The Inertial Hydrodynamic Interaction of Particles and Rising Bubbles with Mobile Surfaces

The collection efficiency of single bubbles rising through a very dilute pulp of hydrophobized quartz particles has been determined. Measurements have been performed under conditions in which the bubble surface is mobile, as a function of electrolyte concentration, particle diameter (7 to 70 &mgr;m), bubble diameter (0.77 x 10(-3) to 1.52 x 10(-3) m), and particle advancing water contact angle. Situations in which the product of attachment and stability efficiency is at its maximum value have been identified, permitting a stringent, critical test of collision theory to be performed. A collision theory has been developed which accounts for the influence of positive and negative inertial forces in the case of bubbles with mobile surfaces. The approach considers only long-range hydrodynamic interactions under conditions where short-range interactions are strongly suppressed (i.e., high particle contact angle and high electrolyte concentrations) and attachment occurs at first collision. In this instance, good agreement between theory and experiment is achieved for particle diameters between 7 and 60 &mgr;m and Stokes numbers up to 0.27. The analytical equation developed is termed the generalized Sutherland equation (GSE). Copyright 1998 Academic Press. Copyright 1998Academic Press