A new model for contact angle hysteresis

Antonio DeSimone; Natalie Grunewald; Felix Otto; Antonio DeSimone; Natalie Grunewald; Felix Otto

doi:10.3934/nhm.2007.2.211

Networks and Heterogeneous Media

2007, Volume 2, Issue 2: 211-225. doi: 10.3934/nhm.2007.2.211

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A new model for contact angle hysteresis

1.
SISSA-International School for Advanced Studies, Via Beirut 2-4, 34014 Trieste
2.
Institut für Angewandte Mathematik, Wegelerstr. 10, 53115, Bonn

Received: 01 July 2006 Revised: 01 January 2007
Primary: 76B45, 49S05; Secondary: 74C05.

We present a model which explains several experimental observations relating contact angle hysteresis with surface roughness. The model is based on the balance between released capillary energy and dissipation associated with motion of the contact line: it describes the stick–slip behavior of drops on a rough surface using ideas similar to those employed in dry friction, elasto–plasticity and fracture mechanics. The main results of our analysis are formulas giving the interval of stable contact angles as a function of the surface roughness. These formulas show that the difference between advancing and receding angles is much larger for a drop in complete contact with the substrate (Wenzel drop) than for one whose cavities are filled with air (Cassie-Baxter drop). This fact is used as the key tool to interpret the experimental evidence.
- Surface tension and related phenomena,
- Wetting,
- Drops and bubbles
Citation: Antonio DeSimone, Natalie Grunewald, Felix Otto. A new model for contact angle hysteresis[J]. Networks and Heterogeneous Media, 2007, 2(2): 211-225. doi: 10.3934/nhm.2007.2.211

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Abstract

We present a model which explains several experimental observations relating contact angle hysteresis with surface roughness. The model is based on the balance between released capillary energy and dissipation associated with motion of the contact line: it describes the stick–slip behavior of drops on a rough surface using ideas similar to those employed in dry friction, elasto–plasticity and fracture mechanics. The main results of our analysis are formulas giving the interval of stable contact angles as a function of the surface roughness. These formulas show that the difference between advancing and receding angles is much larger for a drop in complete contact with the substrate (Wenzel drop) than for one whose cavities are filled with air (Cassie-Baxter drop). This fact is used as the key tool to interpret the experimental evidence.
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