WebJul 9, 2024 · Note. Equation (6.5.6) is a key equation which occurs when studying problems possessing spherical symmetry. It is an eigenvalue problem for Y(θ, ϕ) = Θ(θ)Φ(ϕ), LY = − λY, where L = 1 sinθ ∂ ∂θ(sinθ ∂ ∂θ) + 1 sin2θ ∂2 ∂ϕ2. The eigenfunctions of this operator are referred to as spherical harmonics. Webstanding of the Young–Laplace equation. Manning1 refers to the basic thermodynamic derivation of the Young–Laplace equation. However, there exists also a mechanical derivation,5,6 the implications of which need to be understood. The normal stress balance for fluids meeting at an interface is DP = r n˜ = g H = g(1/R 1 +1/R 2) (10)
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In physics, the Young–Laplace equation 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 … See more If the pressure difference is zero, as in a soap film without gravity, the interface will assume the shape of a minimal surface. See more In medicine it is often referred to as the Law of Laplace, used in the context of cardiovascular physiology, and also respiratory physiology, though the latter use is often … See more • Maxwell, James Clerk; Strutt, John William (1911). "Capillary Action" . In Chisholm, Hugh (ed.). Encyclopædia Britannica. … See more The equation also explains the energy required to create an emulsion. To form the small, highly curved droplets of an emulsion, extra energy is required to overcome the large pressure that results from their small radius. The Laplace … See more Francis Hauksbee performed some of the earliest observations and experiments in 1709 and these were repeated in 1718 by James Jurin who observed that the height of fluid in a capillary … See more WebApr 1, 2016 · In the present work, the effectiveness of Y-L equation at nanoscale is checked using MD simulations and the influences of surface size, temperature and electrolyte ions on the water surface ... how to say thicket
Laplace’s equation Definition, Uses, & Facts Britannica
WebFeb 17, 2024 · Laplace’s equation is a special case of Poisson’s equation ∇ 2R = f, in which the function f is equal to zero. Many physical systems are more conveniently described by the use of spherical or cylindrical coordinate systems. Laplace’s equation can be recast in these coordinates; for example, in cylindrical coordinates, Laplace’s … Web3 Laplace’s Equation We now turn to studying Laplace’s equation ∆u = 0 and its inhomogeneous version, Poisson’s equation, ¡∆u = f: We say a function u satisfying … WebApr 12, 2024 · Our mathematical derivation of an extension of the law of Laplace, from circular to cloverleaf cross-sectional geometries of the aortic root, has implications for measurement of aortic root “diameter.”. The suggested method is as follows: (1) the “center” of the aortic root is identified by drawing three sinus-to-commissure lines. how to say thibault