The Fokker–Planck Equation for Bubbly Flows and the Motion of Gas Bubble Pairs

A method is proposed to calculate the bubble distribution function in a bubbly flow. First a review is given of the equations of motion and the dynamic behaviour of a pair of bubbles moving through a liquid at moderate Reynolds number. Subsequently, a Fokker–Planck type transport equation is derived for the bubble distribution function. It is assumed that the interaction is primarily by frequent and binary encounters, each with weak hydrodynamic interaction between the bubbles. The bubble collision cross-section, which needs to be known for the transport coefficients, is presented. A comparison with PDF-methods for fluid particles in turbulent reacting flows is made.