Contact angle; Young's equqtion.

Contact angle
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side view of a drop of water on a gray cloth. Looks like about a 120 degree angle.
Cloth, treated to be hydrophobic, shows a high contact angle.

The contact angle is the angle, conventionally measured through the liquid, where a liquid–vapor interface meets a solid surface. It quantifies the wettability of a solid surface by a liquid via the Young equation. A given system of solid, liquid, and vapor at a given temperature and pressure has a unique equilibrium contact angle. However, in practice contact angle hysteresis is observed, ranging from the so-called advancing (maximal) contact angle to the receding (minimal) contact angle. The equilibrium contact is within those values, and can be calculated from them. The equilibrium contact angle reflects the relative strength of the liquid, solid, and vapor molecular interaction.

Contents

1 Thermodynamics
1.1 Hysteresis
1.2 Effect of roughness to contact angles
1.3 Dynamic Contact Angles
2 Contact angle curvature
3 Typical contact angles
4 Control of contact angles
5 Measuring methods
5.1 The static sessile drop method
5.2 The pendant drop method
5.3 The dynamic sessile drop method
5.4 Dynamic Wilhelmy method
5.5 Single-fiber Wilhelmy method
5.6 Single-fiber meniscus method
5.7 Washburn's equation capillary rise method
6 See also
7 References
8 Further reading

Thermodynamics
Schematic of a liquid drop showing the quantities in the Young equation.

The shape of a liquid–vapor interface is determined by the Young–Laplace equation, with the contact angle playing the role of a boundary condition via the Young equation.

The theoretical description of contact arises from the consideration of a thermodynamic equilibrium between the three phases: the liquid phase (L), the solid phase (S), and the gas or vapor phase (G) (which could be a mixture of ambient atmosphere and an equilibrium concentration of the liquid vapor). (The "gaseous" phase could be replaced by another immiscible liquid phase.) If the solid–vapor interfacial energy is denoted by γ S G {\displaystyle \gamma _{SG}} \gamma_{SG}, the solid–liquid interfacial energy by γ S L {\displaystyle \gamma _{SL}} \gamma_{SL}, and the liquid–vapor interfacial energy (i.e. the surface tension) by γ L G {\displaystyle \gamma _{LG}} \gamma_{LG}, then the equilibrium contact angle θ C {\displaystyle \theta _{\mathrm {C} }} \theta_\mathrm{C} is determined from these quantities by the Young equation:

γ S G − γ S L − γ L G cos ⁡ θ C = 0 {\displaystyle \gamma _{\mathrm {SG} }-\gamma _{\mathrm {SL} }-\gamma _{\mathrm {LG} }\cos \theta _{\mathrm {C} }=0\,} \gamma _{{\mathrm {SG}}}-\gamma _{{\mathrm {SL}}}-\gamma _{{\mathrm {LG}}}\cos \theta _{{\mathrm {C}}}=0\,

The contact angle can also be related to the work of adhesion via the Young–Dupré equation:

γ ( 1 + cos ⁡ θ C ) = Δ W S L V {\displaystyle \gamma (1+\cos \theta _{\mathrm {C} })=\Delta W_{\mathrm {SLV} }\,} \gamma (1 + \cos \theta_\mathrm{C} )= \Delta W_\mathrm{SLV} \,

where Δ W S L V {\displaystyle \Delta W_{\mathrm {SLV} }} \Delta W_\mathrm{SLV} is the solid – liquid adhesion energy per unit area when in the medium V.