Series Development of the Stress Tensor for the Shear Viscosity of Gases in the Transition Regime

• Germán Urbina-Villalba Centro de Física, Instituto Venezolano de Investigaciones Científicas
• Máximo García-Sucre Centro de Física, Instituto Venezolano de Investigaciones Científicas
• Rixio Parra Centro de Física, Instituto Venezolano de Investigaciones Científicas
• Luis Araque-Lameda Departamento de Física, Universidad de Oriente, Núcleo Sucre
• Gustavo J. Mata Departamento de Física, Universidad Simón Bolívar

Resumen

We discuss some relevant features of the variation of the effective viscosity of gases with the pressure in the transition regime. Both qualitative arguments and formal ones are given in order to explain the regular pattern of oscillation of the effective viscosity with pressure that has been experimentally observed in gases under the transition regime. Using the Boltzmann equation under the relaxation time approximation, an infinite series expression for the tangential stress Pzx in terms of the spatial derivatives of the gas velocity is deduced. For constant boundary conditions an appropriate cut off of this series up to fifth order in the mean time between collisions produces an ordinary differential equation that can be easily solved for Pzx assuming laminar flow and a small dependence of the fluid velocity with the spatial distance “z”, from the walls of the container