Geometric transition in friction for flow over a bubble mattress

TL;DR

This paper models how bubble geometry affects flow friction, revealing a transition from reduced to increased friction depending on bubble protrusion angle, supported by analytical and computational results.

Contribution

It introduces an analytical model predicting the geometric transition in friction for flow over bubbles, aligning with numerical findings.

Findings

Friction decreases with shear-free bubble surfaces in certain conditions.

A critical bubble protrusion angle causes a transition from reduced to increased friction.

Model accurately reproduces numerical results on bubble-induced friction changes.

Abstract

Laminar flow over a bubble mattress is expected to experience a significant reduction in friction since the individual surfaces of the bubbles are shear-free. However, if the bubbles are sufficiently curved, their protrusion into the fluid and along the flow direction can lead to an increase in friction as was recently demonstrated experimentally and computationally. We provide in this paper a simple model for this result. We consider a shear flow at low Reynolds number past a two-dimensional array of bubbles, and calculate analytically the effective slip length of the surface as function of the bubble geometry in the dilute limit. Our model is able to reproduce quantitatively the relationship between effective friction and bubble geometry obtained in numerical computations, and in particular: (a) The asymmetry in friction between convex and concave bubbles, and (b) the existence of a geometric transition from reduced to enhanced friction at a critical bubble protrusion angle.