Exact analytic solutions of the lubrication equations for squeeze-flow of a biviscous fluid between two parallel disks

摘要

Based on lubrication approximation, the squeezing flow of biviscous fluids between two parallel disks with partial slip boundary condition was investigated. In addition to the solution of the kinematics in the bi-viscosity region leading to a cubic equation of the yield surface, the full explicit expressions of radial pressure gradient, pressure and squeeze force are given in the exact relationships. According to three dimensionless numbers, different behaviors are covered including Bingham fluid as a limiting case of bi-viscosity model. Besides, a critical force separating the Newtonian and biviscous regions of the flow is provided. However, for a flow of a Bingham fluid without wall slip, the expression of the applied force may be expressed or not according to the yield stress. This depends on the ratio value of the characteristic time of the fluid to the time scale of observation if it is very lower or higher than unity.