Phase equilibrium interfacial tensions

In this equation. Act is taken as the maximum possible surface tension lowering. Hence for a solute-free continuous phase, Aa is the difference between the interfacial tension for the solvent-free system and the equilibrium interfacial tension corresponding to the solute concentration in the dispersed phase. Equation (10-6) indicates a strong effect of the viscosity ratio k on the mass transfer coefficient as found experimentally (LI 1). For the few systems in which measurements are reported (Bll, Lll, 04), estimates from Eq. (10-6) have an average error of about 30% for the first 5-10 seconds of transfer when interfacial turbulence is strongest. 

The simplest expectation is that the critical length dc is attained when the equilibrium interfacial tension a is approached in the course of phase decomposition ... 

Perhaps the most striking property of a microemulsion in equilibrium with an excess phase is the very low interfacial tension between the macroscopic phases. In the case where the microemulsion coexists simultaneously with a water-rich and an oil-rich excess phase, the interfacial tension between the latter two phases becomes ultra-low [70,71 ]. This striking phenomenon is related to the formation and properties of the amphiphilic film within the microemulsion. Within this internal amphiphilic film the surfactant molecules optimise the area occupied until lateral interaction and screening of the direct water-oil contact is minimised [2, 42, 72]. Needless to say that low interfacial tensions play a major role in the use of micro emulsions in technical applications [73] as, e.g. in enhanced oil recovery (see Section 10.2 in Chapter 10) and washing processes (see Section 10.3 in Chapter 10). Suitable methods to measure interfacial tensions as low as 10 3 mN m 1 are the sessile or pendent drop technique [74]. Ultra-low interfacial tensions (as low as 10 r> mN m-1) can be determined with the surface light scattering [75] and the spinning drop technique [76]. 

Because there can be degrees of wetting of particles at an interface, another quantity is needed. The contact angle, 6, in an oil—water—solid system is defined as the angle, measured through the aqueous phase, that is formed at the junction of the three phases. Whereas interfacial tension is defined for the boundary between two phases, the contact angle is defined for a three-phase junction. If the interfacial forces that act along the perimeter of the drop are represented by the interfacial tensions, then an equilibrium force balance can be written as... 

Van Oene [1978] studied the mechanisms of two-phase formation in a mixture of two viscoelastic fluids. He pointed out that, besides the viscosity ratio and the equilibrium interfacial tension of the two liquids, the elasticity of the liquids plays an important role in deformability of drops. Thermodynamic considerations led to the following relation for the dynamic interfacial tension coefficient ... 

For the given emulsion formulation, the equilibrium interfacial tension yoo between the continuous and disperse phases was 8 x 10 N/m and the contact angle 6 between the disperse phase and the membrane surface was assumed to be 0. Therefore, from Equation (16.20), one obtains Pcap = 6.7 kPa for = 4.8 x 10 m, which corresponds to 7 kPa deduced from Figure 16.16. 

Hu et al. [48] studied the addition of PS-h-PDMS diblock copolymer to the PS/PDMS blend. A maximum interfacial tension reduction of 82% was achieved at a critical concentration of 0.002% diblock added to the PDMS phase. At a fixed PS homopolymer molecular weight, the reduction in interfacial tension increases with increasing the molecular weight of PDMS homopolymer. Moreover, the degree of interfacial tension reduction was found to depend on the homopolymer the diblock is mixed with when the copolymer was mixed into the PS phase, the interfacial tension reduction was much less than that when the copolymer was blended into the PDMS phase. This behavior suggested that the polymer blend interface may act as a kinetic trap that limits the attainment of global equilibrium in these systems. 

Studied the time evolution of the interfacial tension when polyisobutylene (PIB)-b-PDMS was introduced to PIB/PDMS blend, with the copolymer added to the PIB phase in that study both homopolymers were poly disperse. The time dependence of the interfacial tension was fitted with an expression that allowed the evaluation of the characteristic times of the three components. The characteristic time of the copolymer was the longest, whereas the presence of the additive was found to delay the characteristic times of the blend components from their values in the binary system. The possible complications of slow diffusivities on the attainment of a stationary state of local equilibrium at the interface were thoroughly discussed by Chang et al. [58] within a theoretical model proposed by Morse [279]. Actually, Morse [279] suggested that the optimal system for measuring the equilibrium interfacial tension in the presence of a nearly symmetric diblock copolymer would be one in which the copolymer tracer diffusivity is much higher in the phase to which the copolymer is initially added than in the other phase because of the possibility of a quasi-steady nonequilibrium state in which the interfacial coverage is depleted below its equilibrium value by a continued diffusion into the other phase. 

Knowing the dynamic storage and loss moduli of both components and those of the blend, and the droplet size distribution of the dispersed phase, it is possible to determine the equilibrium interfacial tension using Eqs. (3.7) and (3.8). 

By virtue of their simple stnicture, some properties of continuum models can be solved analytically in a mean field approxunation. The phase behaviour interfacial properties and the wetting properties have been explored. The effect of fluctuations is hrvestigated in Monte Carlo simulations as well as non-equilibrium phenomena (e.g., phase separation kinetics). Extensions of this one-order-parameter model are described in the review by Gompper and Schick [76]. A very interesting feature of tiiese models is that effective quantities of the interface—like the interfacial tension and the bending moduli—can be expressed as a fiinctional of the order parameter profiles across an interface [78]. These quantities can then be used as input for an even more coarse-grained description. 

In flotation it is clear by now that there are three phases air, mineral, and water. The three are shown in Figure 2.23 (A) to meet at a common boundary. In this condition there will be a balance of interfacial tension forces. These can be resolved so that, for equilibrium at the point of intersection ... 

The interfacial tension always depends on the potential of the ideal polarized electrode. In order to derive this dependence, consider a cell consisting of an ideal polarized electrode of metal M and a reference non-polarizable electrode of the second kind of the same metal covered with a sparingly soluble salt MA. Anion A is a component of the electrolyte in the cell. The quantities related to the first electrode will be denoted as m, the quantities related to the reference electrode as m and to the solution as 1. For equilibrium between the electrons and ions M+ in the metal phase, Eq. (4.2.17) can be written in the form (s = n — 2)... 

Petroleum recovery typically deals with conjugate fluid phases, that is, with two or more fluids that are in thermodynamic equilibrium. Conjugate phases are also encountered when amphiphiles fe.g.. surfactants or alcohols) are used in enhanced oil recovery, whether the amphiphiles are added to lower interfacial tensions, or to create dispersions to improve mobility control in miscible flooding 11.21. 

A two-dimensional illustration of three phases a, ft and % in equilibrium is shown in Figure 6.9. Two phases coexist in equilibrium in planes perpendicular to the lines indicated in the two-dimensional figure and all three phases coexist along a common line also perpendicular to the plane of the drawing. Each of the three two-phase boundaries, which meet at the point of contact, has a characteristic interfacial tension, e.g. ca for the interface, which tends to reduce the area of the... 

Components of interfacial tension (energy) for the equilibrium of a liquid drop on a smooth surface in contact with air (or the vapor) phase. The liquid (in most instances) will not wet the surface but remains as a drop having a definite angle of contact between the liquid and solid phase. 

The sketch in Fig. 10 shows the equilibrium of forces with an obtuse contact angle in the oil phase (6o). In this case the wetting tension, j, of the aqueous phase is positive, which means that the adhering oil droplet is pushed together by the aqueous phase. With the increase in j the tendency of an oil droplet to be cut off and removed from a solid substrate increases. Because of this, the impeding force for the removal of oil is the interfacial tension oil/water (Yq )> which should be minimized. By minimization of the interfacial tension, moreover, the requirements for emulsification and stabilization of soil in the washing and cleaning liquid will be improved. 

Mixed film theories (4-8) The essential feature of the mixed film theories is to consider the film as a liquid, two dimensional third phase in equilibrium with both oil and water, implying that such a monolayer could be a duplex film, i.e., one giving different properties on the water side than on the oil side (4). According to these theories, the interfacial tension Y is given by the expression,... 

Wetting Parameters in the Detergency Equation. The detergency system has three interfaces which have three interfacial tensions at equilibrium with all three phases Ksw> Yfs and Yfw When only two phases are in equilibrium, three other surface tensions are possible Ysw> Yfs> Yfw (however, when the fiber is an insoluble solid, Ysw Y w> Ysw will be... 

The film pressure values for the detergency system are also listed in Table 2. These quantities represent the difference in interfacial tension between two pure phases and the interfacial tension of the same two phases which are at saturation equilibrium with the third phase. Since the PEG fiber surface was assumed insoluble in either the bath or soil, = 0. 

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