Surfaces, constant curvature solid/liquid

Now place a small drop of liquid on the surface (see Fig. 1.12a) it forms part of a spherical surface because, as the liquid pressure is constant, the curvature is also constant (Laplace). Its surface subtends the solid surface at a contact angle 9e, which can be measured by projecting an image of the droplet onto a screen (see Fig. 1.13). 

In order to facilitate the calculation of capillary forces, several approximations on the meniscus shape have been proposed. They are mainly applied for experimental conditions where the radius of curvature of the meniscus interface is much smaller than the radius of curvature of the solid surfaces. This is relevant for the surface force apparatus where the surface has centimetric radius, while the meniscus is typically tens of hundreds of nanometers. The most used approximation is the toroidal approximation assuming the liquid interface has a circular profile. Obviously, such a meniscus does not exhibit a constant curvature. Nevertheless, this approximation gave good results, in particular for small contact angles, and is therefore widespread (see Ref. 15 for its application in various geometries and section 9.3.1.1 for an example of its application in atomic force microscopy [AFM]). In the case of capillary condensation between a plane and a sphere with a large radius of curvature R, in contact, the tension term of the capillary force is negligible and the Laplace term leads to the simple formula F = AnRy cos 9 A parabolic profile is also sometimes used to eliminate some numerical difficulties inherent in circle approximation. 

The profile of the solid surface is defined by a continuous function z(x) in both cases, with x measuring the distance to the symmetry axis in axial symmetry or to the symmetry plane in cylindrical symmetry (see Figure 5) the z axis is directed into the liquid. The surface of the drop has constant curvature, that is, it is either spherical or cylindrical. When the contact line is at a position x with slope a (positive or negative)... 

When an object is partly immersed in a wetting liquid, a concave meniscus is spontaneously formed where solid and liquid meet. The resulting negative capillary pressure Ap may be interpreted as the upward force on the liquid. The rise continues until Ap is just balanced by the gravity pressure. So, the surface tension can in principle be obtained from the curvature of the meniscus, the capillary rise, the density difference between the two fluids and the gravitational constant. Similar reasoning can be applied to capiUcuy depression, the situation encountered for non-wetted objects. 

Noncomposite Surface. The calculation of F by Equation 18 requires as a function of p at constant volume. The volume of a drop on the model surface can be derived from consideration of Figure 1. Let c be the center of curvature of the liquid surface and h the radius of curvature. Let the z coordinate of c be -a. The included angle between the zaxis and the radius to the edge of the drop is then < = (0 + a). Let z be the value of z at the liquid-solid interface and z the value of z at the liquid-air interface. The volume of the liquid is given by... 

A foam is a dispersion of a gas in a liquid or a solid. The formation of foam relies on the surface activity of the surfactants, polymers, proteins, and colloidal particles to stabilize the interface. Thus, the foamability increases with increasing surfactant concentration up to critical micelle concentration because above critical micelle concentration, the unimer concentration in the bulk r ains nearly constant. The structure and molecular architecture of the foam is known to influence foam-ability and its stability. The packing properties at the interface are not excellent for very hydrophilic or very hydrophobic drug. The surfactant promoting a small spontaneous curvature at interface is ideal for foams. Nonionic surfactants are the most commonly used one. The main advantage with foams is its site-specific delivery and multiple dosing of the drug. ... 

Capillarity is the phenomena that arises due to the existence of a finite (or even zero) contact angle that a liquid makes with the solid substrate. One example is the height-of-rise of a liquid in an open capillary tube, as shown in Fig. 10. The associated liquid motion due to surface tension is known as capillary flow. Assuming the meniscus to be approximately hemispherical with constant radius of curvature Ri = R2 = R/cos0, where 2R is the capillary diameter, the pressure variation across the interface from Eq. (11) is then... 

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