Sedimentation in a dilute emulsion

✍ Scribed by E. Wacholder

• Publisher: Elsevier Science
• Year: 1973
• Tongue: English
• Weight: 520 KB
• Volume: 28
• Category: Article
• ISSN: 0009-2509
• DOI: 10.1016/0009-2509(73)85149-8

✦ Synopsis

In the present work the method of Batchelor [ l] is adopted to calculate the statistical mean speed of sedimentation in a dilute dispersion of identical spherical droplets. The mean settling speed is shown to be u, l-( [ e+K(o)]c) where U,, is the settling velocity of a single fluid sphere falling under gravity through an unbounded quiescent fluid, m is the ratio of the viscosities /.L'/P where the upper prime indicates the disperse phase, c is the volume fraction of the spheres, and K(u) is a numerical factor whose values are displayed in Table 1. An exact evaluation of K(u) requires knowledge of the solutions for the drag force components acting on two fluid spheres in the directions of their line of centre and perpendicular to it. Such a solution for the latter case is not yet available, hence, an approximate solution based on the 'method of reflections' is used. This causes some error in the numerical results for K(u), the magnitude of which is examined and discussed.