Viscoplastic fluids in 2D plane squeeze flow: A matched asymptotics analysis

Abstract

A matched asymptotic expansions approach is used to determine the flow behaviour of Casson and Herschel�Bulkley fluids between two parallel plates that are approaching each other with a constant velocity. The present study is based on the earlier work of Muravleva (2015), who has analyzed the squeeze flow of a Bingham fluid using the method of matched asymptotic expansions. A naive application of classical lubrication theory leads to a kinematic inconsistency in the predicted plug region - the well known �squeeze flow paradox� for a viscoplastic fluid. The objective of this work is to determine a consistent solution for the aforementioned constitutive equations. Based on the technique of matched asymptotic expansions, the solution is formulated in terms of separate expansions in the regions adjacent to the two plates where the shear stress is dominant, and a central pseudo-plug (plastic) region where the normal stresses become comparable to the shear stress; the two regions being separated by a pseudo-yield surface. In this manner, a complete asymptotic solution is developed for the squeeze flow of both Casson and Herschel�Bulkley fluid models. Using this solution, we derive expressions for the velocity, pressure and stress fields, and the squeeze force acting to retard the plates. The effect of the yield threshold on the pseudo-yield surface that separates the sheared and plastic zones, pressure distribution and squeeze force is investigated. � 2018 Elsevier B.V.