^{1}, Nhan Phan-Thien

^{1,a)}and Boo Cheong Khoo

^{1}

### Abstract

The short-term and long-term irreversible behaviors of suspensions of rigid particles in oscillatory shear flow are studied by measuring the evolution of complex viscosity in time and applying of nonlinear analysis of the responded strain signal under the controlled-stress mode, and complemented by optical measurements on the particle motion. The short-term transition time for the system to reach a quasisteady state is an approximately bell-shaped function of the amplitude of the strain response, thus showing a critical strain amplitude accounting for the peak transition time. The short-term behavior is caused by the particle self-organization due to collisions between particles. At longer time scales, the complex viscosity of the suspension increases when probed by forces that elicit small strain amplitudes and decreases when stresses that result in large strain amplitudes are applied. It is proposed that the long-term behavior for stresses eliciting small strain amplitude is induced by the shear-induced diffusion of particles which self-organize into a crystal-like microstructure that can be easily annulled in oscillatory flow with large strain amplitude, while for stresses causing large strain amplitude the dominant microstructure is formed immediately via the oscillation.

This work is supported by The Agency for Science, Technology and Research (A*STAR) through Grant No. 102 164 0147. The support is gratefully acknowledged.

I. INTRODUCTION

II. EXPERIMENT

A. Materials

B. Rheological experiments

C. Optical experiments

III. RESULTS

A. Nonlinear behavior in oscillatory shear flows

B. Short-term rheology in time-sweep oscillatory shear experiments

C. Long-term rheology in time-sweep oscillatory shear flows

D. Optical measurements in time-sweep oscillatory shear flows

IV. DISCUSSION

A. Nonlinear behavior in oscillatory shear flows

B. Short-term self-organization of microstructure

C. Long-term self-organization of microstructure

V. CONCLUSIONS

## Figures

(a) Size distribution of the glass spheres used in the experiment. The number distributions are normalized by the peak value; (b) viscosity as a function of steady shear rate for suspensions of various volume fractions of glass particles; (c) the magnitude of complex viscosity as a function of strain amplitude for suspensions with various volume fractions in stress-amplitude-sweep oscillatory shear flow at the frequency of 1 Hz; the stress-amplitude-sweep curve for 50% suspension after long-term oscillation (t = 10 000 s) in time-sweep oscillatory shear flow with stress amplitude of 0.9 Pa (the responded strain amplitude at 200 s is 0.05) is included. The temperature is 25 °C. A cone-plate geometry with diameter of 35 mm was adopted.

(a) Size distribution of the glass spheres used in the experiment. The number distributions are normalized by the peak value; (b) viscosity as a function of steady shear rate for suspensions of various volume fractions of glass particles; (c) the magnitude of complex viscosity as a function of strain amplitude for suspensions with various volume fractions in stress-amplitude-sweep oscillatory shear flow at the frequency of 1 Hz; the stress-amplitude-sweep curve for 50% suspension after long-term oscillation (t = 10 000 s) in time-sweep oscillatory shear flow with stress amplitude of 0.9 Pa (the responded strain amplitude at 200 s is 0.05) is included. The temperature is 25 °C. A cone-plate geometry with diameter of 35 mm was adopted.

(a) Normalized Lissajous–Bowditch curves as and for suspensions of volume fraction of 50%; (b) normalized Lissajous–Bowditch curves for 50% suspension after long-term oscillation (t = 10 000 s) in time-sweep oscillatory shear flow with ; (c) dependence of the magnitude of the third and fifth harmonic overtones on with suspensions of volume fractions of 40% and 50% (t = 200 s); the curve for suspension of 50% after long-term oscillation (t = 10 000 s) in time-sweep oscillatory shear flow with is included.

(a) Normalized Lissajous–Bowditch curves as and for suspensions of volume fraction of 50%; (b) normalized Lissajous–Bowditch curves for 50% suspension after long-term oscillation (t = 10 000 s) in time-sweep oscillatory shear flow with ; (c) dependence of the magnitude of the third and fifth harmonic overtones on with suspensions of volume fractions of 40% and 50% (t = 200 s); the curve for suspension of 50% after long-term oscillation (t = 10 000 s) in time-sweep oscillatory shear flow with is included.

Dependence of the short-term transition behavior of on for suspensions with volume fractions of (a) 25%, (b) 40%, and (c) 50% in the time-sweep oscillatory shear flow.

Dependence of the short-term transition behavior of on for suspensions with volume fractions of (a) 25%, (b) 40%, and (c) 50% in the time-sweep oscillatory shear flow.

Dependence of the short-term transition time, , on for suspensions with volume fractions of 25%, 40%, and 50%. The error bars indicate the uncertainty of the determination of the transition time from the complex viscosity curve in Fig. 3 when it reaches the quasisteady state.

Dependence of the short-term transition time, , on for suspensions with volume fractions of 25%, 40%, and 50%. The error bars indicate the uncertainty of the determination of the transition time from the complex viscosity curve in Fig. 3 when it reaches the quasisteady state.

(a) Dependence of the long-term evolution of on in the time-sweep oscillatory shear experiment for suspension with volume fraction of 50% with from small to large; (b) evolution of with and (medium and large strain amplitude).

(a) Dependence of the long-term evolution of on in the time-sweep oscillatory shear experiment for suspension with volume fraction of 50% with from small to large; (b) evolution of with and (medium and large strain amplitude).

Evolution of in the time-sweep oscillatory shear flow with for suspensions with volume fractions of 40% and 50%, respectively.

Evolution of in the time-sweep oscillatory shear flow with for suspensions with volume fractions of 40% and 50%, respectively.

Images of three tracer particles at (a) 0 s and (b) 4861 s in time-sweep oscillatory shear flow with for suspension with volume fraction of 50%.

Images of three tracer particles at (a) 0 s and (b) 4861 s in time-sweep oscillatory shear flow with for suspension with volume fraction of 50%.

Displacement of particles along flow (x) and vorticity (z) directions in time-sweep long-term oscillatory shear flows with (a) and (b) , for suspension with volume fraction of 50%; (c) particle diffusivity as a function of with error bars indicating the variation of the result between tracing three particles and tracing six particles in a single test.

Displacement of particles along flow (x) and vorticity (z) directions in time-sweep long-term oscillatory shear flows with (a) and (b) , for suspension with volume fraction of 50%; (c) particle diffusivity as a function of with error bars indicating the variation of the result between tracing three particles and tracing six particles in a single test.

Dependence of the normalized (a) third order elastic Chebyshev coefficient and (b) third order viscous Chebyshev coefficient on in strain decomposition method for suspension of volume fraction of 50% (t = 200 s), and for the 50% suspension after long-term oscillation in time-sweep oscillatory shear flow with (t = 10 000 s).

Dependence of the normalized (a) third order elastic Chebyshev coefficient and (b) third order viscous Chebyshev coefficient on in strain decomposition method for suspension of volume fraction of 50% (t = 200 s), and for the 50% suspension after long-term oscillation in time-sweep oscillatory shear flow with (t = 10 000 s).

Evolution of the positions of particles A and B relative to particle C in time-sweep oscillatory shear flow for suspension volume fraction of 50%, with (a) and (b) . The solid lines refer to the evolution of at the corresponding .

Evolution of the positions of particles A and B relative to particle C in time-sweep oscillatory shear flow for suspension volume fraction of 50%, with (a) and (b) . The solid lines refer to the evolution of at the corresponding .

## Tables

The critical strain amplitude accounts for peak transition time with suspensions of different volume fractions from the experiment of this study and the work of Corte et al. (2008) .

The critical strain amplitude accounts for peak transition time with suspensions of different volume fractions from the experiment of this study and the work of Corte et al. (2008) .

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