Solution of the Stokes Flow of a Sphere by Minimization of the Dissipation of Energy
Kenneth C. DuPont, Philip Rosen · American Journal of Physics · 1963
A detailed derivation of the velocity flow field of a sphere moving slowly through an incompressible viscous fluid of infinite extent (Stokes' flow) can be accomplished by simultaneously satisfying the equations of motion and continuity for the fluid particles. An alternate method is used here which makes use of Onsager's principle of least dissipation of energy. To simplify the problem a constant velocity U equal and opposite in direction to the velocity of the sphere is superposed on the system to allow the fluid to flow slowly in the +x direction past the now stationary sphere. A variational problem is then stated and a Euler-Lagrange equation is obtained, the solution of which specifies the velocity flow field dependence on r, the distance from the center of the sphere.