Pressure difference, interfacial

Eq. (132) states that the interfacial tension has to be balanced by a pressure difference between the two phases. The terms containing derivatives of crin Eqs. (133) and (134) are non-zero only if there are local variations of the interfacial tension, which might be due to differences in concentration or temperature. The flow induced by such an effect is known as Marangoni convection. 

Since it is relatively easy to transfer molecules from bulk liquid to the surface (e.g. shake or break up a droplet of water), the work done in this process can be measured and hence we can obtain the value of the surface energy of the liquid. This is, however, obviously not the case for solids (see later section). The diverse methods for measuring surface and interfacial energies of liquids generally depend on measuring either the pressure difference across a curved interface or the equilibrium (reversible) force required to extend the area of a surface, as above. The former method uses a fundamental equation for the pressure generated across any curved interface, namely the Laplace equation, which is derived in the following section. 

Procedure. To form a BLM, a small amount (.— 0.005 ml.) of lipid solution was applied via a Teflon capillary attached to a micrometer syringe. The formation characteristics leading to the black state were observed under reflected light at 20-40 X magnification. Other precautions that should be exercised are essentially those described previously (10). The bifacial tension of BLM was measured as follows. After the membrane had become completely black (except at the Plateau-Gibbs border), the infusion-withdrawal pump was started. The pressure difference across the BLM was continuously monitored and reached a maximum when the membrane was hemispherical. The interfacial tension was calculated from this point using Equation 3. 

The results of interfacial tension measurements on BLM formed from five different lipid solutions are given in Table I. One of the immediate questions is whether the measured values represent the true bifacial tension of BLM. It is implicitly assumed in order to apply equation 3 that yb is a characteristic property of BLM and should be independent of the extension of the BLM area. It is generally recognized that if the BLM also possessed elastic properties, the measured yb would be different when it is stretched. To answer this question, yb was measured during both expansion and contraction of the membrane. A typical trace of pressure difference vs. time in which the membrane was being expanded and contracted is shown in Figure 3. The symmetric nature of the curve indicates that little hysteresis was present during inflation and deflation of the BLM. Therefore, it seems safe to conclude that for BLM formed from lipid materials alone the membrane does not appear to possess appreciable elastic properties. 

The apparatus developed for yb measurements of BLM deserves brief comment since it can be used not only to examine the effects of various substances on BLM but is readily adaptable for studying other types of interfacial films and related adsorption phenomena at either air-water or oil-water interfaces (and bifaces). Unlike both the Wil-helmy plate and film balance methods, the present technique measures 7i directly. From the description of the apparatus and procedure that the present method relies on the ability to measure the very small pressure difference across an interface (or biface). For certain BLM s, the pressure heads measured are only fractions of a millimeter of water. Therefore, the method described here has been possible only as a result of developing pressure transducers of high sensitivity. 

An interface has an effective driving pressure if its displacement decreases the total system s free energy. This effective pressure can derive from any mechanism by which a material stores energy, but for many cases it arises from only two sources the volumetric free-energy differences between the interface s adjacent phases, and mechanical pressure differences due to reduction of the interfacial energy. 

The surface energy per area, 7, has the same units as a force per length and for some interfacial geometries can lead to an interfacial net force that is balanced by a difference in pressure between the two adjacent phases. If 7 is isotropic, this pressure difference is directly proportional to the interfacial curvature through the the Gibbs-Thomson equation (see Sections C.2.1 and C.4.1),... 

Curvature relates to the local change in interface area when an interface moves. The energy change per unit volume swept out by the interface is equal to the product of k and the interfacial energy per unit area 7. Normally, for fluids, 7 is independent of the interface inclination h in this case, the interface is isotropic. For example, a soap bubble has isotropic interface tension. If perturbed, a floating individual soap bubble will quickly re-establish its equilibrium form—a sphere of fixed volume. Such a soap bubble will also shrink slowly—the gas will diffuse out of the bubble because of a pressure difference across the soap film (AP = jk = /Rc). Thus,... 

If the interface is chosen to be at a radius r, then the corresponding value for dV13/dA is r /2. The pressure difference T>f) — Pa can in principle be measured. This implies that pp pa 2-y/r and l,f) — Pa = Pf /r are both valid at the same time. This is only possible if, dependent on the radius, one accepts a different interfacial tension. Therefore we used 7 in the second equation. In the case of a curved surface, the interfacial tension depends on the location of the Gibbs dividing plane In the case of flat surfaces this problem does not occur. There, the pressure difference is zero and the surface tension is independent of the location of the ideal interface. 

Capillary forces interfacial forces between immiscible fluid phases, resulting in pressure differences between the two phases. 

Interfacial tension causes a pressure difference to exist across a curved surface, the pressure being greater on the concave side (i.e., on the inside of a droplet or bubble). Consider an interface between phase A, in a droplet or bubble, and phase B, surrounding the droplet or bubble. These will have pressures pA and pB. If the principal radii of curvature are Rx and R2 then,... 

The Young-Laplace equation forms the basis for some important methods for measuring surface and interfacial tensions, such as the pendant and sessile drop methods, the spinning drop method, and the maximum bubble pressure method (see Section 3.2.3). Liquid flow in response to the pressure difference expressed by Eqs. (3.6) or (3.7) is known as Laplace flow, or capillary flow. 

Multiphase microflows are dominated by pressures (Aota et al., 2007a, 2009a). One important parameter needed to describe the multiphase microflows is the pressure that drives the fluids. The pressure decreases in the downstream part of the flow because of the fluids viscosity. When two fluids in contact with one another have different viscosities, the pressure difference (APfiow) between the two phases is a function of the contact length and the flow velocity. Another important parameter is the Laplace pressure (APLapiace) caused by the interfacial tension between two phases. The position of the interface is fixed within a point in the microchannel by the balance established between the APLaplace and APFlow. 

This splitting-up is driven by the interfacial tension, which causes pressure differences between parts of the thread with positive and negative curvature. Only the viscosity counteracts the growth of the distortion and limits its rate of growth. 

The interfacial tension of the binary system a-tocopherol/carbon dioxide was measured using the pendant drop method in the pressure range between 10 and 37 MPa at nine different temperatures 313, 333, 343, 353, 363, 373, 383, 393 and 402 K. The interfacial tension decreases with rising pressure at a constant temperature and increases with increasing temperature at a constant pressure. The interfacial tension was found to be mainly a function of the mutual solubility of the two system components and of the density of pure carbon dioxide. 

This diffusion occurs because the pressure is greater in the smaller droplets. The pressure difference is proportional to the interfacial tension and to the difference between the inverse radii (A P/y I/R2 1/Ri)- Diffusion is thought to be a relatively slow process, but it increases when pressure increases or other changes increase the solubility of the components of the dispersed phase in the dispersing fluid. 

This gives rise to a mobilization pressure which is higher than gas-liquid flow with no surfactant. Viscous effects of the Bretherton type are included in a network model to derive permeability expressions cor responding to different interfacial mobilities. The significant reduction in gas permeability of foams is attributed to (1) the significant decrease in the fraction of channels containing flowing gas (compared to gas-liquid flow with no surfactant), and (2) the increase in viscous and capillary effects associated with bubble train lamellae. 

Capillary Forces The interfacial forces acting among oil, water, and solid in a porous medium. These determine the pressure difference (capillary pressure) across an oil-water interface in a pore. Capillary forces are largely responsible for oil entrapment under typical reservoir conditions. 

So, in this case the dispersion equation contains the modulus rather than the interfacial tension. We would expect this outcome because the interface remains flat, so there is no capillary pressure difference across it. 

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) ... 

Fig. 10,3. Drop in chemical potential (io2 across bulk and interfacial zones of a membrane imposed to an oxygen partial pressure difference, P02 > Poi"- The largest drop occurs aaoss the least permeable...

The terms pk)Ai — Pk)vk) oik + < k)Ai otk are referred to as the interfacial pressure difference effect (or the concentration gradient effect) and the combined interfacial shear and volume fraction gradient effect [67] [115], respectively. The interfacial pressure difference effect is normally assumed to be insignificant for the two-fluid model [54, 4, 125, 119]. That is, for two-phase flows one generally assumes that... 

However, it may be practically impossible to increase the viscosity or velocity by such a magnitude because doing so would require or result in a very high pressure difference between the injector and producer. Such high pressure difference would fracture the formation. Another way to increase capillary number is to reduce interfacial tension, which can be achieved through injection of surfactants. Recall that ultralow interfacial tension is one of the main mechanisms in surfactant-related processes. 

Using a unique device that incorporates different interfacial techniques, such as surface film balance and Brewsfer angle microscopy (BAM), we have analyzed fhe sfrucfural characferisfics of profein-LMWE mixed films spread on fhe air-water interface (Pafino ef al., 2003 Lucero, in press). At surface pressures lower than that for profein collapse a mixed monolayer of LMWE and protein may exist. At surface pressures higher than that for protein collapse, collapsed protein residues may be displaced from the interface by LMWE molecules fhaf is, fhe mixed film is practically dominated by LMWE molecules the tt-A isotherms of fhe mixed film are parallel to that of the lipid. 

Now, consider again a spherical liquid drop. Because of the curvature of the interface, there is a pressure difference between the inside and outside of the drop. This difference exists because of the interfacial tension, which tends to reduce the area of the liquid system, so that equilibrium is maintained with a higher pressure inside the drop than the atmospheric pressure outside. If the radius of the drop is r, its surface area is 4nr. The incremental work dvrs done in increasing the radius by dr is... 

In order to describe a liquid meniscus and hence to obtain the interfacial tension from the shape of a drop or bubble the Laplace equation is used. This equation describes the mechanical equilibrium of two homogeneous fluids separated by an interface (Rusanov and Prokhorov 1996, Neumann and Spelt 1996) and relates the pressure difference across the interface to the surface tension and the curvature of the interface... 

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