Recent Mathematical Analysis of Contact Angle Hysteresis

Keywords Wenzels equation, Cassies equation, contact angle hysteresis, 

The study of wetting phenomena is of critical importance for many industrial applications [ 1 -4], from oil recovery in petroleum reservoirs to microscopic flows in microfluidics. Generally speaking, wetting is the ability of liquid to maintain contact with or spread on a solid surface. In principle, the wetting property is determined by microscopic molecular interactions of liquid, air and the solid surface, including short-ranged chemical 

Mittal (ed.) Advances in Contact Angle, Wettabilty and Adhesion Volume 2, (111-127) 2015 Scrivener Publishing LLC 

Wetting on rough or chemically patterned surfaces has also been studied for a long time. Two well-known equations, the Wenzel s equation [11] and the Cassie s equation [12] are introduced to characterize the macroscopic apparent contact angle in terms of surface roughness and inhomogeneity (see Equations (4.6) and (4.7) in Section 4.3). There have been many works on the derivation and validity of these two equations [10,13-17], despite some controversies on their correctness [18-22]. In particular, they cannot describe the contact angle hysteresis and cannot explain some of the experimental observations [18,23]. Various modifications or variations of these two equations are proposed and studied [10,20,24-26]. 

In this paper, we review some of our recent mathematical analysis for wetting and contact angle hysteresis phenomena. We concentrate mainly on the illustration of the analysis results and our understanding of wetting, but ignore the technical details, which can be found in our published papers. The outline of the paper is as follows. In Section 4.2, we introduce 

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Recent Mathematical Analysis of Contact Angle Hysteresis 113... 

Recent Mathematical Analysis of Contact Angle Hysteresis 121 Equivalently, the relative position of the contact point is given by ... 

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