On the viscoplastic squeeze flow between two identical infinite circular cylinders

TL;DR

This paper investigates the flow behavior and lubrication forces between two infinite cylinders in a Bingham viscoplastic fluid, highlighting the importance of macroscopic flow effects on lubrication predictions.

Contribution

It demonstrates that lubrication pressure predictions require the surrounding flow to be yielded, impacting sub-grid-scale modeling in viscoplastic suspension simulations.

Findings

Macroscopic flow significantly influences lubrication pressure.

Lubrication solutions are valid only when the matrix is yielded.

Results inform better modeling of particulate suspensions in viscoplastic fluids.

Abstract

Direct numerical simulations of closely interacting infinite circular cylinders in a Bingham fluid are presented, and results compared to asymptotic solutions based on lubrication theory in the gap. Unlike for a Newtonian fluid, the macroscopic flow outside of the gap between the cylinders is shown to have a large effect on the pressure profile within the gap and the resulting lubrication force on the cylinders. The presented results indicate that the asymptotic lubrication solution can be used to predict the lubrication pressure only if the surrounding viscoplastic matrix is yielded by a macroscopic flow. This has implications for the use of sub-grid-scale lubrication models in simulations of non-colloidal particulate suspensions in viscoplastic fluids.