Interfacial Thermal Resistance
From ThermalFluidsPedia
In very thin films, as noted above, the attractive force from the solid surface to the liquid produces a pressure difference (disjoining pressure) across the liquidvapor interface, in addition to the capillary effect. These two effects reduce the saturated vapor pressure over a thin film with curvature in comparison with the normal saturated condition. Consider a thin liquid film with liquid thickness δ over a substrate with liquid interface temperature T_{δ} and normal saturation vapor pressure corresponding to T_{δ} of . At equilibrium, the chemical potential in the two phases must be equal:

Integrating the GibbsDuhem equation,
dμ = − sdT + vdp 
at constant temperature from the normal saturated pressure to an arbitrary pressure gives

Using the ideal gas law for the vapor phase, and assuming the liquid phase is incompressible , one obtains the following relations upon integration of eq. (3) for the vapor and liquid chemical potentials, respectively:


Since , substituting eqs. (4) and (5) into eq. (2) yields

The pressure difference in the vapor phase p_{v,δ} and the liquid phase due to capillary and disjoining effects are related as follows:

where p_{cap} is capillary pressure. Equation (7) can be used to eliminate in eq. (6).

When the interface is flat and pd = 0, . For a curved interface and pd = 0, eq. (8) is reduced to the following Kelvin equation:

References
Faghri, A., and Zhang, Y., 2006, Transport Phenomena in Multiphase Systems, Elsevier, Burlington, MA.