Consider a fluid sphere of radius R moving through a large volume of stagnant liquid at a constant velocity U. The sphere may be a gas bubble or a droplet of an immiscible liquid. The internal and external viscosities are J.L1 and J.L2, respectively. Both fluids are Newtonian with constant properties. It is convenient to choose a reference frame fixed at the center of a stationary sphere, as shown in Fig. 8-6. (a) Assuming that Stokes' equation is valid everywhere, find the general solutions for the internal and external velocities, v(1) and v(2), and identify all boundary conditions that must be satisfied. (b) Show that general solution for axisymmetric 2D creeping flow in spherical coordinates (Eq. 8.4-39 in Deen) to show that