Squeeze flow of a viscoplastic Bingham medium: an asymptotic solution

We obtain an asymptotic solution for the 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 predict a plug, but really it is weakly yielded at higher order.