Piecewise linear model for field-responsive fluids

The Frohlich-Kennelly model provides a constitutive law for saturation that is field dependent and has been widely used for studying nonlinear properties for a variety of electric and magnetic applications. Under the Frohlich-Kennelly model, saturation begins to occupy the entire conducting domain even at low-moderate applied fields, in this paper, we first present a new nonlinear constitutive law for field-responsive fluids that depends on the local fields and allows regions where the fields have not reached a critical value to remain unsaturated. We then study numerically the nonlinear saturated model and compare the results to the Frohlich-Kennelly model and experiments performed at the Lord Corporation, Cary, NC.