Young-Laplace equation from Newton mechanics

1 Young-Laplace equation from Newton mechanics 

We can derive the simplest form of the Young-Laplace equation for a spherical vapor bubble in equilibrium with liquid in a one-component system (or a liquid drop in air) from Newton mechanics. In the absence of any external field such as gravitational, magnetic or electrical fields, the bubble will assume a spherical shape, and the force acting towards the boundary of the bubble (or liquid drop) from the interior of the bubble is given as 

the work to diminish the radius of the spherical bubble is, dW7 = FydRsph from Newton mechanics, and dWr= ycLA, from Equation (189), and A = 4 Rsph, from spherical geometry, then we have 

Finterior = Fexteiioi at equilibrium, then by combining Equations (289)—(291), we obtain, 

By rearrangement of Equation (292), we may write for the pressure difference between the inside and outside of the spherical bubble (or liquid drop) 

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