Capillarity, fundamental equation

Equation II-7 is the fundamental equation of capillarity and will recur many times in this chapter. 

Equation (3) is the fundamental equation of Capillarity. It permits the calculation of the forms of liquid surfaces when the weight of the liquid is not negligible, for the pressures can be expressed in terms of the height above a fixed point in the fluids, and their densities. 

The exact calculation of the weight of liquid lifted, in terms of the surface tension and density, is difficult and requires usually special solutions of the fundamental equation of Capillarity, for figures which often are not figures of revolution. The pull may reach a maximum some distance before the object is completely detached and the measurement of this maximum is considered more satisfactory than that of the pull at the moment of detachment.7 In most cases, however, the pull is applied by means of a torsion balance, and the upward motion of the object cannot be checked after the maximum pull is past, so that the detachment takes place almost immediately the maximum pull is reached. 

To describe wettability in a porous reservoir rock requires inclusion of both the fluid surface interaction and curvature of pore walls. Both are responsible for the capillary rise seen in porous media. The fundamental equation of capillarity is given by the equation of Young and Laplace [2]... 

Equation 9.6 and Equation 9.9 through Equation 9.12 are the basis of the classic theory of capillarity [9], The moderate surface curvature that was assumed for these equations follows the fundamental Gibbs Equation 9.1 and Equation 9. lb. However, there was a problem of application of the classic theory of capillarity to the region of high surface curvatures that corresponds to the nanoparticles (down to 2 nm). 

Young-Laplace Equation The fundamental relationship giving the pressure difference across a curved interface in terms of the surface or interfacial tension and the principal radii of curvature. In the special case of a spherical interface, the pressure difference is equal to twice the surface (or interfacial) tension divided by the radius of curvature. Also referred to as the equation of capillarity. 

In his classic investigation of capillarity, Laplace [76] explained the adhesion of liquids to solids in terms of central fields of force between the volume elements of a continuous medium. This approach was illuminating about the origin of surface tension and energy and their relation to the internal pressure, and it resulted in the fundamental differential equation of capillarity which has been the basis of all... 

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