SYMBOLIC OPERATOR SOLUTIONS OF LAPLACE'S AND STOKES' EQUATIONS PART II STOKES FLOW PAST A RIGID SPHERE

Symbolic operator methods are employed to derive a general solution of the Stokes' and continuity equations of low Reynolds number hydrodynamics for arbitrary flow past an immobile sphere. The novelty of the final working formula lies in the fact that the velocity and pressure fields are explicitly and directly expressed in terms of the prescribed velocity field and its derivatives at infinity. Hence, apart from these trivial differentiations, no further operations of any kind are required to effect a solution. The computational scheme is illustrated for the case of a rigid sphere embedded in a general undisturbed quadratic velocity field, of which Poiseuille flow in a circular lube is the pre-eminent example. Results obtained by this method accord with those obtained by other, more traditional, schemes requiring preliminary expansion of (certain functions of) the prescribed data into surface spherical harmonics.