The Modified Reynolds Equation — Gas Flow
Thin-film gas flow is often isothermal, and in many cases the ideal gas law can be assumed. The ideal gas assumption relates the gas density to the pressure as:
here, T0 is the (constant) temperature of the gas, Mn is the molar mass, and R is the universal gas constant. The total gas pressure, pA = pref + pfilm, is written in terms of the reference pressure level pref and the pressure developed in the thin-film flow, pfilm. Substituting this density into Equation 9-3 and dividing it by Mn/RT0 results in the modified Reynolds equation for ideal (isothermal) gases:
(9-10)
The average flow rate and the forces acting on the walls are computed in the same manner as for the standard Reynolds equation.
Slip Boundary Condition 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 Thin-Film Flow interfaces:
The variable in the physics interfaces is named Equivalent free path, following the definition and naming given in Ref. 3.
The slip length is then defined as:
Values for the a tangential momentum accommodation coefficient, α for various gas- surface combinations are given in Ref. 2.