Effective Interfacial Tension

The value of interfacial tension of a droplet during break-up is the one that governs the break-up, but it may not be easy to establish its magnitude. 

Another aspect is that the composition of the surfactant mixture in solution may 

During droplet deformation, its interfacial area is increased. The drop will commonly have acquired some surfactant, and it may even have a F value close to equilibrium at the prevailing (local) surfactant activity. Will this surfactant be able to distribute itself evenly over the enlarged interface in the very short times available Evening out can occur by surface diffusion or by spreading. 

The rate of surface diffusion is governed by the surface diffusion coefficient A. Its magnitude will depend on several factors it will anyway be inversely proportional to the effective viscosity felt. Assuming A = 10 m s for a small molecule at an air/water interface, D 10 / / (in SI units) in almost all other cases, taking for rj the value of the most viscous of the two phases. would decrease with increasing molar mass of surfactant and with increasing F. It has been observed by Clark et al that for such conditions (proteins) A is indeed very small. 

Sudden extension of an interface or sudden local application of a surfactant to an interface, however, can produce a fairly large -gradient, and in such a case spreading of surfactant can occur. This proceeds as a longitudinal wave, according to Lucassen. He derived for the linear velocity of such a wave on an air/water surface 

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How large a velocity gradient would be needed to make an O W emulsion with droplets of 1 pm diameter in plane hyperbolic laminar flow, assuming the effective interfacial tension to be 0.01 N m 1 Is the resulting gradient likely to be achievable in practice ... 

The first question is, What is the effective interfacial tension during droplet deformation and breakup This depends on surface load T, which depends on the adsorption rate of the surfactant. Actually, this rate can be very high, since surfactant is not transported by diffusion but by convection. This would imply that T can be fairly high. However, every breakup event occurs... 

The Wenzel Eq. (21) was derived by assuming that the roughness increases the surface solid/liquid and solid/vapor interfacial tensions by the factor r, the surface roughness coefficient, so that the effective interfacial tensions become ry L Tsv and by direct substitution into Young s equation yields,... 

Li et al. [43] appHed the pendent-drop method to study the interfacial tension of a PS/CO2 system. A Hnear decrease in interfadal tension was observed in the temperature range 190-240 °C. Interfadal tension reduced from 24 to 12 dyn cm up to a pressure of 70 atm, but at higher pressure the rate of reduction was suppressed. These observations were explained by two competing effects interfacial tension reduction with temperature increase combined with a reduc-... 

Interfacial effects Interfacial tension gradient Viscosity gradient Marangoni effect (near interfacial liquid layers move from area of low interfacial tension to areas of higher interfacial tension) Interfacial turbulences caused by interfacial tension gradient increase the mass transfer to the interphase compared to the mass transfer by only diffusion [6.5]... 

Because (T in Equation (66) pertains to a hypothetical isotropic nucleus, it cannot be measured. Furthermore, true (anisotropic) solid-liquid interfacial energies are measured near the melting temperature [86], whereas what would be needed for an independent confirmation of the theory is Cf(T) in the supercooled region. Consequently, the theory of homogeneous nucleation, as it applies to supercooled liquids, has been used mainly to calculate effective interfacial tensions from measurements of nucleation rates [82,86]. In summary, the application of nucleation theory to supercooled liquids involves two major simplifications the replacement of the true, anisotropic embryo by an "equivalent" spherical object, and the ad-hoc introduction of a diffusion-like activation energy barrier to account for hindered molecular mobility in the dense supercooled liquid. It is therefore not surprising that the resulting theory has been mostly used descriptively rather than predict vely. 

The I.D.T. apparatus enables determination of each of the variables in equation (4) as described in the following section. Hence the validity of the assumptions listed above can be tested, and values of the effective interfacial tension obtained during displacement... 

The effective interfacial tension between the two homopolymer phases in blends of immiscible homopolymers can be altered appreciably by adding different types of materials that can behave as interfacially active agents. 

Elias, L., Fenouillot, F., Majeste, J.C., Alcouffe, P., and Cassagnau, P. (2008) Immiscible polymer blends stabilized with nano-silica particles rheology and effective interfacial tension. Polymer, 49, 4378-4385. 

Levine S, Bowen BD. Capillary interactions of spherical particles adsorbed on the surface of an oil-water droplet stabilized by the particles 3. Effective interfacial tension. Colloids Surf A 1993 70(1) 33 5. 

FIG. 24 Origin of equality of collapse pressure and interfacial tension. Particles repel through the oil phase, and the oil/water interface tends to contract. When the forces balance, the effective interfacial tension of the particle-covered interface is... 

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