CONTACT TIME DURING IMPACT OF A SPHERICAL-PARTICLE AGAINST A PLANE GAS-LIQUID INTERFACE - THEORY

Bubble-particle impact in flotation is usually approximated to the par ticle approaching against a plane gas-liquid interface. In this paper we theoretically re-investigate this interaction and deal with its non -linear problems. It is evident that the restoring force is a non-line ar 'mixed' function of the transition angle and the maximum depth of t he deformed gas-liquid interface. This 'mixed' expression makes analyt ical prediction of collision time impossible. In this paper, the resto ring force is approximately predicted in terms of the maximum depth of the deformed gas-liquid interface. Dynamics of the impacting particle can be described solely by the maximum depth, The non-linear differen tial equation describing the particle oscillation is analytically solv ed using an approximation method. Collision time is analytically predi cted. Two characteristic dimensionless parameters, viz., the Bond numb er and the Weber number of collision, are introduced to describe the i mpact interaction. A critical analysis of the so-called effective mass effect on collision time is performed and indicates that the effect o f oscillation effective mass on collision time is small and can be ign ored. The theoretical collision time model presented in this paper is based on the following parameters: the particle radius and the particl e density, the density and viscosity of the liquid phase, and the tens ion of the gas-liquid interface.