Asymptotic Solutions of the Planar Squeeze Flow of a Herschel-Bulkley Fluid

Abstract

In this study, we present the analysis of the squeeze flow of a Herschel-Bulkley fluid between parallel plates that are approaching each other with a constant squeeze motion. The classical lubrication analysis predicts the existence of a central unyielded zone bracketed between near-wall regions. This leads to the well-known squeeze flow paradox for viscoplastic fluids. Since the kinematic arguments show that there must be a finite velocity gradient even in the unyielded zone, thereby precluding the existence of such regions. This paradox may, however, be resolved within the framework of a matched asymptotic expansions approach where one postulates separate expansions within the yielded and apparently unyielded (plastic) zones. Based on the above technique, we circumvent the paradox, and develop complete asymptotic solutions for the squeeze flow of a Herschel-Bulkley fluid. We derive expressions for the velocity, pressure and squeeze force. The effects of the yield threshold on the pseudo-yield surface that separates the sheared and plastic zones, and squeeze force for different values of non-dimensional yield stress have been investigated. © Published under licence by IOP Publishing Ltd.