Modeling of micro flows using perturbation method

Abstract

A new method for modeling micro flows is presented in this research. The basis of this method is the development of governing continuum equations on fluid dynamics using perturbation expansion of the velocity, pressure, density and temperature fields in dependence of Knudsen number. In the present work, we use three-term perturbation expansions and reach three order of equations O(1), O(Kn), O(Kn2). Required boundary conditions (BC) for solving each order of these equations are obtained by substitution of the perturbation expansions into the general boundary conditions for the velocity slip and temperature jump. This set of equations is discretized in two-dimensional state on a staggered grid using the finite volume method. A three-part computer program has been produced for solving the set of discretized equations. Each part of this code, solve one order of the equations with the SIMPLE algorithm. Incompressible slip micro Poiseuille and micro Couette flows are solved either analytically or numerically using the perturbation method (PM). Good agreement is found between analytical and numerical results in the low Knudsen numbers, whereas numerical results deviate from analytical results by increasing the Knudsen number. The results of perturbation method are also compared with the results obtained from different slip models.