 1 is not, in the case of dough, the consequence of a yield stress behaviour. Dus and Kokini (1990) published dough shear-thinning curves of the classical shape, with m w 0.7–0.8. However no evidence was given that the data obtained in their shear rate sweep experiments corresponded indeed to steady-state flow viscosity values; the fact that, in all probability, steady flow was not reached could explain the lower value of m they found. All doughs displayed the same type of steady flow behaviour, although their Newtonian viscosities, ranging from 3.1 106 Pa s (50% hydration Gabo 00 dough) to 44  106 Pa s (42.7% Caphorn dough), and their critical shear rates, ranging from 1.5  105 s1 (42.7% Caphorn dough) to 12  105 s1 (50% hydration Gabo 00 dough), differed by a factor of w10. The data for the different doughs studied, plotted in terms of the reduced viscosity h/h0 versus the reduced shear rate g_ =g_ c , all fell on a single master curve (not shown; R2 ¼ 0.99, 134 experimental points); h/h0 varied in the range 104–1, and g_ =g_ c in the range of 103–104. 3.3. Elastic strain versus irreversible strain We focused so far on the flow properties of the material, i.e. on the irreversible contribution to the total creep deformation. The

3.4. The response to step-shear rate tests Within the experimentally accessible range of shear rates, all the stress (or the transient viscosity hþ ðtÞ ¼ sðtÞ=g_ ) versus time (or strain g ¼ g_ t) curves, recorded in response to the application of a constant shear rate value, displayed a stress overshoot, passing _ through a maximum ðgm ; hþ m ¼ sm =gÞ at t ¼ tm. At large strain values (when g / gp ¼ 100), hþ tended towards a plateau _ hþ p ¼ sp =g, but in most cases, steady state was still not actually reached at g ¼ 100; increasing the final strain above this value resulted in general in sample fracture, as has been observed by others (Bagley et al., 1998; Bloksma and Nieman, 1975; Phan-Thien et al., 1997). Several papers reported curves with a similar shape for dough (Amemiya and Menjivar, 1992; Bloksma and Nieman, 1975; Lindborg et al., 1997; Phan-Thien et al., 1997), but the experiments were stopped at lower maximum strain values.

Final recovered strain (creep recovery) Final non-recovered strain (creep recovery)

log(η η) (Pa.s)

7

267

104 Non recovered strain 10

2

10

0

y=0.5 γ(S)

Recovered strain 10-2

10-4 10-4

10-2

100

102

104

Total strain at the end of creep γ(S)

Fig. 4. Elastic (recoverable) strain (gr)N and non-recoverable (irreversible) strain (gf)N, measured on the plateau of the creep recovery curves, as a function of final creep strain g(S). Circles: data for the different doughs studied. Empty squares: non-recoverable strain for Begra gluten; empty triangles: recoverable strain for Begra gluten. See text.

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Although the curves recorded with the controlled strain and with the controlled stress instruments at nominally the same constant value of the shear rate are of the same (stress overshoot) type, the results differ quantitatively. The reason is that, with the controlled stress instrument, the actual shear rate reaches the fixed value only after some lapse of time during which it shows large oscillations, in opposition to the way the controlled strain rheometer operates. Thus, the mechanical history undergone by the sample is not the same during the initial part of the test, and this will induce differences in the subsequent response curves in the case of nonlinear behaviour, and even more when viscosity is timedependent. Stress overshoot could be the manifestation either of nonlinear viscoelasticity or of time-dependent flow viscosity, or it could result from the combination of both effects. Direct evidence allowing us to decide between these hypotheses would be extremely hard to obtain, but the results provided indirect support in favour of the second one. The different sets of viscosity data obtained from the creep tests (h1and h2), and from the step-shear rate viscometric tests (hþ m and hþ p ) performed with the strain-controlled and the stress-controlled rheometers, were plotted against the corresponding shear rates for the 46.2% hydration Caphorn dough (not shown). The hþ m values obtained in the controlled strain mode agreed indeed with the creep viscosity flow curve. But the hþ m values obtained in the controlled stress mode were systematically larger than creep viscosity data in the experimental range covered, and the power law they nicely followed too as a function of g_ had a lower slope. As to the hþ p data, those obtained in the controlled stress mode did match the power law region of the creep viscosity flow curve, but not those obtained in the controlled strain mode, which, as far as the scatter of the data allows, seemed to line up on a power law curve with the same slope as creep data but lying below it. In Fig. 5, the same results are plotted in terms of the stress (creep stress sc, stress overshoot sm, or stress pseudo-plateau sp) versus U, the corresponding value of the mechanical energy absorbed by unit volume of dough. The general expression for U up to time t, UðtÞ ¼ Rt _ 0 sðuÞgðuÞdu (Tschoegl, 1989), reduces to

UðtÞ ¼ gðtÞsc

(2)

and to

UðtÞ ¼ g_ 2

Z

t

hþ ðtÞdt

(3)

0

Stress σc, σm, σp (N/m2)

104 103 102 101 10

slope 0.5

0

10-1 10-4

10-2

100

Mechanical energy U

(N/m2)

102

104

106

absorbed by unit volume

Fig. 5. Creep and step-shear rate data plotted in terms of stress values sc, sm, and sp versus the mechanical energy U absorbed by unit volume of dough up to time t* and S (creep), tm and tp (step-shear rate experiments) (see text). Filled symbols: 46.2% hydration Caphorn dough; empty symbols: 46.1% hydration CNS dough. Circles: creep data; triangles: step-shear rate experiments data.

in the cases of creep and step-shear rate experiments, respectively. Up to U w 500 N/m2 (s w 270 Pa), creep and viscometric data coincide, suggesting that indeed the decrease of the transient þ viscosity hþ from hþ m to hp in step-shear rate tests is of the same nature as that of the steady-state viscosity from h1 to h2 in the course of creep, and therefore is due to time-dependentpflow ffiffiffiffi viscosity behaviour. In addition, we can notice that s varies as U in 2 this region of the plot. Beyond U w 500 N/m , the two sets of data begin to diverge. Whereas sc reaches almost immediately a plateau, sm and sp continue to increase with U. The slope of this ascending short branch of the bilogarithmic plot has a slope larger than 0.5, but lower than 1, as far as it can be judged (Fig. 5). The results obtained on 46.1% hydration CNS dough are similar; the U(s) plot almost superimposes on that of 46.2% Caphorn dough (Fig. 5), the main difference being that the bifurcation occurs now at U w 1400 N/m2. The number of the experimental points available in the case of Caphorn dough at 42.7% and 49.4% hydration was not large enough to allow comparison. The bifurcation means probably that creep and application of steady shear rates do not affect the structure of dough in the same way when U (or s) exceeds some critical value, which has perhaps the significance of a ‘‘tolerance’’ limit. As already mentioned, viscometric tests appear to have much more drastic effects on dough structure than creep. This is probably the reason why, in step-shear rate experiments, the ‘‘first steadystate flow regime’’ is not observable, and why in most cases viscosity does not reach really a final plateau, but shows a slow decay. 3.5. Irreversibility of shear-induced dough structure changes A decrease of viscosity during flow under a constant shear rate (or under a constant shear stress) is generally associated with thixotropy. However, thixotropy implies at least partial reversibility of the phenomenon. Thixotropy is classically investigated by applying stepwise increases and stepwise reductions in shear rate from different initial values of the shear rate after steady state has been reached (see for example Dullaert and Mewis, 2006); such procedures are necessary to separate thixotropy from viscoelasticity effects. Upon a stepwise reduction in shear rate, a progressive increase of stress up to an equilibrium value, following its initial decrease, manifests the reversible character of thixotropy. When such a test was applied to dough, only a sudden drop followed by a slow decrease of the stress, due to viscoelasticity (relaxation), was observed, but no thixotropic recovery. Similar results were obtained with both the strain-controlled and the stress-controlled rheometers, whatever the initial shear rate value was in the accessible experimental range. They suggest that the shear-induced steady-state viscosity decrease of dough is totally irreversible, or nearly so; i.e. dough does not seem to manifest thixotropy sensu stricto. Therefore, this classical approach, laborious and timeconsuming, turns out to be not really adapted to the study of the time-dependent rheological behaviour of dough. On the other hand, it is unsuitable to investigate shear-induced structural modifications at low or moderate strain values. For these reasons, we turned to the repeated strain oscillation tests described in Section 2, although in the response to oscillations the effects of shear on flow viscosity and on the viscoelastic response proper are involved at the same time. Since the amplitude of the applied strain (go ¼ 1) was fairly large in the ‘‘ROS sequence 2’’ test applied to 46.2% hydration Caphorn dough, and thus the viscoelastic response highly nonlinear, the non-sinusoidal character of the stress signal oscillations was directly observable in the ROS1 and the ROS2 steps of the test. In effect, in the nonlinear viscoelastic domain, a sinusoidal excitation of a material results in a periodic response that is no longer sinusoidal, but contains odd harmonics. In response to the strain

J. Lefebvre / Journal of Cereal Science 49 (2009) 262–271

the stress will be given by the general expression

sðtÞ ¼

K X

so;k cosðkux t þ 4k Þ with ðk ¼ 1; 3; 5; .Þ

(5)

k¼1

However, besides this expected distortion of the response, we observed that the amplitude of the stress signal decreased continuously as the number of the cycles increased. In order to adequately fit the stress signal one had to multiply the right hand member of Eq. (5) by a front factor, which was a power law tz of the time (z z 0.15). Finally, after the 12 h rest following the first oscillation train (ROS1) of the test, the response to the second oscillation train (ROS2) started with the same value of so as that reached at the end of the first train, and so continued to decrease according to the same power law in time. A few complementary experiments with different values of go showed that these findings had a general character, although of course the departure of the stress signal from the sine wave shape, and the magnitude of the decrease of its amplitude with time decreased with the value of go. We can conclude from ‘‘ROS sequence 2’’ experiments as follows: (i) Oscillations cause a progressive slow decrease of the stress amplitude so as the number of cycles increases, following a power law in time. (ii) This softening is an irreversible phenomenon. Thus, the effect of repeated oscillatory strain is cumulative. Is it limited to the flow contribution to the response, or does it concern the (visco)elastic contribution too? What is (are) the factor(s) governing the softening effect: strain amplitude, stress amplitude, time, or something else? Application of ‘‘ROS sequence 1’’ tests to 46.2% hydration Caphorn dough addressed these issues. The LMS steps, which in principle cause minimal perturbation, intercalated in ‘‘ROS sequence 1’’ experiments are intended to monitor the state of the system after each ROS step. These mechanical spectra always remained similar in shape to the initial one, characteristic of a network structure, whatever their rank was in the sequences and whatever the strain amplitudes were in the ROS steps, but they were shifted to lower moduli after each ROS step. Their analysis showed that the shift was not the consequence of the decrease of the sole viscous contribution to G0 and G00 , but that indeed the viscoelastic plateau GoN decreased, meaning the progressive, although limited, weakening of the network structure. Since in ‘‘ROS sequence 2’’ experiments the LMS2 spectra (recorded after 12 h rest) gave GoN values lower than those of the LMS1 ones, the effect of oscillatory shear on the plateau modulus is irreversible, as it is for dough viscosity. We found that the only way to obtain a coherent evolution for GoN, taking into account results of all of the ROS sequence 1 and ROS sequence 2 experiments, was to plot GoN against the ‘‘accumulated strain’’ (Pine et al., 2005) G ¼ 4Ngo after N cycles of amplitude go (Fig. 6a). This ‘‘accumulated strain’’ (the strain being taken as positive at each instant) is a measure of the total material deformation. In spite of large scatter of the data, Fig. 6 shows that GoN decreases linearly with log(G). The decrease is far from being spectacular (slope w 0.4), but it is steady and there is no evidence of a strain threshold: even the smallest strain would result in a weakening of the network. This explains for example why the LMS recorded on fresh dough samples do differ, very slightly but definitely, according to the direction (increasing or decreasing frequencies) of the frequency sweep. It could also account for the lack of a real linear viscoelastic region in the dynamic mode observed long ago in strain amplitude sweep experiments on doughs, even at the lowest accessible strain amplitude values (Hibberd and Parker, 1975; Smith et al., 1970),

a Viscoelastic plateau modulus GN° (103 Pa)

(4)

3.5

2.5

1.5

0.5 10-1

100

101

102

103

Accumulated strain

b

GN° (103 Pa)

gðtÞ ¼ go cosðux tÞ

269

3.5

2.5

1.5

0.5

10-1

100

101

Accumulated Hencky strain E Fig. 6. The cumulative effect of strain on the height of the viscoelastic plateau of dough. (a) The height of the viscoelastic plateau GoN, extracted from the LMS steps of all ROS sequence 1 and ROS sequence 2 tests applied to 46.2% hydration Caphorn dough, is plotted against the strain G accumulated up to the record of the corresponding LMS step (see text). Frequency of the imposed strain oscillations in ROS steps: 102 rad/s (filled circles, continuous line), and 103 rad/s (empty circles, interrupted line). Symbols: data. Lines: fits of GoN ¼ b  a log(G) (R2 ¼ 0.80). (b) Same data, with the accumulated strain G replaced by the corresponding Hencky value E (see text).

and also reported recently in large-amplitude oscillation studies (Lefebvre, 2006). In opposition to the above results pointing to irreversible shear effect, partially reversible shear softening was observed in the case of dough by different authors (Berland and Launay, 1995; Hibberd and Wallace, 1966; Smith et al., 1970) in the dynamic mode at fixed frequency (in the range w10–100 rad/s), and ascribed by them to thixotropy although no evidence was given that the effect concerns essentially the contribution of flow to the response signal. In their work on ‘‘jammed suspensions’’, Coussot et al. (2006) used the transient oscillations at the start of creep to monitor the elasticity of the systems as a function of the time of rest tw left between preshear and creep in the solid regime of the materials behaviour. The elastic modulus thus obtained increased with tw (G ln(tw)), showing that destructuring induced by the preshear step (at shear rates of the order of magnitude of 100 s1, and therefore in the liquid regime of the materials) was reversible, at least to some extent. Whereas in these studies, including those on dough, the effect of shear was found to be partially reversible in opposition to our observations, our results could perhaps be compared in some respects to those of Pine’s group on suspensions of macroscopic particles subjected to oscillatory shear (Gollub and Pine, 2006; Pine et al., 2005). These authors showed that, beyond a concentration threshold in the suspension, the non-Brownian particles followed non-reversible, irregular and apparently random trajectories when strain amplitude was larger than a concentration-dependent

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critical value. The mean square particle displacements after N cycles increased linearly with the accumulated strain G. The authors attributed the irreversible behaviour of the systems to the chaotic nature of the hydrodynamic interactions between particles. Our results thus seem to bear some loose connection with those of Pine et al., but it is impossible to draw a closer parallel, because of the complex and ill-defined structure of dough on physical grounds, and because the kind of irreversibility which is monitored is of a different nature. It is tempting to relate this aspect of dough rheological behaviour to starch granules, the spatial distribution of which within the matrix would be modified irreversibly under the effect of shear, with the result of ‘‘tearing up’’ the gluten matrix. However, one should refrain from hasty conclusion at least until having checked that gluten does not exhibit the same kind of characteristic by itself. Following very recently a different approach, Tanner et al. (2007, 2008a,b) investigated the effect of strain on dough response (in the time range <1000 s) to different deformation modes. They described the results using a Lodge-type model with a power law memory function, combined with a ‘‘damage function’’. In the case of finite-amplitude shear strain oscillations, the storage modulus G0 (go,u) measured at a given frequency u in response to the strain amplitude go was given simply by G0 (go,u) ¼ fGo0 (u), where Go0 (u) is the modulus of the undamaged material; the damage factor f was defined as f h (1  D) where D is the damage function (0  D  1), assumed to be a function of strain only (Tanner et al., 2008a). The concept of the damage function can be used to describe our results on the cumulative effect of strain on GoN in ‘‘ROS sequence’’ experiments. Fig. 6a shows that f is a linear function of log(G), independent of the frequency of the ROS steps. But the values of the parameters of this function are known within the factor (GoN)o only, since the value (GoN)o of GoN for the undamaged material is actually unknown; in effect, the plateau modulus at the start of the sequences was obtained as the result of the first LMS in the sequences, during which the sample is already submitted to repeated oscillations. In the papers of Tanner et al., deformations are expressed as Hencky strains; the Hencky strain 3H is related to shear strain g by (Tanner et al., 2008a):

3H

2 sffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 g2 g2 5 1 4 ¼ ln 1 þ þg 1þ 2 2 4

(6)

In Fig. 6b, the GoN data are plotted as a function of the Hencky strain values E obtained from G values using Eq. (6); E varied in the range 0.08–5.3. Despite the large scatter of the data, the shape of the GoN(log(E)) curve is quite similar to that of the f versus log(3H) curve Tanner et al. (2007) obtained in the 0.1  3H  w3 range (see their Fig. 3). Because our data do not extend below E ¼ 0.08, we cannot draw a closer parallel with the results of these authors, who studied the variation of f with log(3H) down to extremely low values of the Hencky strain. 4. Conclusion The work summarised in the present paper is a survey of some important aspects of dough nonlinear flow properties in shear and of shear-induced effects. It could not aim to be exhaustive, considering the complexity of the material and the practical limitations it imposes to rheological investigation. We think nevertheless that the results help to clarify a few issues, to point out remarkable features of dough behaviour, and to open the way to more thorough studies of these features. Dough viscosity displays a highly shear-thinning character with a power law exponent practically equal to 1; however, confirming our previous work (Lefebvre, 2006), the results do not give any

evidence for the existence of a yield stress or of a critical strain, but substantiate that of a Newtonian plateau at very small shear rate values. Doughs with different water contents, protein composition and technological characteristics show all the same type of flow behaviour, and a master curve for steady-state viscosity versus shear rate is obtained in reduced coordinates. Furthermore, the equilibrium recoverable compliance of the doughs seems to exhibit global similarity as well. The complexity of dough flow behaviour is actually due to the time-dependence of viscosity, a property we just pointed out previously (Lefebvre, 2006) but that we have studied in some depth in the present work. It seems to result from irreversible viscosity modification induced by shear. Shear-induced structural changes under constant stress cause flow to shift from a high viscosity steady-state regime to a low viscosity one; the behaviour is somewhat similar under constant shear rate. Shear-induced viscosity changes seem to be controlled by the mechanical energy absorbed by unit volume of dough. On the other hand, they appear to be irreversible, differing in this respect from classical thixotropic behaviour. In addition, shear causes also an irreversible progressive decrease of dough network viscoelastic plateau modulus, an effect which appears to be governed by the accumulated strain. It is likely that the effects of shear on flow behaviour and on viscoelastic behaviour are linked, as suggested in another context by Coussot et al. (2002, 2006). The irreversible character of these effects, which differentiates dough behaviour from that of model concentrated colloidal suspensions, would require further investigation, the more so as partial reversibility was observed in other studies on dough. Dough can be viewed as a matrix, the gluten highly viscoelastic hydrated network, filled with rigid particles, the starch granules. However, little is known about the distribution of the gluten, the starch and the water phases in the material, and about their interactions. Moreover, it has been shown that the minor components of flour, in particular water-soluble polysaccharides, have a noticeable effect on dough rheology (see for example Rouille´ et al., 2005). The main problem in understanding dough nonlinear rheology, and in particular its flow behaviour, would be in a first step to distinguish the respective contributions of the rheology of the matrix and of the presence of the filler to dough remarkable flow properties. A systematic comparison of gluten nonlinear rheological properties, a thorough investigation of which is still lacking, with those of dough would help to clarify this central question.

References Amemiya, J.I., Menjivar, J.A., 1992. Comparison of small and large deformation measurements to characterize the rheology of wheat flour doughs. Journal of Food Engineering 16, 91–108. Bagley, E.B., Chistianson, D.D., Martindale, J.A., 1988. Uniaxial compression of a hard wheat flour dough: data analysis using the upper convected Maxwell model. Journal of Texture Studies 19, 289–305. Bagley, E.B., Dintzis, F.R., Chrakrabarti, S., 1998. Experimental and conceptual problems in the rheological characterization of wheat flour doughs. Rheologica Acta 37, 556–565. Barro, F., Rooke, L., Be´ke´s, F., Gras, P., Tatham, A.S., Fido, R., Lazzeri, P.A., Shewry, P.R., Barcelo´, P., 1997. Transformation of wheat with high molecular weight subunit genes results in improved functional properties. Nature Biotechnology 15, 1295–1299. Berland, S., Launay, B., 1995. Shear softening and thixotropic properties of wheat flour doughs in dynamic testing at high shear strain. Rheologica Acta 34, 622–625. Bloksma, A.H., 1962. Slow creep of wheat flour doughs. Rheologica Acta 2, 217–230. Bloksma, A.H., Nieman, W., 1975. The effect of temperature on some rheological properties of wheat flour doughs. Journal of Texture Studies 6, 343–361. Bloksma, A.H., 1990a. Rheology of the breadmaking process. Cereal Foods World 35, 228–236. Bloksma, A.H., 1990b. Dough structure, dough rheology, and baking quality. Cereal Foods World 35, 237–244. Coussot, P., Nguyen, Q.D., Huynh, H.T., Bonn, D., 2002. Viscosity bifurcation in thixotropic, yielding fluids. Journal of Rheology 46, 573–589.

J. Lefebvre / Journal of Cereal Science 49 (2009) 262–271 Coussot, P., Tabuteau, H., Chateau, X., Tocquer, L., Ovarlez, G., 2006. Aging and solid or liquid behavior in pastes. Journal of Rheology 50, 975–994. Dobraszczyk, B.J., Morgenstern, M.P., 2003. Rheology and the breadmaking process. Journal of Cereal Science 38, 229–245. Dobraszczyk, B.J., Roberts, C.A., 1994. Strain hardening and dough gas cell–wall failure in biaxial extension. Journal of Cereal Science 20, 265–274. Dobraszczyk, B.J., Smewing, J., Albertini, M., Maesmans, G., Schofield, J.D., 2003. Extensional rheology and stability of gas cell walls in bread doughs at elevated temperatures in relation to breadmaking performance. Cereal Chemistry 80, 218–224. Dullaert, K., Mewis, J., 2006. A structural kinetics model for thixotropy. Journal of Non-Newtonian Fluid Mechanics 139, 21–30. Dus, S.J., Kokini, J.L., 1990. Prediction of the nonlinear viscoelastic properties of a hard wheat flour dough using the Bird–Carreau constitutive model. Journal of Rheology 34, 1069–1084. Gollub, J., Pine, D., 2006. Microscopic irreversibility and chaos. Physics Today August 2006, 8–9. Hibberd, G.E., Parker, N.S., 1975. Measurement of the fundamental rheological properties of wheat flour doughs. Cereal Chemistry 52, 1r–23r. Hibberd, G.E., Wallace, W.J., 1966. Dynamic viscoelastic behaviour of wheat flour doughs. Part 1: linear aspects. Rheologica Acta 5, 193–198. Kokelaar, J.J., van Vliet, T., Prins, A., 1996. Strain hardening properties and extensibility of flour and gluten doughs in relation to breadmaking performance. Journal of Cereal Science 24, 199–214. Launay, B., 1990. A simplified nonlinear model for describing the viscoelastic properties of wheat flour doughs at high shear strain. Cereal Chemistry 67, 25–31. Lawrence, G.J., MacRitchie, F., Wrigley, C.W., 1988. Dough and baking quality of wheat lines deficient for glutenin subunits controlled by Glu-A1, Glu-B1 and Glu-D1 loci. Journal of Cereal Science 7, 109–112. Lefebvre, J., Popineau, Y., Deshayes, G., Lavenant, L., 2000. Temperature-induced changes in the dynamic rheological behavior and size distribution of polymeric proteins for glutens from wheat near-isogenic lines differing in HMW glutenin subunit composition. Cereal Chemistry 77, 193–201. Lefebvre, J., Pruska-Kedzior, A., Kedzior, Z., Lavenant, L., 2003. A phenomenological analysis of wheat gluten viscoelastic response in retardation and in dynamic experiments over a large time scale. Journal of Cereal Science 38, 257–267. Lefebvre, J., Rousseau, C., Popineau, Y., 2004. Viscoelastic and flow behaviour of doughs from transgenic wheat lines differing in HMW glutenin subunits. In: Lafiandra, D., Masci, S., D’Ovidio, R. (Eds.), The Gluten Proteins. The Royal Society of Chemistry, Cambridge (UK).

271

Lefebvre, J., 2006. An outline of the non-linear viscoelastic behaviour of wheat flour dough in shear. Rheologica Acta 45, 525–538. Lindborg, K.M., Tra¨gårdh, C., Eliasson, A.-C., Dejmek, P., 1997. Time-resolved shear viscosity of wheat flour doughsdeffect of mixing, shear rate, and resting on the viscosity of doughs of different flours. Cereal Chemistry 74, 49–55. ˜ o, A., 1997. Oscillatory and simple Phan-Thien, N., Safari-Ardi, M., Morales-Patin shear flows of a flour–water dough: a constitutive equation. Rheologica Acta 36, 38–48. Phan-Thien, N., Safari-Ardi, M., 1998. Linear viscoelastic properties of flour–water doughs at different water concentrations. Journal of Non-Newtonian Fluid Mechanics 74, 137–150. Pine, D.J., Gollub, J.P., Brady, J.F., Leshansky, A.M., 2005. Chaos and threshold for irreversibility in sheared suspensions. Nature 438, 997–1000. Popineau, Y., Deshayes, G., Lefebvre, J., Fido, R., Tatham, A., Shewry, P.R., 2001. Prolamin aggregation, gluten viscoelasticity, and mixing properties of transgenic wheat lines expressing 1Ax and 1Dx high molecular weight glutenin subunit transgenes. Journal of Agricultural and Food Chemistry 49, 395–401. Rouille´, J., Della Valle, G., Lefebvre, J., Sliwinski, E., van Vliet, T., 2005. Shear and extensional properties of bread dough as affected by its minor components. Journal of Cereal Science 42, 45–57. Schweizer, T., 2007. Shear banding during nonlinear creep with a solution of monodisperse polystyrene. Rheologica Acta 46, 629–637. Smith, J.R., Smith, T.L., Tschoegl, N.W., 1970. Rheological properties of wheat flour doughs. III. Dynamic shear modulus and its dependence on amplitude, frequency, and dough composition. Rheologica Acta 9, 239–252. Tanner, R.I., Dai, S.-C., Qi, F., 2007. Bread dough rheology and recoil. 2. Recoil and relaxation. Journal of Non-Newtonian Fluid Mechanics 143, 107–119. Tanner, R.I., Qi, F., Dai, S.-C., 2008a. Bread dough rheology and recoil. 1. Rheology. Journal of Non-Newtonian Fluid Mechanics 148, 33–40. Tanner, R.I., Dai, S.-C., Qi, F., 2008b. Bread dough rheology in biaxial and step-shear deformations. Rheologica Acta 47, 739–749. Tschoegl, N.W., 1989. The Phenomenological Theory of Linear Viscoelastic Behavior – An Introduction. Springer Verlag, Berlin. Uhlherr, P.H.T., Guo, J., Tiu, C., Zhang, X.-M., Zhou, J.Z.-Q., Fang, T.-N., 2005. The shear-induced solid-liquid transition in yield stress materials with chemically different structures. Journal of Non-Newtonian Fluid Mechanics 125, 101–119. van Vliet, T., Janssen, A.M., Bloksma, A.H., Walstra, P., 1992. Srain hardening of dough as a requirement for gas retention. Journal of Texture Studies 23, 439–460.