The rotation of a rigid sphere in a viscous emulsion of gas bubbles

The problem of the rotation of a rigid spherical body of arbitrary size in a homogeneous emulsion of gas bubbles is considered in the Stokes approximation on the basis of the self-consistent field method. An expression is obtained for the correction factor in Stokes' formula for the torque acting on the body in the first approximation with respect to the volume fraction of the dispersed phase. An analytical relation is found between the factor and the sizes of the bubbles and the body. In the limit, when this ratio tends to zero, the factor obtained agrees exactly with Taylor's result for the effective viscosity of a gas bubble emulsion. It is shown that, for “non-point” bubbles, the coefficient on the volume fraction in the expression for the effective viscosity of the emulsion can considerably differ from Taylor's result.