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. (Hint: the interface boundary should remain fixed so that the bubble or drop does not change size. Using this determine a B.C. is a much better idea than the normal stress balance.) b) Using the general solution for axisymmetric 2D creeping flow in spherical coordinates (Eq. 8.4-39 in Deen) to show that vr(1)(r,)v(1)(r,)vr(2)(r,)v(2)(r,)=2(1+)Ucos[1(Rr)2]=2(1+)Usin[2(Rr)21]=Ucos[12(1+)2+3(rR)+2(1+)(rR)3]=Usin[14(1+)2+3(rR)4(1+)R(rR)3] Where =1/2. Discuss the limiting behavior of these results for 0 and . c) Use the general result that FD=4C1, where C1 is the coefficient for the n=1 portion of the general solution, to show that the drag on the fluid sphere is FD=22UR(1+2+3) d) Complete the force balance to show that the terminal velocity is given by U=32(2+31+)2R2g(21) This is called the Hadamard-Rybczynski equation, after 1 . Hadamard and D. Rybczynski, who reported it independently in 1911. Discuss the limiting behavior of the drag and terminal velocity for 0 and