Distorting a bubble: Growth and shear interplay

How does local stress on a bubble affect its growth and thereby 
coarsening? Does coarsening relax bubble shapes?

Local stress can be defined as the surface tensor (deviatoric part of 
Batchelor tensor) evaluated over 1 bubble.

How does coarsening affect local surface tensor? Does the stress become 
anisotropic?

Must distinguish between scaling state and the approach towards scaling 
state.

2nd invariant of the local surface tensor, Q, as a measure of the local 
stress invariant. In an annealed foam, Q varies between 0 and 1.

How is the distribution of Q. Peaked or broad?

Q is very different for a coarsened foam than it is for a partitioned 
structure: Q is quasi independent of the cell volume for a coarsened foam 
(simulated with Potts model) whereas Q is an increasing function of the 
cell volume for a granular packing (Voronoi cells of spherical beads)

In 2D, experiments and Potts simulations can provide Q.

Curvature tensor might also be useful. 

Do T1s change Q? How far do these changes propagate (ie decay away from 
the location of the T1)?

Can T1s be described in the framework of continuum mechanics as 
multipoles?

The range of T1s should matter for the coupling to the macroscopic 
response.

As T1s proceed, surface energy always decreases. A priori the total shear 
stress can increase or decrease. However a decrease of the stress is 
always observed in numerical simulations of steady flowing foams (without 
coarsening). Why?

In coarsening 2D foams, simulations show that stress can increase 
following a T1.

Does the time for a gas molecule to cross a film change when there is flow 
(as foam is sheared)?