Theory of nonlinear ac susceptibilities of dynamic electrorheological fluids under a dc electric field

By using a perturbation approach, we theoretically investigate nonlinear ac susceptibilities of dynamic electrorheological fluids under a dc electric field. We consider the effect of a finite volume fraction. It is shown that the dynamic effect arising from a shear flow plays an important role in the ac responses. Meanwhile, the effect of a finite volume fraction offers a correction. The collective relaxation time is also derived by using our recently-established dielectric dispersion spectral representation, and it is shown to generally increase with the volume fraction of particles. Some theoretical results are compared favorably with the experimental observations by others.