Notes on the contribution of thin films vs. Plateau borders (PB)


Discussion on dry vs. wet foam

Very dry limit: no diffusion of gas through PB, the presence of PB 
decreases the surface where diffusion can happen. Electrokinetic analogy: 
there is less resistance through the films.

Wet limit: other regime => is there a cross over between the two regimes?

When is the contribution of both comparable? 

In real systems (wet), expelled gas from one bubble diffuses into the 
liquid and not necessarily towards adjacent bubbles: large-scale picture 
required. 

Wet limit: contribution of curvature?

Necessity to perform experiments at different liquid fraction: 2D 
microfluidic approach shows that, at intermediate liquid fraction (film 
height about 10% of the cavity height), Von Neumann's law holds with lower 
D_{eff}

Crossover or a continuous change between the two regimes? It is easier to 
discriminate the two regimes in emulsions.

Discussion about the role of small bubbles:
     -	Important role - absolute bubble size may play a significant role 
for different reasons: they are in the cross-over since they are 
surrounded by .more. liquid, and they are responsible for topological 
transformations 
     -	no significant role - main gas flux stems from larger (average 
size) bubbles 

Are there two crossovers? In terms of liquid fraction and in terms of 
bubble size? 
Small bubbles shrink, films disappear and gas diffuses into the liquid -> 
transport in the liquid phase? If there is no transport, bubbles cannot 
disappear.
  - ratio bubble radius (wet limit)/ Plateau border length (dry limit) 
important to determine cross-over.

Numerical simulations do not take into account gas diffusion at the 
molecular scale. Envisaging a bottom up approach at molecular, film, cell 
and then foam, requires mapping out a lot of parameters, a huge technical 
task.

Regarding cross-over:
-	at 2D: happens at finite liquid fraction (intuitively)
-	at 3D: very large Plateau borders are required to have equivalent 
contribution with films. Hypothesis: size of the film needs to be less 
than the film thickness x radius of PB

Instead of looking at the diffusion of gas from one bubble to another it 
is necessary to consider the exchange of gas with the liquid reservoir.