Surface shear, concepts

Figure 10. The concepts of surface shear and surface dilational viscosities (a) deformation of a soap film and (b) dilation of a soap film.

Some approaches analyzed directly flic influence of flic stabilizing adsorption layers and concluded that diere is a dependence of the stability of an emulsion on flic interfacial concentration and the sum of inter-molecular interactions (8—10). Murdoch and Leng (11) pointed out the role of bulk and interfacial rheological parameters to describe these processes. This concept was further treated by several authors (12—14). A very comprehensive approach was given by Wasan and co-workers (15,16) who considered the surface shear and dilational rheology, and also some hy-drody-namic parameters in their analysis of emulsion films. 

Another widely used concept is that of a planetary boundary layer (PBL) in contact with the surface of the Earth above which lies the "free atmosphere." This PBL is to some degree a physically mixed layer due to the effects of shear-induced turbulence and convective overturning near the Earth s surface. 

In order to describe the effects of the double layer on the particle motion, the Poisson equation is used. The Poisson equation relates the electrostatic potential field to the charge density in the double layer, and this gives rise to the concepts of zeta-potential and surface of shear. Using extensions of the double-layer theory, Debye and Huckel, Smoluchowski,... 

To model this, Duncan-Hewitt and Thompson [50] developed a four-layer model for a transverse-shear mode acoustic wave sensor with one face immersed in a liquid, comprised of a solid substrate (quartz/electrode) layer, an ordered surface-adjacent layer, a thin transition layer, and the bulk liquid layer. The ordered surface-adjacent layer was assumed to be more structured than the bulk, with a greater density and viscosity. For the transition layer, based on an expansion of the analysis of Tolstoi [3] and then Blake [12], the authors developed a model based on the nucleation of vacancies in the layer caused by shear stress in the liquid. The aim of this work was to explore the concept of graded surface and liquid properties, as well as their effect on observable boundary conditions. They calculated the hrst-order rate of deformation, as the product of the rate constant of densities and the concentration of vacancies in the liquid. 

Using this concept, Erwin [9] demonstrated that the upper bound for the ideal mixer is found in a mixer that applies a plane strain extensional flow or pure shear flow to the fluid and where the surfaces are maintained ideally oriented during the whole process this occurs when N = 00 and each time an infinitesimal amount of shear is applied. In such a system the growth of the interfacial areas follows the relation given by... 

Although this chapter is concerned with bulk acoustic wave (BAW) devices, some of the concepts apply to shear horizontal surface acoustic wave (SH-SAW) devices in a similar way [33,34]. When modeling SH-SAW devices, one usually decomposes the wave vector into a vertical and a lateral component. The vertical component obeys similar laws as the shear wave in a BAW resonator. This being said, we confine the discussion to BAW devices (also termed thickness-shear resonators) in the following. 

In an analysis of the near initial rate of biofilm accumulation Bryers and Characklis [1981] related the development of biofilm to the concept of a continuous stirred tank reactor. They took into account the effects of shear forces and associated removal of biofilm and assumed that the subsequent effects were dependent on the biofilm already on the surface, i.e. 

In the last section we introduced the concept of two asymptotic viscosity limits for shear thinning colloidal suspensions as a function of shear rate. One is the high shear limit which corresponds to high values of the Peclet number where viscous forces dominate over Brownian and interparticle surface forces. Generally this limit is attained with non-colloidal size particles since to achieve large Peclet numbers by increase in shear rate alone requires very large values for colloidal size particles. In this limit, non-Newtonian effects are negligible for colloidal as well as non-colloidal particles. 

---