Bubble-bubble interactions in a 2d foam, close to the wet limit

Abstract

Following the general approach of Morse and Witten for the deformation of a bubble in contact with neighbouring bubbles, we develop a model for contacting bubbles in two dimensions which can be solved analytically. The force-displacement relations are derived by elementary methods; unlike the case of 3d, no logarithmic factors arise in two dimensions. We also discuss the case of a uniform compression of a symmetric foam structure; the (osmotic) compressibility depends on the number of contacts, as was shown in earlier work by Lacasse et al. Our model, which is based on first principles, without any free parameters, may be extended to simulate 2d foams.

A simple formula for the estimation of surface tension from two length measurements for a sessile or pendant drop

“…As we have shown 20 above, the determination of these lengths is high accuracy is important for an accurate estimation of surface tension. Finally, the derivation shown in Section 2 can also be carried out for two-dimensional drops, using the corresponding 2d equations of the Morse-Witten model [20]. This results in the following expression (exact for the model), 25γ…”

“…However, this force may be replaced by the distributed force at a flat boundary in either case of Figure 2, without affecting the solution away from the boundary. The remaining solution for the displacement R(θ) is small for all angles θ, for small F. 20 In general our method can be applied in various situations, such as Figure 1 (1) and (2). Only the parts indicated by thick solid lines represent the physical drops of Figure 1.…”

The evolution of numerical methods for predicting the distribution of surfactant in the bubble-scale dynamics of foams

“…In these cases the Potts model [19] provides similar (but less accurate) information about the structure, again using minimization of energy, in a stochastic manner, and hence offers an easier route to simulating many realisations of a disordered foam. Recently, a "Morse-Witten" theory [20] for the way in which compressed droplets (or bubbles in this case) deform has been used to generate equilibrium structures of monodisperse [21,22] and polydisperse foams in which bubble deformation is small [23], up to 10% of the bubble diameter. It remains to be seen whether this method can provide a route to predicting foam flow.…”

Juggling bubbles in square capillaries: an experimental proof of non-pairwise bubble interactions

“…(26), adding Eqs. (30) and (31) provides an expression for the bubble contact displacements along the tube axis as a function of the sum of the wall and inter-bubble contact forces. f Cv…”