Viscoelastic response of electrorheological fluids. I. Frequency dependence

Abstract

We calculate the linear frequency‐dependent modulus of a model electrorheological (ER) fluid at low and intermediate concentrations, assuming that particle strings are the dominant structures. At low concentrations hydrodynamic interactions along a single string act to reduce the dissipation of modes with low wave number (just as in the case of random‐coil polymers). At higher concentrations we expect hydrodynamic screening to be effective. This results in a dissipative part to the modulus. G ‘(ω) which has a broad plateau over a frequency bandwidth (L/a)2, where L is the characteristic string length and a of the order of the particle size. By contrast, the magnitude of G ‘(ω) is limited by the fraction of incomplete or broken strings. The real part of the dynamic modulus G ’(ω) is dominated by strings which span the electrodes, and shows very little structure with frequency when the majority of strings are complete.