Drag and torque on clusters of N-arbitrary spheres at low Reynolds number

Hydrodynamics of particle clusters suspended in viscous fluids is a subject of considerable theoretical and practical importance. Using a multipole ex pansion of the flow velocity in a series of spherical harmonics, Lamb's fun damental solution of the Stokes flow outside a single sphere is generalized in this work to the case of N nonoverlapping spheres of arbitrary size wit h slip boundary conditions. The expansion coefficients are found by transfo rming the boundary conditions to the Lamb form and by transforming the sphe rical coordinates and solid spherical harmonics centered at different spher es. The problem is reduced to the solution of the linear system of equation s for the expansion coefficients, which is carried out numerically. Based o n 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 aggrega te hydrodynamic radius on the Knudsen number and the number of particles is found by performing calculations of drag forces acting on the gas-borne fr actal-like and straight chain aggregates. A good agreement is shown in comp aring predictions of the described theory with available experimental and t heoretical results on motion of various small sphere clusters in viscous fl uid. (C) 2000 Academic Press.