Two-dimensional flows of foam: drag exerted on circular obstacles and dissipation

TL;DR

This study investigates the drag forces and dissipation in a two-dimensional foam flow around a circular obstacle, revealing how various parameters influence elastic and viscous contributions to drag and dissipation.

Contribution

It provides systematic measurements of foam drag and dissipation, quantifies parameter influences, and distinguishes elastic and viscous contributions in a controlled 2D flow experiment.

Findings

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

Drag decreases with bubble size and increases with obstacle size.

Pressure gradient shows no dependence on obstacle presence, varies with flow parameters.

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, solution viscosity, obstacle size 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 solution viscosity and the flow rate with two different exponents. Moreover, we show that the drag decreases with bubble size, increases with obstacle size, and that the effect of boundary conditions is small. Measurements of the streamwise pressure gradient, associated to the dissipation along the flow of foam, are also presented: they show no dependence on the presence of an obstacle, and pressure gradient depends on flow rate, bubble volume and solution viscosity with three independent power laws.