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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 earliest study on the relationship between contact angle and surface tensions for sessile droplets on flat surfaces was reported by Thomas Young in 1805. [2] A century later Gibbs [3] proposed a modification to Young's equation to account for the volumetric dependence of the contact angle.
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 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.
Here the key difference to notice is that there is no surface tension between the solid and the vapor for the second surface tension component. This is because of the assumption that the surface of air that is exposed is under the droplet and is the only other substrate in the system. Subsequently, the equation is then expressed as (1 – f ...
The surface tension can be determined using the Young–Laplace equation in the reduced form for spherical bubble shape within the liquid. [3] = (σ: surface tension, ΔP max: maximum pressure drop, R cap: radius of capillary)
Young's equation describes the contact angle of a liquid drop on a plane solid surface as a function of the surface free energy, the interfacial free energy and the surface tension of the liquid. Young's equation was developed further some 60 years later by Dupré to account for thermodynamic effects, and this is known as the Young–Dupré ...
The Young Equation explains that the surface tension between the liquid and vapor phases is scaled to the cosine of the contact angle. As shown in the figure to the right, the contact angle between a condensed liquid and the inner wall of a capillary can affect the radius of curvature a great deal.