Analytical solutions for squeeze flow of Bingham fluid with Navier slip condition

Squeeze flow between closely spaced parallel disks of a plastic material is considered for a Bingham fluid described by a bi-viscosity model with Navier slip condition. The flow field is divided into a Newtonian part with high viscous Newtonian fluid and a bi-viscosity part with yielded/unyielded fluids. The radial velocities and pressure gradients in the two parts are obtained, respectively. The slip velocity at the disk is proportional to the pressure gradient, which is proportional to r in the Newtonian part and is approximately proportional to large r in the bi-viscosity part. Furthermore, the explicit expressions of the pressure and the squeeze force are acquired through the approximately linear relationship between the pressure gradient and r in the bi-viscosity part. Also, distributions of the radial velocity and shear stress, and the effects of the slip coefficient, plastic viscosity and viscosity ratio on the radial velocity, pressure gradient, squeeze force and yield surface are discussed.