Slide 7 of 12
Notes:
I would be remiss if I didn’t at least briefly describe the form of interparticle forces augmenting the Young-Laplace equation. Keeping in mind that the computations explicitly use pressure relations, I show the more familiar F/R forms for surface force studies - force over the radius of curvature.
The van der Waals interaction with Hamaker constant A is supplemented by a hard-wall term with atomic spacing ro. The electrostatic double-layer force for constant surface charge density boundary conditions, sigma 1 and 2, and Debye length, inverse kappa, is appropriate for weak to moderately strong double-layer overlaps. We’ve also included the pseudo steady-state drainage, where f* = 1 for the Reynolds equation. If necessary, this is further generalized for less restrictive conditions.
Lastly, and perhaps of primary interest, is the hydrophobic effect which is expected to manifest itself as a long-range attraction between the oil drop and any hydrophobic or even hydrophilic material in water.
A great preponderance of data from numerous sources supports the empirical description of an exponential decay with separation, where lambda and C1 are fitted parameters. These two are the only variables in our theoretical model.