“…Since the dimensions of the bead and the bubble together are much less than that of the liquid in the container, the later can be assumed to be infinite in extent so that the edge effects can safely be neglected and that the viscous drag can be calculated using Stokes formula, F v = 6πη rv , where we have approximated
Furthermore, viscosity of a binary liquid mixture can roughly be estimated from the empirical expression, η = x 1 2 η 1 + x 2 2 η 2 + x 1 x 2 η‘, where η is the viscosity of the mixture, x i and η i are respectively the mole fraction and viscosity of species i in the mixture and η‘ is a composition independent cross coefficient, nearly equal to η 1 + η 2 . Since the bubble does not get detached from the bead during the motion, we may assume that the force resulting from the excess pressure inside the gas bubble F P , is balanced by the capillary force F C .…”