# Liquid Flow through Aqueous Foams: The Node-Dominated Foam Drainage Equation

## Overview

• [1] Koehler, S., Hilgenfeldt, S., & Stone, H. Physical Review Letters. 82, 21. 4232-4235 (1999).
• Keywords: Foam, Drainage, Plateau Border, Tetrakaidecahedron (Kelvin Cell)

## Summary

Koehler, Hilgenfeldt, and Stone write about fluid flow through the network of channels in a soap foam. The article presents an existing theory, a new theory, and experimental evidence supporting their new theory.

Figure 1 from [1]

The first hurdle the researchers crossed was figuring out how to quantify such a complex flow. They decided to look at the bulk flow driven by gravity rather than attempt to observed the flow in any one channel.

The experimenters were able to change the bubble size and the amount of fluid added to the top of the foam tube. They recorded two velocities using fluorescing markers.

Old Theory: Equation 6 "rigid channel walls" $\nu_f=(V_0^{rigid}V_s)^{1/2}$, $V_0^{rigid}=\frac{\delta_a\rho gL^2}{3\delta_\epsilon\delta_\mu \mu}$

• the exponent of 1/2 is what the experimental data disagree with
Figure 3 from [1]

New Theory: "channel-slip theory" $\nu_f=((V_0^{slip})^2V_s)^{1/3}$, $V_0^{slip}=\frac{2\delta_a\rho gL^2}{\mu\delta_\epsilon^{1/2}I}$

• I is dimensionless, viscous forces in nodes

## Soft Matter Details

Experimental Methods:

Testing that the theory is robust

Deciding which term dominates in equation 4

Dimensional analysis equation 7

Foam- further applications?