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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).
Schematic of capillary rise of water to demonstrate measurements used in the Young-Laplace equation. 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:
In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties.This is often written as = or =, where = = is the Laplace operator, [note 1] is the divergence operator (also symbolized "div"), is the gradient operator (also symbolized "grad"), and (,,) is a twice-differentiable real-valued function.
Experimental demonstration of Laplace pressure with soap bubbles. 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 ...
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 ...
In mathematics, and specifically in potential theory, the Poisson kernel is an integral kernel, used for solving the two-dimensional Laplace equation, given Dirichlet boundary conditions on the unit disk. The kernel can be understood as the derivative of the Green's function for the Laplace equation.
He first solved Young-Laplace equation for equilibrium shapes and showed that the Legendre condition for the second variation is always satisfied. Therefore, the stability is determined by the absence of negative eigenvalue of the linearized Young-Laplace equation. This approach of determining stability from second variation is used now widely. [8]