ABSTRACT
The bubble-particle interaction strongly depends upon the dynamic response of the particle to the liquid flow, disturbed by both the bubbles and the particles. The dynamic response of the particle to the flow disturbance by the particle itself was previously discussed in the context of the particle transient settling in Chapter 4. This dynamic response is measured by the particle relaxation time, t"' which is defined as the ratio of the particle inertia to the viscous drag force and is described by Eq. (4.21). Dividing both sides ofEq. (7.30) by 6rrpRP and rearranging gives
P 2p dt P p Dt 111 P p dt
RdV dW)~6 lp Is --- -~~-Vstokcs=O 0 dt dt 21rP t-~ (10.1)
As the velocity of particles (and water) decreases when it approaches the bubble surface, the drag force acting on the particles fmally becomes small enough so that Stokes' law applies and the drag correction factor fd in Eq. (10.1) is approximately equal to 1. We may also assume further that the correction factors associated with the added-mass and the Basset forces are about unity. As the first approximation, the motion Eq. (10.1) for the particles diverted by air bubbles yields
(10.2)
where the scaled time 1], known as the Fourier number, is defined by Eq. (10.3).
