Master of Science in Mechanical Engineering (MSME)
A thin liquid film experiences additional intermolecular forces when the film thickness h is less than roughly 100 nm. The effect of these intermolecular forces at the continuum level is captured by the disjoining pressure . Since dominates at small film thicknesses, it determines the stability and wettability of thin films. To leading order, a thin film can be treated as uniform and . This form, however, cannot be applied to films with non-zero contact angles. A recent ad-hoc derivation to include the slope leads to a that allows a contact line to move without slip. This work derives a new disjoining-pressure formula by minimizing the total energy of a drop on a solid substrate. The minimization yields an equilibrium equation that relates to an excess interaction potential . By considering a fluid wedge on a solid substrate, is found by pairwise summation of van der Walls potentials. This gives in the small-slope limit , where is the contact angle and is a material constant. The term containing the curvature is new; it prevents a contact line from moving without slip. Equilibrium drop and meniscus profiles are calculated for different B. Evolution of a film step is solved by a finite-difference method with the new disjoining pressure included; it is found that at the contact line is sufficient to specify the contact angle.
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Wu, Qingfang, "A disjoining pressure for small contact angles and its applications" (2003). LSU Master's Theses. 739.