Theory and Simulation of Angular Hysteresis on Planar Surfaces

Abstract

A simple model is proposed to simulate contact angle hysteresis in drops on a planar surface. The model is based on assuming a friction force acting on the triple contact line in such a way that the contact line keeps fixed for contact angles comprised between the advancing angle and the receding one and is allowed to move in order to avoid angles outside this interval. The model is straightforwardly applied to axisymmetric drops for which a simple solution of the Young-Laplace equation can be obtained. A variation of the method has also been implemented for nonaxisymmetric drops by resorting to the public-domain "Surface Evolver" software. Comparison with experiments shows the excellent performance of the model.

Quantitative particle microscopy in self‐metered fluids

“…This is due to the involvement of mixed second‐order derivatives of the shape functions describing the menisci (Pozrikidis, ). An alternative approach is to simulate the equilibrium shape of the fluid using the public domain program surface evolver (Brakke, ), which has been applied to fluids on flat surfaces (Prabhala et al ., ; Santos & White, ) and nonplanar geometries (Chatain et al ., ; Dorrer & Ruhe, ; Kitron‐Belinkov et al ., ; Xiao et al ., ; Chou et al ., ). We have used surface evolver to provide a general solution that may be transferrable to other similar but non‐axisymmetric systems.…”

“…The equilibrium geometry of static fluids can be described by the Young–Laplace equation, which states that the pressure difference across a fluid interface at equilibrium is proportional to the surface tension and the mean curvature where R 1 and R 2 are the principal radii of curvature. Under the influence of gravity the Young–Laplace equation is where relates to hydrostatic pressure and is the difference in density of the liquid and vapour phases, g is the acceleration due to gravity and z is the height (Santos & White, ). However, Young–Laplace equations lack an accurate general procedure for solutions to yield equilibrium fluid shapes.…”

“…where − ρgz relates to hydrostatic pressure and ρ is the difference in density of the liquid and vapour phases, g is the acceleration due to gravity and z is the height (Santos & White, 2011). However, Young-Laplace equations lack an accurate general procedure for solutions to yield equilibrium fluid shapes.…”

“…This is due to the involvement of mixed secondorder derivatives of the shape functions describing the menisci (Pozrikidis, 2010). An alternative approach is to simulate the equilibrium shape of the fluid using the public domain program SURFACE EVOLVER (Brakke, 1996), which has been applied to fluids on flat surfaces (Prabhala et al, 2010;Santos & White, 2011) and nonplanar geometries (Chatain et al, 2006;Fig. 2.…”

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“…In addition, the water droplet attains a new Young angle (q Ynew $ 132 ), about 20 below its initial value (q Y ¼ 152 ). 31 Li et al have proposed that the contact angle value is based on local wetting at the contact line. Moreover, EW response (see Fig.…”