Abstract: An analytical approach is described for the axisymmetric flow through a permeable near-sphere with a modification to boundary conditions in order to account permeability.The Stokes equation was solved by a regular perturbation technique up to the second order correction in epsilon representing the deviation from the radius of nondeformed sphere.The drag and the flow rate were calculated and the results were evaluated from the point of geometry and the permeability of the surface.An attempt also was made to apply the theory to the filter feeding problem.The filter appendages of small ecologically important aquatic organisms were modeled as axisymmetric permeable bodies,therefore a rough model for this problem was considered here as an oblate spheroid or near-sphere.

Key words: Stokes flow, perturbation technique, filter feeding