The Inertial Hydrodynamic Interaction of Particles and Rising Bubbles with Mobile Surfaces
✍ Scribed by Zongfu Dai; Stanislav Dukhin; Daniel Fornasiero; John Ralston
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 358 KB
- Volume
- 197
- Category
- Article
- ISSN
- 0021-9797
No coin nor oath required. For personal study only.
✦ Synopsis
form a permanent aggregate, a process which, in modern The collection efficiency of single bubbles rising through a very flotation science, is referred to as orthokinetic heterocoaguladilute pulp of hydrophobized quartz particles has been deter- tion (14, 15). The collection efficiency is the product of the mined. Measurements have been performed under conditions in efficiencies of three steps (or processes) involved in partiwhich the bubble surface is mobile, as a function of electrolyte cle-bubble interaction (16); i.e., concentration, particle diameter (7 to 70 mm) , bubble diameter (0.77 1 10 03 to 1.52 1 10 03 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 perwhere E c is the collision efficiency, E a is the attachment formed. A collision theory has been developed which accounts for the influence of positive and negative inertial forces in the case efficiency, and E s is the stability efficiency of the particleof bubbles with mobile surfaces. The approach considers only bubble aggregate. This dissection of collection efficiency long-range hydrodynamic interactions under conditions where continues to be the foundation for understanding, modeling, short-range interactions are strongly suppressed (i.e., high particle and quantifying the flotation rate. E col may be measured contact angle and high electrolyte concentrations) and attachment experimentally or calculated if E c , E a , and E s are known. E c occurs at first collision. In this instance, good agreement between may be calculated, as we will show, with a reasonable degree theory and experiment is achieved for particle diameters between of confidence and there is now a strong theoretical and exper-7 and 60 mm and Stokes numbers up to 0.27. The analytical imental basis for predicting E s (21-23, 29, 57, 58). The equation developed is termed the generalized Sutherland equation
prediction of E a is more difficult.