Kinematic model of bubble motion in a flotation froth

A kinematic model for bubble motion in a flotation froth is proposed. The model describes bubble trajectories in a two-dimensional vertical section of the froth phase of a flotation cell. If the viscosity and permeability of the froth is constant over the field, then the motion of bubbles is irrotational and Laplace's equation can be used to describe the streamlines of the bubble motion in terms of the air flux across the boundaries of the rectangular region. The justification for this kinematic solution is based on the computation of isobars in the froth using Darcy's law. This procedure offers the possibility of future extension to the more general case where the viscosity and permeability of the froth varies with position. Some examples of the dependence of the streamline pattern on the boundary conditions, which in turn can represent non-uniform distributions of air entering and leaving the region, are given. In particular, the permeability of the upper boundary, which corresponds to the top surface of the froth, is used to model the bursting rate of the bubbles. The unburst bubbles are assumed to cross the overflow weir in the side wall as part of the concentrate flow. The kinematic bubble trajectories will be used in a computer simulation of the dynamic behaviour of an experimental flotation test. It is intended that validation of the model will be based on comparison of visual output of the simulation with video records of experimental tests.