Analytical calculation of the Stokes drag of the spherical particle in a nematic liquid crystal

Abstract

As an approach to the motion of the particles in the anisotropic liquid, we analytically study the Stokes drag of spherical particles in a nematic liquid crystal. The Stokes drag of spherical particles for general anisotropic case is derived in the terms of multipoles. In the case of weak anchoring we use the well-known distribution of the elastic director field around the spherical particle. In the case of strong anchoring the multipoles expansion may be used too by modification the size of the particle to the size of the deformation coat. For the case of zero anchoring (uniform director field) we found that the viscosities along the director η|| and perpendicular direction η are almost the same that is reasonable as in this case the liquid behaves as isotropic. In the case of the non-zero anchoring the general ratio η||/η is about 2 which is satisfied by the experimental observations.

Keywords

• liquid crystal
• diffusion
• Stokes drag
• viscosity