 Translating sphere in Stokes flow

ID: translating-sphere-in-stokes-flow

a

translating with velocity

U

through otherwise stationary fluid has

u = \frac{3 a}{4 r} (I + \frac{xx}{r ^{2}}) U + \frac{a ^{3}}{4 r ^{3}} (I - 3 \frac{xx}{r ^{2}}) U, p = \frac{3 μ a}{2 r ^{3}} U \cdot x .

Its surface traction integrates to the Stokes drag law.

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