# A viscous froth model adapted to wet foams

## TL;DR

This paper extends a viscous froth model to wet foams in Hele-Shaw cells, incorporating liquid content effects and analyzing how increased liquid fraction influences foam dynamics and stability.

## Contribution

The paper introduces a modified viscous froth model that accounts for liquid content via Plateau borders and provides numerical analysis of foam behavior at different velocities.

## Key findings

- Higher liquid fraction slows down foam movement.
- Increased liquid content distorts the spanning film.
- Fast driving velocities cause film detachment.

## Abstract

We describe the extension of a "viscous froth" model to the dynamics of a wet foam in a Hele-Shaw cell. The two-dimensional model includes the friction experienced by the soap films as they are dragged along the cell walls, while retaining accurate geometrical information. To explore the consequences of changing the liquid content in this situation, we consider a simple foam geometry known as a bubble lens: a bubble partially filling a narrow, straight channel with a single film spanning the gap between the bubble and the opposite wall. The triple vertices of this structure are decorated with Plateau borders whose area determines the liquid fraction of the foam. We derive new expressions to allow the pressure in the Plateau borders to be calculated, and determine numerically the range of driving velocities for which the system reaches a steady state. As the liquid fraction increases, the lens moves more slowly and the spanning film is more greatly distorted, reducing the range of stable driving velocities. For higher velocities, the spanning film moves so quickly that it leaves the bubble behind, a situation which must be avoided in any particular application.