Boundary integral equation approach for stokes slip flow in rotating mixers

César Nieto; Mauricio Giraldo; Henry Power

doi:10.3934/dcdsb.2011.15.1019

Article Contents

2011, Volume 15, Issue 4: 1019-1044. Doi: 10.3934/dcdsb.2011.15.1019

This issue Previous Article Determination of effective diffusion coefficients of drug delivery devices by a state observer approach Next Article A class of nonlinear impulsive differential equation and optimal controls on time scales

Boundary integral equation approach for stokes slip flow in rotating mixers

1.
Grupo de Energía y Termodinámica, Escuela de Ingenierías, Universidad Pontificia Bolivariana, Medellín, Circular 1 No. 73-34
2.
Division of Energy and Sustainability, The University of Nottingham, University Park, Nottingham, NG7 2RD

Received: February 28, 2010

Revised: May 31, 2010

Published: May 2011

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Abstract

In order to employ continuum models in the analysis of the flow behaviour of a viscous Newtonian fluid at micro scale devices, it is necessary to consider at the wall surfaces appropriate slip boundary conditions instead of the classical non-slip condition. To account for the slip condition at the nano-scale, we used the Navier's type boundary condition that relates the tangential fluid velocity at the boundaries to the tangential shear rate. In this work a boundary integral equation formulation for Stokes slip flow, based on the normal and tangential projection of the Green's integral representational formulae for the Stokes velocity field, which directly incorporates into the integral equations the local tangential shear rate at the wall surfaces, is presented. This formulation is used to numerically simulate concentric and eccentric rotating Couette mixers and a Single rotor mixer, including the effect of thermal creep in cases of rarefied gases. The numerical results obtained for the Couette mixers, concentric and eccentric, are validated again the corresponding analytical solutions, showing excellent agreements.

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Mathematics Subject Classification: Primary: 74S15; Secondary: 76D07, 76U05.

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