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In physics, the Young–Laplace equation (/ l ə ˈ p l ɑː s /) is an algebraic equation that describes the capillary pressure difference sustained across the interface between two static fluids, such as water and air, due to the phenomenon of surface tension or wall tension, although use of the latter is only applicable if assuming that the wall is very thin.
In contrast, the equilibrium contact angle described by the Young-Laplace equation is measured from a static state. Static measurements yield values in-between the advancing and receding contact angle depending on deposition parameters (e.g. velocity, angle, and drop size) and drop history (e.g. evaporation from time of deposition).
The Young–Laplace equation is the force up description of capillary pressure, and the most commonly used variation of the capillary pressure equation: [2] [1] = where: is the interfacial tension is the effective radius of the interface is the wetting angle of the liquid on the surface of the capillary
Figure 2: Wetting of different fluids: A shows a fluid with very little wetting, while C shows a fluid with more wetting. A has a large contact angle, and C has a small contact angle. The contact angle (θ), as seen in Figure 1, is the angle at which the liquid–vapor interface meets the solid–liquid interface. The contact angle is ...
The Laplace pressure is the pressure difference between the inside and the outside of a curved surface that forms the boundary between two fluid regions. [1] The pressure difference is caused by the surface tension of the interface between liquid and gas, or between two immiscible liquids.
The contact angle is defined as the angle formed by the intersection of the liquid-solid interface and the liquid–vapour interface. [2] The size of the angle quantifies the wettability of liquid, i.e., the interaction between the liquid and solid surface. A contact angle of = can be considered, perfect wetting.
θ is the contact angle of the liquid on the tube wall; ρ is the mass density (mass per unit volume); r 0 is the tube radius; g is the gravitational acceleration. It is only valid if the tube is cylindrical and has a radius (r 0) smaller than the capillary length (= / ()). In terms of the capillary length, the law can be written as
When S > 0, the spontaneous spreading occurs, and if S < 0, partial wetting is observed, meaning the liquid will only cover the substrate to some extent. [ 2 ] The equilibrium contact angle θ c {\displaystyle \theta _{\text{c}}} is determined from the Young–Laplace equation .