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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.
The Laplace pressure is determined from the Young–Laplace equation given as [2] = (+), where and are the principal radii of curvature and (also denoted as ) is the surface tension. Although signs for these values vary, sign convention usually dictates positive curvature when convex and negative when concave.
Surface tension is an important factor in the phenomenon of capillarity. Surface tension has the dimension of force per unit length, or of energy per unit area. [3] The two are equivalent, but when referring to energy per unit of area, it is common to use the term surface energy, which is a more general term in the sense that it applies also to ...
The capillary length or capillary constant is a length scaling factor that relates gravity and surface tension. It is a fundamental physical property that governs the behavior of menisci, and is found when body forces (gravity) and surface forces (Laplace pressure) are in equilibrium.
In mathematics, the Laplace transform, named after Pierre-Simon Laplace (/ l ə ˈ p l ɑː s /), is an integral transform that converts a function of a real variable (usually , in the time domain) to a function of a complex variable (in the complex-valued frequency domain, also known as s-domain, or s-plane).
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 ...
Cloth, treated to be hydrophobic, shows a high contact angle. The theoretical description of contact angle arises from the consideration of a thermodynamic equilibrium between the three phases: the liquid phase (L), the solid phase (S), and the gas or vapor phase (G) (which could be a mixture of ambient atmosphere and an equilibrium concentration of the liquid vapor).
The Laplace number (La), also known as the Suratman number (Su), is a dimensionless number used in the characterization of free surface fluid dynamics. It represents a ratio of surface tension to the momentum-transport (especially dissipation) inside a fluid. It is named after Pierre-Simon Laplace and Indonesian physicist P. C. Suratman. [1]