Squeeze plane flow of viscoplastic Bingham material

We develop an asymptotic solution for the plane squeeze flow of a viscoplastic medium. The standard lubrication-style expansions of the problem predict plug speed which varies slowly in the principal flow direction. This variation implies that the plug region cannot be truly unyielded. Our solution shows that this region is a pseudo-plug region in which the leading order equation predicts a plug, but really it is weakly yielded at higher order. We follow the asymptotic technique suggested earlier by Balmforth and Craster (1999) and Frigaard and Ryan (2004). We also provide comparison between analytical solution and numerical computations using the augmented Lagrangian method. The results of computations show presence of unyielded regions near the two stagnation points of flow close to centers of plates (that was found earlier by many researchers) and new additional unyielded regions at the outer edge of the material (both for short and long plates). The obtained analytical expression for the squeeze force is in a good agreement with the numerical results and previous results of Mitsoulis and Matsoukas (2003). (C) 2015 Elsevier B.V. All rights reserved.