# Boundary elements solution of stokes flow between curved surfaces with nonlinear slip boundary condition

## Authors

• ### Cesar Nieto,

1. Escuela de Ingeniería, Grupo de Energía y Termodinámica, Universidad Pontificia Bolivariana, Medellin, Colombia
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• ### Henry Power,

Corresponding author
1. Department of Mechanical, Materials and Manufacturing Engineering, Faculty of Engineering, The University of Nottingham, Nottingham, United Kingdom
• Department of Mechanical, Materials and Manufacturing Engineering, Faculty of Engineering, The University of Nottingham, Nottingham, UK
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• ### Mauricio Giraldo

1. Escuela de Ingeniería, Grupo de Energía y Termodinámica, Universidad Pontificia Bolivariana, Medellin, Colombia
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## Abstract

This work presents a boundary integral equation formulation for Stokes nonlinear slip flows based on the normal and tangential projection of the Green's integral representational formulae for the velocity field. By imposing the surface tangential velocity discontinuity (slip velocity) in terms of the nonlinear slip flow boundary condition, a system of nonlinear boundary integral equations for the unknown normal and tangential components of the surface traction is obtained. The Boundary Element Method is used to solve the resulting system of integral equations using a direct Picard iteration scheme to deal with the resulting nonlinear terms. The formulation is used to study flows between curved rotating geometries: i.e., concentric and eccentric Couette flows and single rotor mixers, under nonlinear slip boundary conditions. The numerical results obtained for the concentric Couette flow is validated again a semianalytical solution of the problem, showing excellent agreements. The other two cases, eccentric Couette and single rotor mixers, are considered to study the effect of different nonlinear slip conditions in these flow configurations. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013