By Roland Clift
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Extra info for Bubbles, Drops, and Particles
Operutiolzal Sphericity and Circularity Since the sphericity and circularity are so difficult to determine for irregular particles, Wadell (Wl) proposed that $ and $ be approximated by "operational shape factors" : = volume of particle volume of smallest circumscribing projected area of particle hp= [area of smallest circumscribing circle (2-8) (2-9) For rounded particles the operational sphericity, $,, is well approximated (K2, P3) by (e2el)-' 3, which is exact for ellipsoids. However. $, is not generally a good approximation to $.
49 111. Heat and Mass Transfer Substitution of the Stokes surface vorticitj. ;,, frorn Eq. 10 shows that Eq. (3-47) gikes Sh approximatell 10" too low for Pe = lo3. while the deviation becomes worse at lower Re. Acrikos and Goddard (Al) used a perturbation method to obtain the first-order correction to Eq. 92. 10 shows that Eq. (3-48) lies within 37, of the numerical solution for Pe > 30. It is convenient to have a relationship for Sh valid for all Pe in creeping flow. The following equation agrees with the numerical solution within 29;: Sh = 1 + (1 + Pe)' 3.
The first attempt to account for surface contamination in creeping flow of bubbles and drops was made by Frumkin and Levich (F1. L3) who assumed that the contaminant was soluble in the continuous phase and distributed over the interface. The form of the concentration distribution was controlled by one of three rate limiting steps: (a) adsorption-desorption kinetics, (b) diffusion in the continuous phase, (c) surface diffusion in the interface. In all cases the terminal velocity was given by an equation identical to Eq.
Bubbles, Drops, and Particles by Roland Clift