Size distribution functions of dispersions

The size distribution function of bubbles in thermodynamic equilibrium with the surrounding liquid has been derived in the absence of gravity. The derivation has been based on the assumption that the gas is dispersed into bubbles in a completely random way in respect of the energies of the bubbles. The size distribution function of bubbles obtained when surface tension effects are neglected is of the same form as the empirical Nukiyama-Tanasawa distribution, and gives also the size distribution function of droplets consisting of an incompressible liquid when the way the liquid is dispersed into droplets is assumed to be completely random with respect to the volumes of the droplets. The derived size distribution functions agree well with the experimental size distributions of bubbles in water having been generated by an air entrainment process at the surface of the water or behind a ventilated body.