On the Reynolds equation for linearized models of the Boltzmann operator

Rarefied gas flows in ultra-thin film slider bearings are studied in a wide range of Knudsen numbers. The generalized Reynolds equation, first derived by Fukui and Kaneko (1987, 1988, 1990) on the basis of the linearized Bhatnagar-Gross-Krook (BGK) Boltzmann equation (Bhatnagar et al. 1954), has been extended by considering a more refined kinetic model of the collisional Boltzmann operator, i.e., the linearized ellipsoidal statistical (ES) model, which allows the Prandtl number to assume its proper value (Cercignani and Tironi 1966). Since the generalized Reynolds equation is a flow rate–based model and is obtained by calculating the fundamental flows in the lubrication film (i.e., the Poiseuille and Couette flows), the plane Poiseuille-Couette flow problem between parallel plates has been preliminarily investigated by means of the linearized ES model. General boundary conditions of Maxwell’s type have been considered by allowing for bounding surfaces with different physical properties.