Settling slip velocity of a spherical particle in an unbounded micropolar fluid

The gravitational settling of small spherical particles in an unbounded micropolar fluid with slip surfaces is considered. The motion is studied under the assumption of low Reynolds number. The slip boundary conditions on velocity and microrotation at the surface of the spherical particle is used. The solution for the stream function of the fluid flow is obtained analytically. The settling velocity is obtained and is plotted against the Knudsen number for various values of the micropolarity parameter and constants depending on the material of the solid surface. The problem of rotational motion of a particle with slip surface is also solved and the torque coefficient acting on the spherical particle is obtained and is plotted against Knudsen number for different values of micropolarity parameter, spin parameter, and the material constants. The correction to the Basset equation for settling velocity under gravity for slip particle in micropolar fluids is discussed with the range of Knudsen number which has been proven with known results available in the literature