Slow motion of a slightly deformed spherical droplet in a microstretch fluid

The Stokes axisymmetrical microstretch streaming flow problem past a stationary viscous droplet and as well as the related problem of a viscous streaming flow past a stationary microstretch fluid droplet are studied. The droplets are considered either perfect spherical or deformed spherical in shape. For these flows, the microstretch scalar function is uncoupled from the stream function and microrotation component function. As boundary conditions, continuity of velocity, continuity of shear stress, vanishing of microstretch and the spin–vorticity relation at the droplet surface are used. Analytical solutions are obtained in each case for the stream functions and microstretch scalar. The drag acting, in each case, on the fluid droplet is evaluated. Numerical results for the drag force coefficient versus the relative viscosity, micropolarity parameter and spin parameter (a non-dimensional scalar factor relating the microrotation and vorticity at the droplet surface) are presented both in tabular and graphical forms. The results for the drag coefficient are compared with the available solutions in the literature for the limiting cases.