The Modified Reynolds Equation — Gas Flow
Thin-film gas flow is often isothermal, and in many cases the ideal gas law can be assumed. Under these circumstances, the ideal gas law can be written on the form:
where T0 is the (constant) temperature of the gas, Mn is the molar mass of the gas, and R is the universal gas constant. Here, the total gas pressure is pA = pref + pf, where pA is the absolute pressure and pf is the pressure developed as a result of the flow. Substituting this relation into Equation 7-3 and dividing it by Mn/RT0 results in a modified form of the Reynolds equation:
(7-10)
This equation can be used to model isothermal flows of ideal gases. The average flow rate and the forces acting on the bearings are computed in the same manner as for the standard Reynolds equation.
Slip Boundary Conditions for Gases
For a gas, the slip length is often expressed using the mean free path, λ, and a tangential momentum accommodation coefficient, α. The following definition of the mean free path is used in the Hydrodynamic Bearing interface:
where μ is the gas viscosity, p is the gas pressure, R is the molar gas constant, T is the temperature, and Mn is the molar mass of the gas. The slip length is then defined as
Values for the tangential momentum accommodation coefficients for various gas surface combinations are given in Ref. 2.