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Homework answers / question archive / Stokes flow with a far-field elongational flow

Stokes flow with a far-field elongational flow. Find the solution to Stokes flow past a sphere where the far-field velocity satisfies the elongational flow defined as vx = ?γ x, vy = γ? y, and vz = −2γ?z. First verify that the continuity equation is satisfied. Then transform the velocity to spherical coordinates to show that the flow is symmetric if z is chosen as the direction of symmetry. Now set up the boundary conditions for ψ. In particular, show that only the Q2 term remains for the above far-field velocity. Complete the solution for ψ by boundary-condition fitting. What is the force on the sphere?