Axisymmetric squeeze flow of a Casson medium.

• The axisymmetric squeeze flow of a viscoplastic Casson material is studied. • The no-slip and threshold stick-slip boundary conditions are considered. • We develop an asymptotic solution. • Numerical solution is done by Accelerated proximal gradient and Augmented Lagrangian methods. We develop an asymptotic solution for the axisymmetric squeeze flow of a viscoplastic Casson medium following the asymptotic technique suggested earlier by Balmforth and Craster (1999) and Frigaard and Ryan (2004). The no-slip and slip yield boundary conditions at the wall are considered. Depending on the ratio of two dimensionless parameters partial slip (stick-slip) or full slip at the wall (slip) are possible. We confirm numerically obtained solution, using Accelerated proximal gradient and Augmented Lagrangian methods. [ABSTRACT FROM AUTHOR]