The onset of recirculation flow in periodic capillaries: Geometric effects

Abstract

In this paper we examine the onset of flow circulation in expansion regions of infinite tubes of periodic, non-constant cross-section. Three types of axisymmetric capillary shapes were considered; sinusoidal, parabolic and triangular. A full boundary element method (BEM) solution of Stokes’ equations was formulated for the specific case of an infinite periodic tube. Geometric parameters were varied to establish conditions for the onset of recirculation. Recirculation flow is first predicted to appear beyond a critical amplitude, for all types of tubes studied, with zones in tubes of triangular sections appearing at a lower amplitude. Second order recirculation zones were predicted for still higher amplitudes, in all the capillaries. A numerical study was undertaken to characterise the onset of first and second order recirculation flows in terms of geometric factors.