Fundamental equations Young-Laplace equation

Relation 9.77 is usually called the Washburn equation [55,237], One should consider it as a special case of the fundamental Young-Laplace equation [3,9-11], Washburn was the first to propose the use of mercury for measurements of porosity. Now, it is a common method [3,8,53-55] of psd measurements for a range of sizes from several hundreds of microns to 3 to 6 nm. The lower limit is determined by the maximum pressure, which is applied in a mercury porosimeter the limiting size of rWl = 3 nm is achieved under PHg = 4000 bar. The measurements are carried out after vacuum treatment of a sample and filling the gaps between pieces of solid with mercury. Further, the hydraulic system of a device performs the gradual increase of PHg, and the appropriate intmsion of mercury in pores of the decreasing size occurs. 

The Young-Laplace equation has several fundamental implications ... 

The capillary pressure of interest in water-air-GDM systems is the difference between the pressures of the liquid and gas phases across static air-water interfaces within a GDM. This pressure difference is fundamentally related to the mean curvature H of the air-water interfaces through the well-known Young-Laplace equation 22... 

Young—Laplace Equation The fundamental relationship giving the pres-... 

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. 

As indicated above, the Young-Laplace equation (Equation 1.22) is one fundamental result obtained from the theory of interfaces. Because this equation relates interfadal tension to the pressure difference between fluids at each point along an interface, it can be used with the equations of hydrostatics to calculate the shape of a static interface. Or, if interfadal shape can be determined... 

The equation of Young and Laplace describes one of the fundamental laws in interface science If an interface between two fluids is curved, there is a pressure difference across it provided the system is in equilibrium. The Young-Laplace equation relates the pressure difference between the two phases AP and the curvature of the interface. In the absence of gravitation, or if the objects are so small that gravitation is negligible, the Young-Laplace equation is... 

The classical theories of Young,1 Laplace,2 Gauss,8 and Poisson4 all led to the fundamental equation (3) and to some others. It is not proposed... 

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]... 

Any review on the shape of a liquid droplet on top of a solid surface has to start with the pioneering work by P. S. Laplace and Sir Thomas Young almost two centuries ago [1,2], Young and Laplace set out to describe the phenomenon of capillary action in which the liquid inside a small capillary tube may rise several centimeters above the liquid outside the tube [3], To understand this elfect, two fundamental equations were derived by Young and Laplace. The first equation, known as the Laplace or Young Laplace equation [1], relates the curvature at a certain point of the liquid surface to the pressure difference between both sides of the surface, and we consider it next in more detail. The second equation is Young s equation [2], which relates the contact angle to the surface tensions involved. 

Similarly to wetting, the flow of liquids through nanotubes has renewed interest in the area of capillary flow. The fundamental equations used to describe liquid flow in capillaries and tubular structures are the Young-Laplace equation (Eq. 10.4), the Hagen-Poiseuille equation (Eq. 10.5), and the Washburn equation (Eq. 10.6). The first describes the capillary pressure difference across the interface between two fluids (such as at the air-water interface). The second describes the well-developed, laminar flow of an incompressible fluid in a capillary under pressure alone. A simplified version of the third is used to describe the filling of an empty capillary by capillary pressure only, as a function of the wettability of the liquid ... 

Surface and colloid chemistry have only a few fundamental equations that are (almost) always true and they control many practical phenomena. All these general equations were developed more than a century ago. One of these fundamental equations is the Young equation for the contact angle, which is presented next. The other equations are the Young-Laplace, Kelvin and the famous Gibbs adsorption equation. They are also discussed in this chapter. 

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