The Modified Reynolds Equation — Gas Flows
Thin-film gas flows are 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, 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 9-3 and dividing through by the constant Mn/RT0 results in a modified form of the Reynolds equation:
(9-10)
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 by COMSOL Multiphysics in the Thin-Film Flow interfaces:
This definition is different from the one in Ref. 5, and the variable in the physics interfaces is named Equivalent free path, not mean free path, following the definition and naming given in Ref. 3.
The slip length is then defined as:
Values for the tangential-momentum-accommodation coefficients for various gas surface combinations are given in Ref. 2.