Thickness of Wetting Films on Rough Solid Substrates

5 THICKNESS OF WETTING FILMS ON ROUGH SOLID SUBSTRATES 

Let ns now consider the case of thin equilibrium liquid films on rough solid substrates when there is complete wetting. In such a case, it is possible to measure only the mean thickness of the film, h. It appears that the mean thickness, h, of wetted films on rongh solid surfaces is bigger than the corresponding thickness of a flat film, h, on a smooth substrate. It also appears that the mean thickness, h, approaches the valne, h, at high and low film thicknesses when the latter are 

When a wetting film of uniform thickness covers a curved surface, its equilibrium with the vapor of the same liquid is determined by Equation 2.23 in Section 2.2, which can be rewritten as 

Let us make a further examination for nonpolar one-component liquids (complete wetting), where the disjoining pressure isotherm, Il(fi), is determined only by the dispersion forces. The isotherm of the disjoining pressure of a flat film in this case has the same form as in the previous Section 2.4. 

In the general case, the disjoining pressure in thin films on a curved substrate, is different from the corresponding disjoining pressure in films on a flat substrate, Il(ft). Thus, for example, for films at the internal surface of a capillary of radius, r, the disjoining pressure, 11, (in the approximation h r) is given by [10] 

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