Analysis of a Stokes Flow Past a Cube (Friction and Diffusion Coefficients for Brownian Dynamics Simulations)

Magnetorheological properties significantly depend on the regime of aggregate structures. In the case of cubic particles, closely-packed clusters that are significantly different from those for the case of spherical or rod-like particles are formed in the system since magnetic cube-like particles prefer a face-to-face contact with the neighboring particles. Therefore, a cubic particle suspension is expected to exhibit a sufficiently strong magnetorheological effect, which may be investigated by means of Brownian dynamics simulations. However, the translational and rotational diffusion (or friction) coefficients of a cube are not known and indispensable in order to develop this simulation technique. From this background, in the present study, we have analyzed the flow field around a cube in a Stokes flow regime in order to estimate the diffusion (or friction) coefficients of cube-like particles that are required for performing Brownian dynamics simulations of a cubic particle suspension. In the situation of a uniform flow field with a Reynolds number sufficiently smaller than unity, the force acts on the cube only in the flow field direction, and the torque acting on the cube may be regarded as negligible. In the situation of a rotational flow field with a sufficiently low Reynolds number, the torque acts on the cube only in the direction of angular velocity of the rotational flow field, and the force negligibly act on the cube. These characteristics are in significantly similar to those for the case of spheres in a Stokes flow situation. From these results, we may conclude that the diffusion coefficients of cube-like particles can be expressed by introducing a correction factor to those of the spherical particles.