Abstract
We outline a statistical mechanics of the triple gas-solid-liquid contact line on a rough plane. The analysis regards the neighborhood of the line as a solid dotted with cavities. It adopts the simplest mean-field statistical mechanics, in which each cavity is either full or empty, while being connected to near neighbors by thin necks. The theory predicts equilibrium angles for advance and recession in terms of the Young contact angle and the joint statistical distribution of two quantifiable geometrical parameters representing specific neck cross-section and specific cavity opening. It attributes contact angle hysteresis to first-order phase transitions among adjacent cavities, as they collectively imbibe or reject liquid. It also calculates the potential energy barriers that hysteresis erects against overcoming contact line pinning. By determining whether the phase transitions can release latent energy, this ab initio analysis distinguishes six regimes, including two metastable recession states. We compare predictions with data for superhydrophobia on microscopic rods; for hysteresis in the "Wenzel state"; and for variations of the advancing contact angle with surface energies of the liquid.
Highlights
When liquid advances on a dry solid surface, the triple gas-solid-liquid contact line adopts a greater contact angle θa than when it recedes at the angle θr, 0 < θr ≤ θa < π
We presented a statistical mechanics predicting the equilibrium angles θa and θr of advance and recession of a liquid on a rough solid surface in terms of the Young contact angle θe on a flat plane of the same solid, and as functions of roughness geometry characterized by two parameters λ and α representing, respectively, the specific area of cavities on the solid and the specific cross-section of necks joining them
We showed that contact angle behavior conforms to six possible regimes, including two with receding angle metastability
Summary
When liquid advances on a dry solid surface, the triple gas-solid-liquid contact line adopts a greater contact angle θa than when it recedes at the angle θr , 0 < θr ≤ θa < π. A sessile drop laid on a solid plane under gravity stays put until the plane is sufficiently inclined, with a smaller contact angle at the point of highest elevation than at its lowest [11,12,13,14] Because this difference in θ exists without any visible fluid motion, a thermodynamic approach that does not account for time, but instead recognizes the direction of any quasistatic change in state variables, should be sufficient to describe this hysteretic phenomenon. De Coninck [16] invoked statistical mechanics to describe this phenomenon We revisit this approach to derive explicitly how geometry of the rough surface gives rise to six distinct regimes of contact line behavior, and we identify these regimes in experimental data
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