Pressure surface interface effects

The dynamic surface tension of a monolayer may be defined as the response of a film in an initial state of static quasi-equilibrium to a sudden change in surface area. If the area of the film-covered interface is altered at a rapid rate, the monolayer may not readjust to its original conformation quickly enough to maintain the quasi-equilibrium surface pressure. It is for this reason that properly reported II/A isotherms for most monolayers are repeated at several compression/expansion rates. The reasons for this lag in equilibration time are complex combinations of shear and dilational viscosities, elasticity, and isothermal compressibility (Manheimer and Schechter, 1970 Margoni, 1871 Lucassen-Reynders et al., 1974). Furthermore, consideration of dynamic surface tension in insoluble monolayers assumes that the monolayer is indeed insoluble and stable throughout the perturbation if not, a myriad of contributions from monolayer collapse to monomer dissolution may complicate the situation further. Although theoretical models of dynamic surface tension effects have been presented, there have been very few attempts at experimental investigation of these time-dependent phenomena in spread monolayer films. 

A loss of water from plant shoots—indeed, sometimes even an uptake — occurs at cell-air interfaces. As we would expect, the chemical potential of water in cells compared with that in the adjacent air determines the direction for net water movement at such locations. Thus we must obtain an expression for the water potential in a vapor phase and then relate this P to for the liquid phases in a cell. We will specifically consider the factors influencing the water potential at the plant cell-air interface, namely, in the cell wall. We will find that vFcel1 wal1 is dominated by a negative hydrostatic pressure resulting from surface tension effects in the cell wall pores. 

The irregularly shaped pores between soil particles contain both air and water (Fig. 9-9). The soil pores, or voids, vary from just under 40% to about 60% of the soil by volume. Thus a soil whose pores are completely filled with water contains 40to60% water by volume. In the vicinity of most roots, moist soil contains 8 to 30% water by volume the rest of the pore space is filled with air. Therefore, the pores provide many air-liquid interfaces (Fig. 9-9) where surface tension effects can lead to a negative hydrostatic pressure in the soil water (Chapter 2, Sections 2.2G and 2.4E). Such a negative P is generally the main contributor to the water potential in the soil, especially as the soil dries. The thermal properties of soil are discussed in Chapter 7 (Section 7.5), so here we focus on soil water relations. 

In order to properly solve (17.5), sharp changes in the properties as well as pressure forces due to surface tension effects have to be resolved. In particular, surface tension results in a jump in pressure across a curved interface. The pressure jump is discontinuous and located only at the interface. This singularity creates difficulties when deriving a continuum formulation of the momentum equation. The interfacial conditions should be embedded in the field equations as source terms. Once the equations are discretized in a finite-thickness interfacial zone, the fiow properties are allowed to change smoothly. It is therefore necessary to create a continuum surface force (CSF) equal to the surface tension at the interface, or in a transitional region, and zero elsewhere. Therefore, the surface integral term in (17.5) could be rewritten into an appropriate volume integral... 

It is found that there exists a pressure difference across the curved interfaces of liquids (such as drops or bubbles). For example, if one dips a tube into water (or any fluid) and applies a suitable pressure, then a bubble is formed (Figure 1.13). This means that the pressure inside the bubble is greater than the atmosphere pressure. It thus becomes apparent that curved liquid surfaces induce effects, which need special physicochemical analyses in comparison to flat liquid surfaces. It must be noticed that in this system a mechanical force has induced a change on the surface of a liquid. This phenomenon is also called capillary forces. Then one may ask, does this also require similar consideration in the case of solids The answer is yes, and will be discussed later in detail. For example, in order to remove liquid, which is inside a porous media such as a sponge, one would need force equivalent to these capillary forces. Man has been fascinated with bubbles for many centuries. As seen in Figure 1.13, the bubble is produced by applying a suitable pressure, AP, to obtain a bubble of radius R, where the surface tension of the liquid is y. 

The total stress normal to the surface must be balanced by atmospheric pressure plus the surface tension contribution across the curved interface. We can usually neglect surface tension effects for melts, and we can always take atmospheric pressure to be zero. The tangential stress at the surface is finite because of aerodynamic drag it is conventional to represent the stress from air drag as jPaV co, where pa is the density of the air, v is the magnitude of the relative velocity between the surface and the air, and cd is a dimensionless drag coefficient that depends on shape and on... 

Because so many applications of surfactants involve surfaces and interfaces with high degrees of curvature, it is often important to understand the effect of curvature on interfacial properties. What is usually considered to be the most accurate procedure for the determination of the surface tension of liquids, the capillary rise method, depends on a knowledge of the relationship between surface curvature and the pressure drop across curved interfaces. Because of the existence of surface tension effects, there will develop a pressure differential across any curved surface, with the pressure greater on the concave side of the interface that is, the pressure inside a bubble will always be greater than that in the continuous phase. The Young-Laplace equation... 

A very important thermodynamic relationship is that giving the effect of surface curvature on the molar free energy of a substance. This is perhaps best understood in terms of the pressure drop AP across an interface, as given by Young and Laplace in Eq. II-7. From thermodynamics, the effect of a change in mechanical pressure at constant temperature on the molar h ee energy of a substance is... 

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