Drag on an axially symmetric body vibrating slowly along its axis in a viscous fluid

Abstract

Let D0 be the Stokes drag on an axially symmetric body moving parallel to its axis with velocity U0 through an unbounded fluid. The drag D experienced by the same body oscillating with velocity U = U0eiσt along its axis in the unbounded fluid is given by the expression $\frac{D}{D_0} = \left \{{1 +{\frac {d_0}{6 \surd{(2)} \pi \mu a U_0}}(1+i)M+O(M^2)}\right \}e^{i \sigma t},$ where a is any characteristic particle dimension and $M^2 = a^2 \sigma \rho |\mu$ is a dimensionaless number. The part of this drag formula which gives the energy dissipation is calculated for bodies of various shapes.