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.
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" <math>\nu_f=(V_0^{rigid}V_s)^{1/2}</math>, <math>V_0^{rigid}=\frac{\delta_a\rho gL^2}{3\delta_\epsilon\delta_\mu \mu}</math>
- the exponent of 1/2 is what the experimental data disagree with
New Theory: "channel-slip theory" <math>\nu_f=((V_0^{slip})^2V_s)^{1/3}</math>, <math>V_0^{slip}=\frac{2\delta_a\rho gL^2}{\mu\delta_\epsilon^{1/2}I}</math>
- I is dimensionless, viscous forces in nodes
Soft Matter Details
Experimental Methods:
Question about constant foam generation
Testing that the theory is robust
Deciding which term dominates in equation 4
Dimensional analysis equation 7
Foam- further applications?
