ABSTRACT

We consider a particle having a mass mp. a volume !J1 and a surface area S, immersed in a flotation cell. Let dS be a directed element of surface area normal to the particle and pointing outward into the fluid phase. The obvious forces associated with the particle volume are the particle inertia and its weight. The other forces associated with the particle surface are calculated by integration of the liquid stress (force per unit area) over an infinitesimal surface area dS. The momentum balance yields the motion equation of the particle

(7.1)

The closed surface integral is to be taken over the surface of the particle. Tis the liquid stress tensor, which is a linear operator that transforms the unit normal into the stress vector, and has a number of components. The first components are the hydrostatic pressure, P~n and the pressure (often called the "disjoining" pressure), n, due to the surface force interaction between the solid particles and bubbles. The latter component is obviously significant if the interacting surfaces are very close as shown by the detailed analysis given in Chapter 14. This component of colloidal surface forces is relevant to the motion of particles during the bubble-particle attachment.