Stokes flow characterizes the steady and non ? axisymmetric flow of an incompressible, viscous fluid at low Reynolds number and is described by a pair of partial differential equations connecting the velocity with the pressure field. Spherical geometry provides the most widely used framework for representing small particles embedded within a fluid that flows according to Stokes law and thus, the flow is assumed to be axisymmetric. The two different complete representations of the flow fields are considered here. The first one, named Stokes representation, is obtained, expressing the equation of motion in spherical coordinates, according to which stream function is given in full series expansion in terms of separable eigenmodes. The second ine, also valid in non ? axisymmetric geometries, is the Papkovich ? Neuber differential representation, where the flow fields are provided in terms of harmonic spherical eigefunctions. In the interest of producing ready-to-use basic functions for axisymmetric Stokes flow in spherical coordinates by showing the different approach of solving such problems, we calculate the Stokes (2-D) and Papkovich ? Neuber (3-D) eigensolutions, demonstrating the full series expansion. In the present work, connection formulae are obtained which relate the spherical harmonic eigenfunctions of the Papkovich ? Neuber representation, considering rotational symmetry, with the separable spherical stream eigenfunctions, excluding singularities. In that way, we transform any solution of the Stokes symmetric system from one representation to the other taking advantages of each one, as the case may be.

Στοιχεία Άρθρου

Περιοδικό	Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
Αρ. Τεύχους	Τεύχος 47
Περίοδος	2003
Συγγραφέας	P. Vafeas
Αρ. Αρθρου	4
Σελίδες	59-73
Γλώσσα	-
Λέξεις Κλειδιά	Stokes flow, creeping flow, differential representations, spherical particles

On the Connection Between Stokes and Papkovich-Neuber Spherical Eigenfunctions in stokes flow