The quasi-steady low-Reynolds-number flow induced by a linear chain of multiple slip spheres translating along their common axis in a Newtonian fluid is investigated. The particles are allowed to differ in radius, Navier slip coefficient, migration velocity, and interparticle spacing. A semi-analytical solution of the governing Stokes equation is obtained using a boundary collocation method. Hydrodynamic interactions among the particles are shown to be significant under appropriate geometric and surface conditions. For the two-sphere configuration, the computed hydrodynamic forces agree closely with previously published asymptotic solutions derived via the twin multipole expansion method. In the three-sphere case, the presence of a third particle substantially modifies the forces acting on the other two, demonstrating non-negligible many-body interaction effects. The interaction strength is found to be more pronounced for smaller particles or those with lower slip coefficients. Calculations for longer particle chains further reveal a clear hydrodynamic shielding effect within the assembly.
Lai et al. (2026) studied this question.