Drag and Torque on Clusters of N Arbitrary Spheres at Low Reynolds Number

• Published in: Journal of colloid and interface science Vol. 229; no. 1; pp. 184 - 195
• Main Author: Filippov, A.V.
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 01.09.2000; Elsevier
• Subjects: aggregated particles; Chemistry; Colloidal state and disperse state; Exact sciences and technology; General and physical chemistry; mobility radius; multipole expansion; Physical and chemical studies. Granulometry. Electrokinetic phenomena; slip regime; Stokes flow; slip regime; mobility radius; multipole expansion; aggregated particles; Stokes flow; Slip flow; Particle; Viscous fluid; Theoretical study; Hydrodynamics; Spherical particle; Particle suspension; Aggregate
• ISSN: 0021-9797; 1095-7103
• DOI: 10.1006/jcis.2000.6981

Hydrodynamics of particle clusters suspended in viscous fluids is a subject of considerable theoretical and practical importance. Using a multipole expansion of the flow velocity in a series of spherical harmonics, Lamb's fundamental solution of the Stokes flow outside a single sphere is generalized in this work to the case of N nonoverlapping spheres of arbitrary size with slip boundary conditions. The expansion coefficients are found by transforming the boundary conditions to the Lamb form and by transforming the spherical coordinates and solid spherical harmonics centered at different spheres. The problem is reduced to the solution of the linear system of equations for the expansion coefficients, which is carried out numerically. Based on the developed theory, the relation between the hydrodynamic and gyration radius of fractal-like aggregates with different structure is established. In another application, an asymptotic slip-regime dependence of the aggregate hydrodynamic radius on the Knudsen number and the number of particles is found by performing calculations of drag forces acting on the gas-borne fractal-like and straight chain aggregates. A good agreement is shown in comparing predictions of the described theory with available experimental and theoretical results on motion of various small sphere clusters in viscous fluid.