With respect to the MR fluid devices operating in squeeze flow mode,how the governing equation of shear stress in the Bingham plastic model can be generalized to the bi viscous relationship?
I am not sure that you question is correct! The biviscosity model is used as an approximation to the strict Bingham model. Thus the effective viscosity when the shear stress is less than the yield stress is taken to be extremely large, rather than as being infinite. There is also the Papanastasious model. Both have the advantage that computations may be undertaken without having to determine the yield surface. That said, I am well aware that there are much more knowledgeable people out there than I am.
Thank you very much sir for your kind information @D. Andrew S. Rees and i have a question that how bi-viscosity model will be useful in the application of magneto-rheological fluids .