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Slow motion of multiple droplets in arbitrary three‐dimensional configurations
Author(s) -
Keh Huan J.,
Tseng Yi K.
Publication year - 1992
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690381205
Subject(s) - spheres , settling , stokes flow , reynolds number , mechanics , radius , viscosity , motion (physics) , slow motion , classical mechanics , physics , newtonian fluid , suspension (topology) , boundary (topology) , flow (mathematics) , cluster (spacecraft) , mathematical analysis , mathematics , thermodynamics , turbulence , optics , computer security , astronomy , homotopy , computer science , pure mathematics , programming language
This article presents a combined analytical‐numerical study for the hydrodynamic interactions of an arbitrary finite cluster of spherical droplets at low Reynolds numbers. The droplets may differ in radius, in viscosity and in migration velocity. The theory developed is the most general solution to the mobility or resistance problem of slow motion of an assemblage of fluid spheres in a three‐dimensional unbounded medium. Using a boundary collocation technique, the creeping flow equations are solved in the quasisteady situation, and the interaction effects among the droplets are evaluated for various cases. For the motion of two‐droplet systems, our results for the droplet interaction parameters at all orientations and separation distances agree very well with the exact solutions obtained by using spherical bipolar coordinates or the asymptotic solutions obtained by using the connector algebra. The mobility parameters of linear chains of three droplets have been calculated, demonstrating that the existence of the third sphere can significantly affect the mobility of the other two spheres. The mobility results are also presented for the motion of chains containing up to 101 identical and equally spaced spheres, and the end effect exhibited by a chain of spheres can be found. Finally, our “exact” solutions for the hydrodynamic interaction between two fluid or solid spheres are used to find the effect of volume fractions of particles of each type on the mean settling velocities of the particles in a bounded suspension.