Lubrication flow of a generalized Casson fluid with pressure-dependent rheological parameters

In this paper we model the flow of a generalized Casson fluid in a channel of non uniform amplitude. We assume that the rheological parameters are given functions of the pressure and we suppose that the aspect ratio of the channel is small, so that we can apply the lubrication approximation. We formulate the mathematical problem writing the balance of the linear momentum of the unyielded phase in an integral form. At the leading order of the approximation and when the flow is driven by a given inlet discharge, the problem is formed by a system of two nonlinear differential equations for the pressure and for the yield surface. When the flow is driven by a given pressure drop the system becomes integro-differential. The solution of the mathematical problem provides the exact location of the yield surface and the velocity field within the channel.