منابع مشابه
Pressurized liquid in nanopores: a modified Laplace-Young equation.
In the current study, we analyze the motion of pressurized water molecules in nanopores of a well-crystallized, hydrophobic zeolite using both experiment and molecular dynamics simulation. It is discovered that, contradictory to the prediction of the classic Laplace-Young equation, the required infiltration pressure is highly dependent on the infiltration volume. A modified Laplace-Young equati...
متن کاملEffectiveness of the Young-Laplace equation at nanoscale
Using molecular dynamics (MD) simulations, a new approach based on the behavior of pressurized water out of a nanopore (1.3-2.7 nm) in a flat plate is developed to calculate the relationship between the water surface curvature and the pressure difference across water surface. It is found that the water surface curvature is inversely proportional to the pressure difference across surface at nano...
متن کاملComputation of Capillary Surfaces for the Laplace-young Equation
A novel hybrid finite-element/finite-volume numerical method is developed to determine the capillary rise of a liquid with a free surface (under surface tension and gravitational forces). The few known exact analytical solutions are used to verify the numerical computations and establish their accuracy for a range of liquid contact angles. The numerical method is then used to ascertain the limi...
متن کاملThe Laplace Equation
Definition 1. Among the most important and ubiquitous of all partial differential equations is Laplace’s Equation: ∆u = 0, where the Laplacian operator ∆ acts on the function u : U → R (U is open in R) by taking the sum of the unmixed partial derivatives. For example: n = 1: ∆u = ∂ 2u ∂x2 = u = 0 In this simple case, the solution u = ax + b is found by integrating twice. n = 2: ∆u = ∂ 2u ∂x1 + ...
متن کاملA Visit with the ∞-laplace Equation
(0.1) F∞(u, U) := ‖|Du|‖L∞(U) among all such functions. Here |Du| is the Euclidean length of the gradient Du of u. We will also be interested in the “Lipschitz constant” functional as well. If K is any subset of IR and u : K → IR, its least Lipschitz constant is denoted by (0.2) Lip(u,K) := inf {L ∈ IR : |u(x)− u(y)| ≤ L|x− y| ∀ x, y ∈ K} . Of course, inf ∅ = +∞. Likewise, if any definition suc...
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ژورنال
عنوان ژورنال: The Quarterly Journal of Mechanics and Applied Mathematics
سال: 1999
ISSN: 0033-5614,1464-3855
DOI: 10.1093/qjmam/52.1.73