ИСТИНА

We develop an asymptotic solution for the axisymmetric 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).The asymptotic solution has the following structure. First, close to the discs there will exist a yielded region, which is a shear flow. Second, in the region surrounding the central plane there is a pseudo-plug region in which extensional strain rates are present. The yield criterion is reached in the pseudo-plug flow zone and exceeded in the shear flow zone. These solutions are joined at the position of the pseudo-yield surface. The obtained analytical expression for the squeeze force is in a good agreement with the previous numerical results of Smyrnaios and Tsamopoulos (2001) and Matsoukas and Mitsoulis (2003). The axisymmetric squeeze flow of a Bingham fluid with slip yield boundary condition at the wall is considered. We provide aasymptotic solution for this type of flow. Depending on the ratio of two dimensionless parameters partial slip (stick-slip) or full slip at the wall (slip) are possible