Image from a video contact angle device. Water drop on glass.

The contact angle is the angle at which a liquid/vapor interface meets the solid surface. The contact angle is specific for any given system and is determined by the interactions across the three interfaces. Most often the concept is illustrated with a small liquid droplet resting on a flat horizontal solid surface. The shape of the droplet is determined by the Young-Laplace equation. The contact angle plays the role of a boundary condition. Contact angle is measured using a contact angle goniometer. The contact angle is not limited to a liquid/vapour interface; it is equally applicable to the interface of two liquids or two vapours. Image File history File links Image from a video contact angle device. ... Image File history File links Image from a video contact angle device. ... This article is about the material. ... This article is about angles in geometry. ... For other uses, see Liquid (disambiguation). ... This article is about the chemical use. ... In fluid dynamics, the Young–Laplace equation describes the pressure difference over a meniscus between two fluids, where is the pressure difference over the interface, the surface tension, and and are the principal radii of curvature at the interface. ... In mathematics, boundary conditions are imposed on the solutions of ordinary differential equations and partial differential equations, to fit the solutions to the actual problem. ... A goniometer is an instrument that either measures angles or allows an object to be rotated to a precise angular position. ...

Typical contact angles

Consider a liquid drop on a solid surface. If the liquid is very strongly attracted to the solid surface (for example water on a strongly hydrophilic solid) the droplet will completely spread out on the solid surface and the contact angle will be close to 0°. Less strongly hydrophilic solids will have a contact angle up to 90°. On many highly hydrophilic surfaces, water droplets will exhibit contact angles of 0° to 30°. If the solid surface is hydrophobic, the contact angle will be larger than 90° . On highly hydrophobic surfaces the surfaces have water contact angles as high as 150° or even nearly 180°. On these surfaces, water droplets simply rest on the surface, without actually wetting to any significant extent. These surfaces are termed superhydrophobic and can be obtained on fluorinated surfaces (Teflon-like coatings) that have been appropriately micropatterned. This is called the Lotus effect, as these new surfaces are based on lotus plants' surface (which has little protuberances) and would be superhydrophobic even to honey. The contact angle thus directly provides information on the interaction energy between the surface and the liquid. In chemistry, hydrophobic or lipophilic species, or hydrophobes, tend to be electrically neutral and nonpolar, and thus prefer other neutral and nonpolar solvents or molecular environments. ... It has been suggested that this article or section be merged into hydrophobe. ... Distinguished from fluorene and fluorone. ... Teflon is a trademark of DuPont and is commonly used for the chemical compound polytetrafluoroethylene. ... Water on the surface of a lotus leaf The Lotus effect in material science is the observed self-cleaning property found with lotus plants. ...

Sometimes the contact angle is measured through the gas instead of through the liquid, which reverses 0 and 180 in the above explination.

Thermodynamics

A contact angle of a liquid sample

The theoretical description of contact arises from the consideration of a thermodynamic equilibrium between the three phases: the liquid phase of the droplet (L), the solid phase of the substrate (S), and the gas/vapor phase of the ambient (V) (which will be a mixture of ambient atmosphere and an equilibrium concentration of the liquid vapor). The V phase could also be another (immiscible) liquid phase. At equilibrium, the chemical potential in the three phases should be equal. It is convenient to frame the discussion in terms of the interfacial energies. We denote the solid-vapor interfacial energy as γ_SV, the solid-liquid interfacial energy as γ_SL and the liquid-vapor energy (i.e. the surface tension) as simply γ, we can write an equation that must be satisfied in equilibrium (known as the Young Equation): Image File history File links Contact_angle. ... Image File history File links Contact_angle. ... Thermodynamics (Greek: thermos = heat and dynamic = change) is the physics of energy, heat, work, entropy and the spontaneity of processes. ... In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, and chemical equilibrium. ... In the physical sciences, a phase is a set of states of a macroscopic physical system that have relatively uniform chemical composition and physical properties (i. ... For other uses, see Liquid (disambiguation). ... This box:      For other uses, see Solid (disambiguation). ... This article is about the chemical use. ... A substance is soluble in a fluid if it dissolves in the fluid. ... In thermodynamics and chemistry, chemical potential, symbolized by μ, is a term introduced in 1876 by the American mathematical physicist Willard Gibbs, which he defined as follows: Gibbs noted also that for the purposes of this definition, any chemical element or combination of elements in given proportions may be considered a... Surface tension is an effect within the surface layer of a liquid that causes that layer to behave as an elastic sheet. ...

where θ is the experimental contact angle. Thus the contact angle can be used to determine an interfacial energy (if other interfacial energies are known). This equation can be rewritten as the Young-Dupré equation:

where ΔW_SLV is the adhesion energy per unit area of the solid and liquid surfaces when in the medium V.

Measuring methods

A modern contact angle goniometer.

The static sessile drop method 

The sessile drop method is measured by a contact angle goniometer using an optical subsystem to capture the profile of a pure liquid on a solid substrate. The angle formed between the liquid/solid interface and the liquid/vapor interface is the contact angle. Older systems used a microscope optical system with a back light. Current-generation systems employ high resolutions cameras and software to capture and analyze the contact angle.

The dynamic sessile drop method 

The dynamic sessile drop is similar to the static sessile drop but requires the drop to be modified. A common type of dynamic sessile drop study determines the largest contact angle possible without increasing its solid/liquid interfacial area by adding volume dynamically. This maximum angle is the advancing angle. Volume is removed to produce the smallest possible angle, the receding angle. The difference between the advancing and receding angle is the contact angle hysteresis.

Dynamic Wilhelmy method 

A method for calculating average advancing and receding contact angles on solids of uniform geometry. Both sides of the solid must have the same properties. Wetting force on the solid is measured as the solid is immersed in or withdrawn from a liquid of known surface tension.

Single-fiber Wilhelmy method 

Dynamic Wilhelmy method applied to single fibers to measure advancing and receding contact angles.

Powder contact angle method 

Enables measurement of average contact angle and sorption speed for powders and other porous materials. Change of weight as a function of time is measured.

Image File history File links M500. ... Image File history File links M500. ... The sessile drop technique is a test performed to determine the chemical affinity that a liquid has to a solid. ... A goniometer is an instrument that either measures angles or allows an object to be rotated to a precise angular position. ... A system with hysteresis exhibits path-dependence, or rate-independent memory. Consider a deterministic system with no hysteresis and no dynamics. ...

See also

• Goniometer
• Sessile drop technique
• Wetting

A goniometer is an instrument that either measures angles or allows an object to be rotated to a precise angular position. ... The sessile drop technique is a test performed to determine the chemical affinity that a liquid has to a solid. ... Wetting of different fluids. ...

References

• P.G. de Gennes "Wetting: statics and dynamics" Reviews of Modern Physics, 57, 3 (part I), July 1985, p.827-863. DOI: 10.1103/RevModPhys.57.827
• Jacob Israelachvili, Intermolecular and Surface Forces, Academic Press (1985-2004)
• D.W. Van Krevelen, Properties of Polymers, 2nd revised edition, Elsevier Scientific Publishing Company, Amsterdam-Oxford-New York (1976)

Pierre-Gilles de Gennes (October 24, 1932 in Paris – May 18, 2007 in Orsay) was a French physicist and the Nobel laureate in 1991. ... Dr. Jacob Israelachvili is a professor of chemical engineering and materials at the University of California, Santa Barbara (UCSB), and currently the associate director of the Materials Research Laboratory (MRL) at UCSB. Dr. Israelachvilis received his Ph. ...

External links

• Theory of contact angle measurements
• Literature about surface chemistry and contact angle
• Introduction to contact angle