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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).
At the turn of the 19th century they independently derived pressure equations, but due to notation and presentation, Laplace often gets the credit. The equation showed that the pressure within a curved surface between two static fluids is always greater than that outside of a curved surface, but the pressure will decrease to zero as the radius ...
With this equation and model, Everett noted the behavior of water and ice given different pressure conditions at the solid-liquid interface. Everett determined that if the pressure of the ice is equal to the pressure of the liquid underneath the surface, ice growth is unable to continue into the capillary.
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.
At the meniscus interface, due to the surface tension, there is a pressure difference of =, where is the pressure on the convex side; and is known as Laplace pressure. If the tube has a circular section of radius r 0 {\displaystyle r_{0}} , and the meniscus has a spherical shape, the radius of curvature is r = r 0 / cos θ {\displaystyle r ...
In the mathematical study of partial differential equations, the Bateman transform is a method for solving the Laplace equation in four dimensions and wave equation in three by using a line integral of a holomorphic function in three complex variables. It is named after the mathematician Harry Bateman, who first published the result in (Bateman ...
At the point of the maximum bubble pressure, the bubble has a complete hemispherical shape whose radius is identical to the radius of the capillary denoted by Rcap. The surface tension can be determined using the Young–Laplace equation in the reduced form for spherical bubble shape within the liquid. [3]