Flow of liquid around the encapsulated drop of another liquid

The problem of the infinite uniform flow of liquid around the spherical drop coated with the porous layer is solved. External liquid permeates into the porous layer but is not mixed with the liquid located in the internal cavity of a capsule. The flow inside the porous layer is described by the Brinkman equation; moreover, the viscosity of the Brinkman medium is assumed to be different than the viscosity of pure liquid. The boundary condition of the jump of tangential stresses at the liquid-porous medium interface is used. Velocity and pressure distributions are found and the hydrodynamic force acting on the capsule is calculated. Different limiting cases are considered.