Boundary element method calculations of the mobility of nonspherical particles—1. Linear chains

Abstract

The utility of the boundary element technique is demonstrated on the problem of linear chains of spheres translating and rotating through a quiescent fluid. The method takes advantage of the linearity of the problem by using superposition of the general solution for the flow generated by point forces on the bounding surfaces of the fluid to satisfy the boundary conditions. The BEM results for translational drag of chains of spheres compare very well with published experimental and computational data. We also show that slender body theory provides an approximate analytic result that is useful in interpreting and correlating the BEM calculations. Slender body theory also revealed that the model of the particle as a single prolate spheroid with equal aspect ratio produced a result equal to that for the chain of spheroids correct to second order, while the model of the chain as a cylinder produced an upper bound on the drag. Slender body theory also gives a reasonable estimate for the rotational resistance for chains, which, together with the BEM results, are reported here for the first time.