Small deformation curved interface

If the flnid interface is already curved in the absence of particles, the approach just discussed has to be modified to consider small deformations about an unperturbed curved interface. The application of the tools of differential geometry, as discussed in, for example, reference [68], is a promising approach that still remains to be developed. So far, several particular cases have been considered like the interfacial deformations of a spherical droplet by the electric field of a particle in the limit of a large droplet radins [34,37,69-71], or of an unperturbed interface that is itself a slight deformation of a flat interface [40]. In these two cases, the key assumption is a good separation of length scales the typical radius of curvature of the unperturbed, smooth interface is much larger than the typical... 

Substitution of Equations (36) and (37) into Equation (35) generates a complicated differential equation with a solution that relates the shape of an axially symmetrical interface to y. In principle, then, Equation (35) permits us to understand the shapes assumed by mobile interfaces and suggests that y might be measurable through a study of these shapes. We do not pursue this any further at this point, but return to the question of the shape of deformable surfaces in Section 6.8b. In the next section we examine another consequence of the fact that curved surfaces experience an extra pressure because of the tension in the surface. We know from experience that many thermodynamic phenomena are pressure sensitive. Next we examine the effecl of the increment in pressure small particles experience due to surface curvature on their thermodynamic properties. 

We have investigated the alteration in mechanical properties of the protein layer caused by the PFBC using a modified surface viscometer. The protein film was placed under a shearing stress by the application of a small torque to a teflon paddle wheel inserted into the interfacial boundary, and the angular deformation of the film was measured. From this data it was possible to obtain stress-strain curves and to determine the surface shear modulus and surface fracture point for the protein layer. In most studies protein was adsorbed to the interface of perfluorotributylamine from either a buffered... 

The adhesion of soil to the fiber surface is caused mainly by van der Waals forces that are effective only over very short distances. Therefore, the soil particle must be brought into close contact with the fiber surface to adhere. Because the surface of the fiber and the soil particle are not microscopically planar, but are usually curved and irregular, the area of contact is small. The contact area increases when the fiber surface or the particle is deformed on impact and conforms to the shape of the interface (Fig. 13.1). Hence, pressure, which causes plastic deformation or indentation of the fiber surface, increases soiling (Fig. 13.2). 

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