Evolution of bubble size distribution in particle stabilised bubble dispersions: Competition between particle adsorption and dissolution kinetics

It is shown that in systems containing bubbles stabilised by nanoparticles, the time scales for the dissolution of small microbubbles can be comparable with those involving the transport and adsorption of the stabilising nanoparticles onto the surface of the bubbles. We have studied the evolution of model bubble size distribution functions in the light of this effect and also the competition between different sized bubbles for the finite number of available particles. It is found that for dispersions moderately rich in nanoparticles, the width of the final distribution function can become broader than the initial one, whereas for cases deficient in particles the reverse is observed. For each given bubble size, there exists a particle to bubble concentration ratio above which the final size of a bubble of this radius is no longer affected by the presence of other bubbles. In a system deficient in particles, this can still hold true for bubbles in the lower end of the size distribution range, but not the ones at the upper end. By considering simple cases consisting of just two bubbles sizes, we show that the degree of shrinkage of the bigger bubbles is significantly increased in the presence of a small amount of gas in the form of smaller bubbles. In contrast, the final bubble size of the smaller bubbles is found to be largely insensitive to the amount of gas included within larger bubbles. The implications of these results for the final fraction of retained gas, in these types of particle stabilised bubble systems, are also discussed.