A singularity method for calculating hydrodynamic forces and particle velocities in low-Reynolds-number flows

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Abstract
A numerical technique is presented which allows one to estimate hydrodynamic forces and torques or translational and angular velocities of particles in a general flow field. Particle–solid wall interactions can be readily included. The base functions used in the technique presented are singular fundamental solutions of the Stokes equation for a point force and a point force and a point source. The least-square approach is used preferentially in order to find the intensities of these singularities. Test calculations show that the results are self-consistent and in fairly good agreement with the exact solutions in a wide range of conditions. For example, for a spherical particle moving with no slip towards the solid wall, it has been shown that the method can provide good estimates of the resistance coefficient up to separations of the order of 5% of the particle radius. We believe that better agreement, for smaller separations, is within reach at the expense of increased computer costs. For spheroidal particles good results were obtained for aspect ratio in the range 0.5–2.0.