An Extension of Faxen’s Law to the Ellipsoid of Revolution

抄録

Simple formulae are presented to calculate the force F and Torque T on a rigid spheroidal particle of semi-axes (a, a, c) immersed in an arbitrary Stokes flow with velocity u(x, y, z) at infinity.
Using the notation ⟨f⟩=(1⁄2ε) ∫_−ε^εf(0, 0, z)dz, ε=(c²−a²)^1⁄2, we have F=μK·⟨w⟩, w=u+A grad p⁄μ, T=3μQ⟨ze×w+2Aω⟩, (Remark: Graphics omitted.), where μ is the viscosity, −μK and −μQ the tensor coefficients of force and torque on the spheroid for unit translational and rotational velocities, p the pressure, e the unit vector along the z axis and ω the vorticity. For the oblate spheroid we have only to take ε=i|ε|.