Dissipative flows of 2D foams

TL;DR

This paper investigates the flow behavior of 2D foams with a large bubble, combining numerical simulations, analytical models, and experiments to understand regimes of plug flow and large bubble migration.

Contribution

It introduces a model for simulating 2D foam flows with a large bubble and compares numerical, analytical, and experimental results to characterize flow regimes.

Findings

At low flux, foam exhibits plug flow.

Above a threshold, the large bubble migrates faster than the mean flow.

Numerical and analytical predictions agree with experimental data.

Abstract

We analyze the flow of a liquid foam between two plates separated by a gap of the order of the bubble size (2D foam). We concentrate on the salient features of the flow that are induced by the presence, in an otherwise monodisperse foam, of a single large bubble whose size is one order of magnitude larger than the average size. We describe a model suited for numerical simulations of flows of 2D foams made up of a large number of bubbles. The numerical results are successfully compared to analytical predictions based on scaling arguments and on continuum medium approximations. When the foam is pushed inside the cell at a controlled rate, two basically different regimes occur: a plug flow is observed at low flux whereas, above a threshold, the large bubble migrates faster than the mean flow. The detailed characterization of the relative velocity of the large bubble is the essential aim of the present paper. The relative velocity values, predicted both from numerical and from analytical calculations that are discussed here in great detail, are found to be in fair agreement with experimental results.