Young-Laplace equation definition

In most cases of interest, the surface excess mass E is small, so that the acceleration and body force terms may be neglected. Then Equation 1.40 simplifies to two conditions. One of them, V y = 0, requires that interfacial tension be uniform. The other is the Young-Laplace equation (Equation 1.22), which was obtained previously from thermodynamics for situations where body force and acceleration terms were unimportant. That the same equation (Equation 1.22) results from independent thermodynamic and mechanical derivations implies that interfacial tension must have the same value whether it is defined as in Equation 1.9 from energy considerations or as in Equation 1.39 from force considraations. Simply put, the force and energy definitions of interfacial tension are eqnivalrait, a conclusion emphasized in the work of Buff (1956). 

For the pendant drop in figure I, the equations above are subjected to the no-slip boundary conditions at solid surfaces and the kinematic condition on the free surfaces. The kinematic condition implies that there is no liquid crossing the boundary into the gas phase, or in other words forms a definite boundary between the phases. For creeping flows into an atmosphere of gas with minimal velocities there will be no interfacial shear stress tangential to the surface and the normal stress inside the fluid is balanced by the surface tension as described by the famous Young-Laplace equation. 

These concepts were formalized by Laplace who derived mathematical expressions for the mean curvature, and developed a differential equation that must be satisfied on S (Laplace, 1805). In modern notation (Gostick et al., 2010) the resulting Young-Laplace equation relates the pressure differential across the surface Ap to the mean curvature H and provides a definition for the surface tension a ... 

The Laplace-Young equation refers to a spherical phase boundary known as the surface of tension which is located a distance from the center of the drop. Here the surface tension is a minimum and additional, curvature dependent, terms vanish (j ). The molecular origin of the difficulties, discussed in the introduction, associated with R can be seen in the definition of the local pressure. The pressure tensor of a spherically symmetric inhomogeneous fluid may be computed through an integration of the one and two particle density distributions. 

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