Time-dependent and nonlinear effects in electrorheological fluids

An integral equation method is used to calculate particle–particle forces in electrorheological fluids. The method focuses on the gap region between particles where large electric-field concentrations occur. Effects due to time-dependent excitation and nonlinear (field-dependent) fluid conductivity are analyzed. It is found that the response to step-function changes in applied field closely follows a simple form that can be derived from the dipole approximation. Qualitatively different stress-vs-time curves are obtained for large dielectric mismatch (e.g., barium titanate/dodecane) relative to large conductivity mismatch (zeolite/silicone oil). In fluids where the conductivity is strongly field dependent, it is found that particle–particle forces scale linearly with applied field $E_0$ at large fields. Likewise, the shear yield stress scales as $E_0^{\text{3/2}}.$