Thickness Change and Disjoining Pressure

If we increase the thickness e of a liquid film by an amount de by adding a number of molecules dN (by unit surface area), we have dN = defVo, where Vb represents the volume per molecule in the liquid phase. The energy varies by /x dN where g is the chemical potential of the liquid. This potential includes a dominant term /xq due to volumetric effects, as well as a correction term P e) associated v ith the interfacial energy  

Following Derjaguin s notation, we will define the disjoining pressure n(e) as the quantity 

When P e) is a decreasing function of e (favoring a thick film), TI(e) is positive. 

We can readily see that this pressure is related to the chemical potential via the relation 

The film under study is in equilibrium with a porous ring filled with the same liquid. The ring can be subjected to a hydrostatic pressure = pgH, 

---