Effect of particle adsorption rates on the disproportionation process in pickering stabilised bubbles

The degree of shrinkage of particle stabilised bubbles of various sizes, in a polydisperse bubble dispersion, has been investigated in the light of the finite adsorption times for the particles and the disproportionation kinetics of the bubbles. For the case where the system contains an abundance of particles we find a threshold radius, above which bubbles are stabilised without any significant reduction in their size. Bubbles with an initial radius below this threshold on the other hand undergo a large degree of shrinkage prior to stabilisation. As the ratio of the available particles to the bubbles is reduced, it is shown that the final bubble size, for the larger bubbles in the distribution, becomes increasingly governed by the number of particles, rather than their adsorption time per se. For systems with "adsorption controlled" shrinkage ratio, the final bubble distribution is found to be wider than the initial one, while for a "particle number controlled" case it is actually narrower. Starting from a unimodal bubble size distribution, we predict that at intermediate times, prior to the full stabilisation of all bubbles, the distribution breaks up into a bimodal one. However, the effect is transient and a unimodal final bubble size distribution is recovered, when all the bubbles are stabilised by the particles.