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화학공학의 이론과 응용 제8권 제1호 2002년

Theories and Applications of Chem. Eng., 2002, Vol. 8, No. 1

안경현, 심훈구, 김승하, 이승종

서울대학교 응용화학부

Large amplitude oscillatory shear behavior of complex fluids investigated by a network model

Kyung Hyun AHN, Hoon Goo SIM, Seung Ha KIM, Seung Jong LEE

School of Chemical Engineering, Seoul National University

Introduction

The microstructure of a complex fluid, which forms the microstructure depending on the deformation history, is reflected in its rheological properties (Larson, 1999). Among the many rheological measurements, a dynamic test or small amplitude oscillatory shear (SAOS) test has been most widely used because it is sensitive to the microstructure, easy to use, and has sound mathematical backgrounds (Macosko, 1994). In many cases, the dynamic test is sensitive enough to distinguish structural difference even in nanometer scale or any subtle structural change evolved during the processing.

However, as the SAOS is based on the linear viscoelasticity theory, its usability is limited only to a very small strain enough to guarantee the linear viscoelasticity. To confirm whether the measurement is within the linear range, a strain sweep test is normally carried out. As the strain increases, the rheological properties stay constant up to a critical strain, after which they deviate. The region before the critical strain is called linear, and the region after the critical strain is called nonlinear. The dynamic test in the nonlinear region is often called a large amplitude oscillatory shear (LAOS) test, because the strain amplitude is not small any more. The LAOS behavior has also been studied in depth but much less than the SAOS because nonlinear phenomenon is much more difficult to analyze (Giacomin and Dealy, 1993). For example, the storage or loss moduli in nonlinear region lose their mathematical background or physical meaning defined in the linear region, and cannot be treated as such. In the nonlinear region, due to the higher harmonic contributions to the stress tensor, the linear viscoelasticity theory does not hold any more, and more sophisticated analysis like a Fourier transformation method needs to be used. Very recently, the LAOS behavior of complex fluids is getting investigated with the concept of Fourier transformation (Wilhelm et al., 2000). Even though the modulus measured in the nonlinear region as most commercial rheometers provide loses their physical meaning as an elastic or loss modulus, it does not necessarily mean that they are meaningless or treated as such. More precise analysis will require the Fourier transformation analysis, however in this paper, we first investigate the LAOS behavior in a less precise way, neglecting the higher harmonic contributions as most rheometers do. This still provides a lot of useful information on the microstructure of complex fluids.

Recently Hyun et al. summarized the phenomenological observations of the LAOS behavior of complex fluids, pointing out that the LAOS behavior of complex fluids can be classified by four types: type I, strain thinning (G, G□ decreasing); type II, strain thickening (G, G□ increasing); type III, weak strain overshoot (G decreasing, G□ increasing followed by decreasing); type IV, strong strain overshoot (G, G□ increasing followed by decreasing).

The purpose of this paper is to investigate the mechanism of such complex LAOS behaviors. For this purpose, we developed a network model. Network models have long been used in many ways because they are easy to implement. Even though there is a family of network models, they share a common feature that the distribution of networks is determined by their creation and loss rates. The main difference between the models is the form of the creation and loss rates. As little is known about the creation and loss rates, and the network itself can be phantom in a sense, most network models assume specific functional forms for the creation and loss rates. A network model can therefore be regarded as a phenomenological model. We will briefly review the theoretical aspects first.

Results

As there are two model parameters, we have swept the parameters on a two-dimensional plane. Even though the large values of a and b do hardly have any physical significance, the circle on the figure does not mean any restriction, but is shown here just for convenience to differentiate some regions, which will later be used as a guide for classification of complex fluids. By sweeping the parameter on the two-dimensional plane, we have found that the pattern of LAOS behavior can be differentiated by five groups. Four out of the five shows the same LAOS behavior as observed in the experiments, and one looks unphysical. Recently, Hyun et al. pointed out that there can be four types of LAOS behavior depending on the interactions between the microstructures, and suggested that the LAOS behavior can be used as a tool for classifying the complex fluids.

In summary, the model predicts the four types of LAOS behavior: type A; strain thinning (G' and G" decreasing), type B; weak strain overshoot (G' decreasing, G" increasing followed by decreasing), type C; strong strain overshoot (G' and G" increasing followed by decreasing), type D; strain hardening (G' and G" increasing). It is noteworthy that the types of LAOS behavior predicted by this model exactly coincides with the experimental observation of Hyun et al. Even though there may exist other types or any variations, these 4 types may be regarded as representative types of LAOS behavior of complex fluids. If a chemical reaction proceeds during the measurement or if the material system is too much complex like an immiscible solution blend of biopolymers with diverse interactions, the LAOS behavior may be more complex, but the results might be a variation or a combination of the fundamental types.

Finally some comments on the theoretical works reporting the complex LAOS behavior will be given. Yziquel et al. proposed a structural network model based on a modified upper convected Jeffreys model with a single relaxation time and a kinetic equation to describe the flow-induced microstructure evolution. By comparing the model prediction with the experimental data of coating color suspensions and fumed silica suspensions, they showed that the model can predict the type B behavior, that is, only G" shows an overshoot followed by a strain thinning. Sollich showed that the soft glassy rheology model, which was developed to describe the rheological properties of soft materials such as foams, emulsions, pastes, and slurries, also predicts the type B behavior. This is in qualitative agreement with the experimental data of dense emulsions and colloidal glasses, for which the model was originally developed. However, there is little explanation for the cause of this overshoot. Simulation of electrorheological (ER) suspensions also predicts the type B behavior as well as type A, which is qualitatively in accordance with the experimental data of ER suspensions of acidic alumina particles in poly(dimethylsiloxane) under large electric field. They explained that the strain overshoot of G" occurs because of viscous dissipation due to the slight rearrangement of unstable clusters under shear, and the decrease at large strain is associated with large scale structural rearrangements. By generating a three dimensional networked particle gels with a Brownian dynamics simulation of soft spherical particles, Whittle and Dickinson predicted the strain hardening behavior. Even though they did not separate the elastic and viscous contributions, the shear modulus shows the strain hardening behavior. The model suspension qualitatively explains the behavior of an enzymatically cross-linked emulsion gels of milk protein. All the models partially predict some types of LAOS behavior, especially type A and type B. It is

Acknowledgement

The authors acknowledge the support from the Korea Science and Engineering Foundation through the Applied Rheology Center at Korea University in Korea.

References

Larson, R.G., The structure and rheology of complex fluids, Oxford university press, New York, 1999.

Macosko, C.W., Rheology: principles, measurements, and applications, VCH, New York, 1994.

Giacomin, A.J. and Dealy, J.M., Large-amplitude oscillatory shear in A.A. Collyer(Ed.), Techniques in rheological measurement, Chapman and Hall, London, 1993, Chapter 4.

Wilhelm, M., Reinheimer, P., Ortseifer, M., Neidh□fer, T., and Spiess, H., The crossover between linear and non-linear mechanical behavior in polymer solutions as detected by Fourier-transform rheology, Rheol.Acta, 39 , 241 (2000).

Hyun, K., Kim, S.H., Ahn, K.H., and Lee, S.J., Rheological properties of some complex fluids: A guideline for classification, submitted to the J.Non-Newtonian Fluid Mech. (2002).

Yziquel, E., Carreau, P.J., Moan, M., and Tanguy, P.A., Rheological modeling of concentrated colloidal suspensions, J.Non-Newtonian Fluid Mech., 86, 133 (1999).

Sollich, P., Rheological constitutive equation for a model of soft glassy materials, Phys.Rev.E, 58, 738 (1998).

Whittle, M. and Dickinson, E., Large deformation rheological behavior of a model particle gel, J.Chem.Soc., Faraday Trans., 94, 2453 (1998).

Fig. 1. Classification of complex fluids according to the model parameters.

Fig. 2. Various types of LAOS behavior: (a) strain thinning (b) strain thickening (c) weak strain overshoot (d) strong strain overshoot.

화학공학의 이론과 응용 제8권 제1호 2002년