Young-Laplace
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.

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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. ... The above relation is generally known as the Young-Laplace equation, and can also be derived by minimizing the free energy of the ...
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 .... In physics, the Young–Laplace equation is a nonlinear partial differential equation that describes the ...
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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 ..... which is the constant volume analog of the Young–Laplace equation.
www.chemistry.uoguelph.ca/goldman/online%20publication.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 ...
www.uv.es/~juliop/docencia/Young-Laplace.pdf
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Comparison of the Young-Laplace law and finite element based ...
BACKGROUND: Both the Young-Laplace law and finite element (FE) based methods have been used to calculate left ventricular wall stress. We tested the ...
www.ncbi.nlm.nih.gov/pubmed/21172505
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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 ...
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CONTACT ANGLES: Laplace-Young Equation and Dupre ... - imal
Apr 16, 2010 ... ○The Fully-Augmented Young-Laplace Equation ... Young-Laplace Equation in Differential Form: 2 p p ... The equation of Young and Laplace: ...
www.imal.santafe-conicet.gov.ar/imagenes/seminario/seminario-IMAL_2010-04-16.pdf
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Young-Laplace in science
[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 ...
Comparison of the Young-Laplace Law and Finite Element Based ...
a Department of Surgery, University of California, San Francisco, California ... We tested the hypothesis that the Young-Laplace law is able to reproduce results ...
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.
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 ...
Comparison of the Young-Laplace law and finite element based ...
Department of Surgery, University of California, San Francisco, Veterans Affairs ... We tested the hypothesis that the Young-Laplace law is able to reproduce ...
[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 ...
[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 ...
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View the profiles of people named Young Laplace on Facebook. ... clock promotions llcStudied at Southeastern Louisiana UniversityLives in LaPlace, Louisiana ...
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 ...
[PDF]Dissipative Interfaces and Departures from the Young-Laplace ...
Young-Laplace Equation. A. Yeung,† T. Dabros,‡ and J. Masliyah*,†. Department of Chemical and Materials Engineering, University of Alberta,. Edmonton ...
Books on the term Young-Laplace
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 ...
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 ... We have obtained the Young-Laplace relationship from normal-stress balance (2-135) by invoking "the limiting case of no motion in the fluids.
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 ...
Emulsions, Foams, and Suspensions
Emulsions, Foams, and Suspensions
Laurier L. Schramm, 2006
If the principal radii of curvature are R1 and R2 then, Dp=pA – pB=c(1/R1 + 1/ R2 ) (3.6) This is the Young–Laplace equation. For spherical droplets or bubbles of radius R in a dilute emulsion or foam, Dp=pA – pB=2 c/R (3.7) so that Dp varies ...
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Young-Laplace
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LaPlace man booked with cruelty to young son who knocked over TV | NOLA.com
Deputies from the St. John the Baptist Parish Sheriff's Office have arrested a LaPlace man on suspicion of striking his 4-year-old son and bursting his eardrum, according to authorities. Kerry Clofer, 21, of 1612 Yorktowne Drive was booked with cruelty to a juvenile after evidence suggested he hit his son for knocking over a television. "The boy had bruises around the left ear, and after a physical examination, it was learned he sustained a busted eardrum," said Capt. Dane Clement, a Sheriff's Office spokesman. On Feb. 7, Clofer picked up his son from the boy's mother for a weeklong custody stay, Clement said. When the boy's mother picked the child up from school later that week, teachers at the school informed her about the boy's injuries, Clement said. St. John deputies met with the mother of the 4-year-old Garyville boy, and she said her son suffered injuries while in the custody of his father, Clement said. "When the boy was asked how he was hurt, he said he got in trouble at his daddy's house for knocking over the television, and his dad hit him," Clement said. After an investigation by St. John detectives, an arrest warrant was issued...
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yovisto blog: Pierre Simon de Laplace and his true love for Astronomy and Mathematics
On March 28, 1749, French mathematician and astronomer Pierre Simon marquise de Laplace was born, whose work was pivotal to the development of mathematical astronomy and statistics. One of his major achievements was the conclusion of the five-volume Mécanique Céleste (Celestial Mechanics) which translated the geometric study of classical mechanics to one based on calculus, opening up a broader range of problems.
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CiteULike: Electrofluidic displays using Young-Laplace transposition of brilliant pigment dispersions
J. Heikenfeld, K. Zhou, E. Kreit et al. Nat Photon, Vol. 3, No. 5. (May 2009), pp. 292-296, doi:10.1038/nphoton.2009.68. e-paper
www.citeulike.org/user/ImranRaoufMalik/article/4450099
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