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Streszczenie:
Exact expressions are derived for the pair and three-body hydrodynamic interactions between a sphere and a number of small particles immersed in a viscous incompressible fluid. The analysis is based on the Stokes equations of low Reynolds number hydrodynamics. The results follow by a combination of the solutions for flow about a sphere with no-slip boundary condition derived by Stokes and Kirchhoff and the result derived by Oseen for the Green tensor of Stokes equations in the presence of a fixed sphere.

Słowa kluczowe:
Hydrodynamics, Tensor methods, Stokes flows, Boundary value problems, Torque

Streszczenie:
Exemplary dynamics of three point particles falling under gravity in Stokes flow with periodic boundary conditions is presented in a movie. Stable and unstable solutions of the equations of Stokesian dynamics are explicitly shown for two initial configurations: equilateral triangles with side lengths close to a critical size.

Słowa kluczowe:
Kinematics, Suspensions, Boundary value problems, Viscosity, Anisotropy

Streszczenie:
Solutions of the equations of Stokesian dynamics for point particles are found for periodic boundary conditions with three particles per unit cell of a simple cubic lattice. Two particles per cell move with equal velocity, but three particles per cell usually lead to irregular motion. For a class of initial conditions with special symmetry motions are found that are periodic in time as well as in space. It is shown that there is a range of stability in which the motions are robust under perturbation.

Słowa kluczowe:
Tensor methods, Boundary value problems, Eigenvalues, Periodic solutions, Equations of motion