Fluid interfaces surface pressure

If only one fluid is present, then this is ail solid-fluid surface and the interaction is simply one of adhesion at the surface. If two fluids are present, then in addition to two kinds of solid-fluid interface there will be a fluid-fluid interface. The pressure difference which can exist across such a fluid-fluid interface is of the form ... 

Surface tension arises at a fluid to fluid interface as a result of the unequal attraction between molecules of the same fluid and the adjacent fluid. For example, the molecules of water in a water droplet surrounded by air have a larger attraction to each other than to the adjacent air molecules. The imbalance of forces creates an inward pull which causes the droplet to become spherical, as the droplet minimises its surface area. A surface tension exists at the interface of the water and air, and a pressure differential exists between the water phase and the air. The pressure on the water side is greater due to the net inward forces... 

A capillary system is said to be in a steady-state equilibrium position when the capillary forces are equal to the hydrostatic pressure force (Levich 1962). The heating of the capillary walls leads to a disturbance of the equilibrium and to a displacement of the meniscus, causing the liquid-vapor interface location to change as compared to an unheated wall. This process causes pressure differences due to capillarity and the hydrostatic pressures exiting the flow, which in turn causes the meniscus to return to the initial position. In order to realize the above-mentioned process in a continuous manner it is necessary to carry out continual heat transfer from the capillary walls to the liquid. In this case the position of the interface surface is invariable and the fluid flow is stationary. From the thermodynamical point of view the process in a heated capillary is similar to a process in a heat engine, which transforms heat into mechanical energy. 

Since the coolant and its vapor are conductive fluids. Toy = TLy = 7, where the subscripts s and f correspond to the saturation parameters and the interface surface, respectively. The saturation pressure and temperature are weakly connected (Sect. 10.9.1), so that Ts is determined practically by the external pressure Pg,oo-... 

The rheological properties of a fluid interface may be characterized by four parameters surface shear viscosity and elasticity, and surface dilational viscosity and elasticity. When polymer monolayers are present at such interfaces, viscoelastic behavior has been observed (1,2), but theoretical progress has been slow. The adsorption of amphiphilic polymers at the interface in liquid emulsions stabilizes the particles mainly through osmotic pressure developed upon close approach. This has become known as steric stabilization (3,4.5). In this paper, the dynamic behavior of amphiphilic, hydrophobically modified hydroxyethyl celluloses (HM-HEC), was studied. In previous studies HM-HEC s were found to greatly reduce liquid/liquid interfacial tensions even at very low polymer concentrations, and were extremely effective emulsifiers for organic liquids in water (6). 

The shape of the melt-fluid interface in a meniscus-defined crystal growth system is set by surface tension, gravitational force, and viscous and dynamic pressure forces on the surface. The Bond number (Bo for hydro-... 

A. u = Tc( + ) M 111P. Laplace-Kelvin equation. Difference in fluid pressure A.11 across two-fluid interface. Related to surface tension Tc and the curvature radii r and r2... 

The fluid phase that fills the voids between particles can be multiphase, such as oil-and-water or water-and-air. Molecules at the interface between the two fluids experience asymmetric time-average van der Waals forces. This results in a curved interface that tends to decrease in surface area of the interface. The pressure difference between the two fluids A/j = v, — 11,2 depends on the curvature of the interface characterized by radii r and r-2, and the surface tension, If (Table 2). In fluid-air interfaces, the vapor pressure is affected by the curvature of the air-water interface as expressed in Kelvin s equation. Curvature affects solubility in liquid-liquid interfaces. Unique force equilibrium conditions also develop near the tripartite point where the interface between the two fluids approaches the solid surface of a particle. The resulting contact angle 0 captures this interaction. 

The equilibrium between two fluids at different pressures (for example, liquid and its vapor, at PL and P8, respectively) in a spherical interface of curvature radius, r, and surface tension, y, is given by the Laplace equation... 

Abstract. Surface pressure/area isotherms of monolayers of micro- and nanoparticles at fluid/liquid interfaces can be used to obtain information about particle properties (dimensions, interfacial contact angles), the structure of interfacial particle layers, interparticle interactions as well as relaxation processes within layers. Such information is important for understanding the stabilisation/destabilisation effects of particles for emulsions and foams. For a correct description of II-A isotherms of nanoparticle monolayers, the significant differences in particle size and solvent molecule size should be taken into account. The corresponding equations are derived by using the thermodynamic model of a two-dimensional solution. The equations not only provide satisfactory agreement with experimental data for the surface pressure of monolayers in a wide range of particle sizes from 75 pm to 7.5 nm, but also predict the areas per particle and per solvent molecule close to the experimental values. Similar equations can also be applied to protein molecule monolayers at liquid interfaces. 

When two immiscible fluids (or a fluid and a gas) are in contact, molecular attractions between similar molecules in each fluid are greater than the attractions between the different molecules of the two fluids and a clearly defined interface exists between them. The force that acts on this interface is called interfacial tension (or surface tension in case of a gas-fluid contact). As a result of this force, a pressure difference exists across the interface. This pressure difference is known as capillary pressure and is given by the following equation (Dake, 1978) ... 

The d)mamics of adsorption of emulsifiers at fluid interfaces have been determined by tensiometry and surface rheology (Figure 14.3) that is, from the time dependence of surface pressure and surface dilatational modulus (E). We found that tt and E increase with time (9), which should be associated with emulsifier adsorption (Patino and Nino, 1999 Nino et al., 2003 Carrera et al., 2005). 

Inside the drop, we require that the velocity and pressure fields be bounded at the origin [which is a singular point for the spherical coordinate system that we will use to solve (7 199)]. Finally, at the drop surface, we must apply the general boundary conditions at a fluid interface from Section L of Chap. 2. However, a complication in using these boundary conditions is that the drop shape is actually unknown (and, thus, so too are the unit normal and tangent vectors n and t and the interface curvature V n). As already noted, we can expect to solve this problem analytically only in circumstances when the shape of the drop is approximately (or exactly) spherical, and, in this case, we can use the method of domain perturbations that was first introduced in Chap. 4. In this procedure, we assume that the shape is nearly spherical, and develop an asymptotic solution that has the solution for a sphere as the first approximation. An obvious question in this case is this When may we expect the shape to actually be approximately spherical ... 

The accurate information about the surface tension-surface coverage relationship which for soluble monolayers is contained in the e0—tt curves, can be used, for example, to interpret rate of adsorption measurements. For fluid-fluid interfaces, adsorption onto an initially clean surface can be assessed only indirectly by measuring the changing interfacial tension. An example is shown in Figure 9, giving the change in surface pressure... 

At a fluid interface (gas liquid or liquid liquid) interfacial tension can be measured, and adsorption leads to lowering of y (Figure 10.4). The extent by which y is decreased is called the surface pressure, defined as... 

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