The Particle–Bubble Behavior in Flotation in Low-Viscous Liquid

The authors discuss dynamics of gas bubble and mineral particle in low-viscous fluid. The particle–bubble interaction model represents a system of associated differential algebraic equations. Dynamics of the disturbed system is described using the Lagrangian method. The model takes into account oscillations of bubble surface and attached solid cylindrical particle in the infinitive volume of perfect incompressible liquid. The capillary force retaining the particle on the bubble is governed by the meniscus shape which conditions the wetting angle. The Legendre series expansion is used to represent small axially symmetrical oscillations of the particle–bubble system. The potential and kinetic energies of the system are expressed in terms of the coefficient of this series. The resultant eddy-free velocity field allows including the viscosity effect with regard to the local rates of energy dissipation.