Hydrodynamic interaction for time‐dependent motions: Steady rotation of a rigid dumbbell

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Abstract
An expression for the flow field resulting from a time‐dependent force with time‐dependent point of action is derived from the linearized Navier‐Stokes equations. The result is written as a sum of terms, the first of which is the “slow‐change limit” corresponding to a stationary force acting at a stationary position. The application to the steady rotation of a dumbbell shows that this sum corresponds to a series expansion in powers of (L2|Ω|/v)1/2 where 2L is the length of the dumbbell, Ω is its angular velocity, and v is the kinematic viscosity of the liquid. It is pointed out that the results obtained are relevant to the problem of rotatory Brownian motion and to that of non‐Newtonian viscosity.