Comparison of Lubrication Theory and Stokes Flow in Corner Geometries with Flow Separation

TL;DR

This paper compares lubrication theory's Reynolds equation with Stokes flow in corner geometries, analyzing flow recirculation and the impact of surface gradients on model accuracy in various geometries.

Contribution

It investigates the sensitivity of the Reynolds equation to surface gradients and compares flow recirculation phenomena between lubrication theory and Stokes flow in corner geometries.

Findings

Error in pressure drop increases with surface gradients and expansion ratio.

Flow recirculation occurs in corner geometries in Stokes solutions.

Occluding corner recirculation regions does not affect bulk flow.

Abstract

The Reynolds equation from lubrication theory and the Stokes equations for zero Reynolds number flows are distinct models for an incompressible fluid with negligible inertia. Here we investigate the sensitivity of the Reynolds equation to large surface gradients, and explore flow recirculation in corner geometries in comparison to the Stokes equation. We compare the solutions for the Reynolds and Stokes equations in the backward facing step (BFS), the regularized BFS, and the lid-driven triangular cavity. For the BFS variations listed above, we compute the error in terms of the average pressure drop through the channel and show how the error increases with increasing expansion ratio and with increasing magnitude of surface gradients. We further investigate the phenomenology of corner flow recirculation that arises in the Stokes solutions. In particular, we observe that occluding the corner separated region in the Stokes solution to the BFS does not disrupt the bulk flow characteristics.