Two-dimensional flow of foam around an obstacle: force measurements

TL;DR

This study investigates the forces exerted by a two-dimensional foam flow around an obstacle, analyzing how parameters like flow rate, bubble size, and obstacle shape influence drag, revealing power-law dependencies and the roles of elastic and viscous contributions.

Contribution

It provides systematic measurements of foam drag around an obstacle, separating elastic and viscous effects, and quantifies how various parameters affect the drag in a controlled experimental setup.

Findings

Drag increases with flow rate and obstacle size.

Drag decreases with bubble size.

Drag exhibits power-law dependence on viscosity and flow rate.

Abstract

A Stokes experiment for foams is proposed. It consists in a two-dimensional flow of a foam, confined between a water subphase and a top plate, around a fixed circular obstacle. We present systematic measurements of the drag exerted by the flowing foam on the obstacle, \emph{versus} various separately controlled parameters: flow rate, bubble volume, bulk viscosity, obstacle size, shape and boundary conditions. We separate the drag into two contributions, an elastic one (yield drag) at vanishing flow rate, and a fluid one (viscous coefficient) increasing with flow rate. We quantify the influence of each control parameter on the drag. The results exhibit in particular a power-law dependence of the drag as a function of the bulk viscosity and the flow rate with two different exponents. Moreover, we show that the drag decreases with bubble size, and increases proportionally to the obstacle size. We quantify the effect of shape through a dimensioned drag coefficient, and we show that the effect of boundary conditions is small.