Young–Laplace equation
In physics, the Young–Laplace equation is a nonlinear partial differential 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 usage on the latter is only applicable if assuming that the wall is very thin. The Young–Laplace equation relates the pressure difference to the shape of the surface or wall and it is fundamentally important in the study of static capillary surfaces. It is a statement of normal stress balance for static fluids meeting at an interface, where the interface is treated as a surface (zero thickness):
\begin{align}<br />
\Delta p &= -\gamma \nabla \cdot \hat n \\<br />
&= 2 \gamma H \\<br />
&= \gamma \left(\frac{1}{R_1} + \frac{1}{R_2}\right)<br />
\end{align}
where \Delta p is the pressure difference across the fluid interface, γ is the surface tension (or wall tension), \hat n is the unit normal pointing out of the surface, H is the mean curvature, and R_1 and R_2 are the principal radii of curvature. (Some authors[who?] refer inappropriately to the factor 2H as the total curvature.) Note that only normal stress is considered, this is because it can be shown that a static interface is possible only in the absence of tangential stress.
The equation is named after Thomas Young, who developed the qualitative theory of surface tension in 1805, and Pierre-Simon Laplace who completed the mathematical description in the following year. It is sometimes also called the Young–Laplace–Gauss equation, as Gauss unified the work of Young and Laplace in 1830, deriving both the differential equation and boundary conditions using Johann Bernoulli's virtual work principles.

This is an excerpt from the article Young–Laplace equation from the Wikipedia free encyclopedia. A list of authors is available at Wikipedia.
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Young–Laplace equation - Wikipedia, the free encyclopedia
In physics, the Young–Laplace equation is a nonlinear partial differential equation that describes the capillary pressure difference sustained across the interface ...
en.wikipedia.org/wiki/Young%E2%80%93Laplace_equation
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Young-Laplace Equation
Young-Laplace Equation. Consider an interface separating two immiscible fluids that are in equilibrium with one another. Let these two fluids be denoted 1 and ...
farside.ph.utexas.edu/teaching/336L/Fluidhtml/node45.html
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The Young-Laplace equation
Chapter 1. The Young-Laplace equation. To examine the relation between the surface tension at the interface between two immiscible liquids and the pressure ...
windw.dk/notes/laplace_young.pdf
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Biomaterials Lecture 12 Surfaces: Surface Tension and Young ...
Surfaces: Surface Tension and Young. Laplace Equation. Unless otherwise noted, source Information for the following slides: 1) B. Ratner, A. Hoffman, ...
www.usm.edu/pattonresearchgroup/PSC475/Lecture%20Notes/Lec12_Surfaces.pdf
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Generalizations of the Young–Laplace equation for the pressure of a ...
The Young–Laplace equation for the pressure of a mechanically stable gas bubble is generalized to include the effects of both surface tension and elastic forces ...
www.chemistry.uoguelph.ca/goldman/online%20publication.pdf
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The Young–Laplace equation links capillarity with geometrical ...
The most important equation of capillarity, the Young–Laplace equation, has the same structure as the Gullstrand equation of geometrical optics, which relates ...
iopscience.iop.org/0143-0807/24/2/356
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Young-Laplace Equation | Facebook
Young-Laplace Equation. 20 likes · 0 talking about this.
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Solution of the Young-Laplace equation for three particles - Massey ...
gration to solve the Young-Laplace equation between two particles. Given the radii ... (3) analysed the Young-Laplace equation in two dimensions, using circular ...
muir.massey.ac.nz/bitstream/handle/10179/4413/Solution_of_the_Young-Laplace_equation_for_three_particles.pdf?sequence=1
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Example problem: The Young Laplace equation - Oomph-lib
Aug 10, 2009 ... other: The Young-Laplace equation is the Euler-Lagrange equation of the variational principle. 1.1.3 Parametric representation. To deal with ...
oomph-lib.maths.man.ac.uk/doc/young_laplace/young_laplace/latex/refman.pdf
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On the demonstration of the Young- Laplace equation
The Young-Laplace equation is usually introduced using mechanical rather than thermodynamic arguments when teaching surface phenomena at an ...
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Solution of the Young-Laplace equation for three particles
Massey Research Online Home; >; Massey University Departments; >; Institute of Natural and ... Solution of the Young-Laplace equation for three particles ...
[PDF]CONTACT ANGLES: Laplace-Young Equation and Dupre ... - imal
Apr 16, 2010 ... The University of Alabama in Huntsville ... ○The Fully-Augmented Young-Laplace Equation ... Young-Laplace Equation in Differential Form: 2 ...
[PDF]Generalizations of the Young–Laplace equation for the pressure of a ...
Physics Institute, University of Guelph, Guelph, Ontario N1G 2W1, Canada ... The Young–Laplace equation for the pressure of a mechanically stable gas bubble ...
Young–Laplace equation - Wikipedia, the free encyclopedia
In physics, the Young–Laplace equation is a nonlinear partial differential equation that describes the .... Cambridge, England: Cambridge University Press, 1928.
Young–Laplace equation for liquid crystal interfaces | Browse ...
Young–Laplace equation for liquid crystal interfaces. Alejandro D. Rey. Department of Chemical Engineering, McGill University, 3610 University Street, Montreal ...
Young–Laplace equation - Nova - University of Newcastle
Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.13/ 33883. OpenURL Link. Title: Empirical equations for meniscus depression by ...
[PDF]Numerical Solutions for Intermediate Angles of the Laplace-Young ...
Numerical Solutions for Intermediate Angles of the Laplace-Young. Capillary Equations. Genevieve Dupuis. University of Notre Dame. Jessica Flores. University ...
[PDF]Young–Laplace equation for liquid crystal interfaces
Young–Laplace equation for liquid crystal interfaces. Alejandro D. Reya). Department of Chemical Engineering, McGill University, 3610 University Street, ...
Generalizations of the Young-Laplace equation for the pressure of a ...
Nov 14, 2009 ... Generalizations of the Young-Laplace equation for the pressure of a ... Guelph- Waterloo Physics Institute, University of Guelph, Guelph, Ontario ...
The Young–Laplace equation links capillarity with geometrical ...
The most important equation of capillarity, the Young–Laplace equation, has the same structure as the Gullstrand equation of geometrical optics, which relates ...
Books on the term Young–Laplace equation
Physics and Chemistry of Interfaces
Physics and Chemistry of Interfaces
Hans-J?rgen Butt, Karlheinz Graf, Michael Kappl, 2006
Since the part is arbitrary the Young–Laplace equation must be valid everywhere . A X C B D d R ... When applying the equation of Young and Laplace to simple geometries it is usually obvious at which side the pressure is higher. For example ...
Introduction to Interfaces and Colloids
Introduction to Interfaces and Colloids
John C. Berg, 2010
Using expressions of the above type for ∆p, the Young-Laplace equation for the special cases of curvature discussed earlier may be written as follows: 1. Sphere: "p = "p0 = 2# R . 2. Circular cylinder: "p = "p0 = 3. General cylindrical surface: "p ...
The Measurement, Instrumentation, and Sensors: Handbook
The Measurement, Instrumentation, and Sensors: Handbook
John-G Webster, 1999
FIGURE 31.4 (a) A pendant drop showing the characteristic dimensions, d, and d, , and the coordinates used in the Young-Laplace equation, (b) A sessile drop showing the characteristic dimensions R and h. where y is the surface tension, and ...
Advanced Transport Phenomena: Fluid Mechanics and Convective ...
Advanced Transport Phenomena: Fluid Mechanics and Convective ...
L. Gary Leal, 2007
(2-136) This equilibrium condition is known as the Young-Laplace equation. The physical significance of (2-136) is that the pressure inside a curved interface at equilibrium is larger than that outside by an amount that depends on the curvature ...
Bacterial Growth and Form
Bacterial Growth and Form
A.L. Koch, 2001
The resulting equation is: P - Ne/ri + N0/r2 Pressure vessel stresses In this equation v\ and r2 are the two principal radii of curvature, as before. This expression is reminiscent of the ' Young-LaPlace equation', where both Ns were replaced by T ...
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Young–Laplace equation
Laplace and the floating needle | Sciencelens
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sciencelens.co.nz/2013/03/05/laplace-and-the-floating-needle/
Aliceland: Young-Laplace or Gibbs-Thomson equation
"Every idea in the study of phase transformations can be traced to Gibbs" is a favourite quote of Abi. The latest American Journal of Physics carries an article about the Young-Laplace equation and its derivation, which, in metallurgical literature goes by the name of Gibbs-Thomson equation.
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The Reference Frame: Pierre-Simon Laplace: 260th birthday
The best theoretical physics blog that the search engine can offer you, by a Czech conservative string theorist, focusing on high-energy physics and the climate change facts
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"A microscale model for thin-film evaporation in capillary wick structu" by Ram Ranjan, Jayathi Y. Murthy et al.
A numerical model is developed for the evaporating liquid meniscus in wick microstructures under saturated vapor conditions. Four different wick geometries representing common wicks used in heat pipes, viz., wire mesh, rectangular grooves, sintered wicks and vertical microwires, are modeled and compared for evaporative performance. The solid–liquid combination considered is copper–water. Steady evaporation is modeled and the liquid–vapor interface shape is assumed to be static during evaporation. Liquid–vapor interface shapes in different geometries are obtained by solving the Young–Laplace equation using Surface Evolver. Mass, momentum and energy equations are solved numerically in the liquid domain, with the vapor assumed to be saturated. Evaporation at the interface is modeled by using heat and mass transfer rates obtained from kinetic theory. Thermocapillary convection due to non-isothermal conditions at the interface is modeled for all geometries and its role in heat transfer enhancement from the interface is quantified for both low and high superheats. More than 80% of the evaporation heat transfer is noted to occur from the thin-film region of the liquid meniscus. The very small Capillary and Weber numbers resulting from the small fluid velocities near the interface for low superheats validate the assumption of a static liquid meniscus shape during evaporation. Solid–liquid contact angle, wick porosity, solid–vapor superheat and liquid level in the wick pore are varied to study their effects on evaporation from the liquid meniscus.
docs.lib.purdue.edu/coolingpubs/142/
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