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contact angle

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

Measuring methods

A modern contact angle goniometer.
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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 Wetting force on the solid is measured as the solid is immersed in or withdrawn from a liquid of known surface tension.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.

Typical contact angles

There are a number of independent methods for determining the surface tension of liquids on solid surface. The interfacial tension between a solid and a liquid is measured by contact angle as discussed in terms of Young's equation in below Thermodynamic section. On extremely hydrophilic surfaces, a water droplet will completely spread (an effective contact angle of 0°). This occurs for surfaces that have a large affinity for water (including materials that absorb water). Theoretically, surface with contact angle larger than 90° will be hydrophobic. And, surface with contact angle lower than 90° will be hydrophilic. On many highly hydrophilic surfaces, water droplets will exhibit contact angles of 0° to 30°. 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.

Thermodynamics

A contact angle of a liquid sample
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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 γSV, the solid-liquid interfacial energy as γSL 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):

0=\gamma_\mathrm{SV} - \gamma_\mathrm{SL} - \gamma \cos \theta \,

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:

\gamma (1 + \cos \theta )= \Delta W_\mathrm{SLV} \,

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

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