Multiscale modelling and simulation of slip boundary conditions at fluid-solid interfaces

In most applications concerning a fluid flowing over a solid surface, the no-slip velocity condition was widely used because it is simple and produces the results in agreement with experiments. However, this dynamical boundary condition is not appropriate when the flow under consideration is at a micro or nano length scale.In order to model this effect at the macroscopic scale, the Navier boundary conditions have been introduced, with the slip length as a parameter. When the fluid is a gas, this length is related to the tangential momentum accommodation coefficient (TMAC) and the mean free path, according to the Maxwell model. The aim of this work is to systematically address this model using a multi-scale approach and to extend it by incorporating both the morphology and the anisotropy of a surface. The thesis consists of five chapters. In Chapter 1, the basics of the kinetic theory of gases, the Boltzmann equation and related solutions (Navier-Stokes-Fourier, Burnett, Grad, Direct Simulation Monte Carlo .) are briefly presented. The models of gas-wall interaction and slip models introduced in the fluid mechanics are also recalled. The chapter ends with a description of the computational method used for the molecular dynamics simulations performed in this work. Chapter 2 is dedicated to the development of a simple technique to simulate the pressure driven flows. The principle is to rely on the atomistic formulas of the stress tensor (Irving Kirkwood, Method of Plane, Virial Stress) and to modify the periodic conditions by maintaining the difference between the kinetic energy of the ingoing and outgoing particles of the simulation domain. Several types of channels are studied with this technique. The results (temperature, velocity .) are discussed and compared. Chapter 3 deals with the study of the gas-wall interaction potential by the ab-initio method. The code CRYSTAL 09 is used to obtain the potential between an atom of argon (Ar) and a surface of platinum (Pt) as a function of distance. Then the gas-wall potential is decomposed into binary potential and approached by an analytic function. This function is then implemented in a MD code to simulate the gas-wall collisions and determine the TMAC coefficient. In Chapter 4, the effect of morphology is studied. The multi-body Quantum Sutton Chen (QSC) potential is used for Pt solid and the binary potential proposed in the previous chapter for the Ar-Pt couple is employed. The QSC potential is needed to reproduce the surface effects that affect the final results. Different surfaces are treated : smooth, nanostructured surface and, random surface obtained by Chemical vapor deposition (CVD). The TMAC is determined using a generalized approach, i.e. depending on the angle of incident flux of gas atoms on the surface. The surface anisotropy and the scattering kernel are also examined. In Chapter 5, we propose a model of anisotropic slip for fluids based on accommodation tensor. The model is obtained by the analytical approximate calculations developed in the framework of the kinetic theory. We thus generalize Maxwell's equation by showing that the slip length tensor is directly related to the accommodation tensor. The model is in good agreement with the MD results. Thanks to our MD simulations, we develop a suitable technique for reproducing the anisotropy of the accommodation tensor. The thesis ends with a conclusion section in which we suggest some perspectives for a continuation of this work