Interfacial gradient effects

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... 

C. V. Stemling and L. E. Scriven, Interfacial turbulence hydrodynamic instability and the Marangoni effect, AIChE J. 5, 514 (1959) L. E. Scriven and C. V Stemling, On cellular convection driven by surface tension gradients effects of mean surface tension and surface viscosity, J. Fluid Mech. 19, 321 (1964). 

The first steps toward such a theory of blend flow behavior were proposed by Helfand and Fredrickson [1989], then by Doi and Onuki [1992]. A greatly simplified constitutive equation for immiscible 1 1 mixture of two Newtonian fluids having the same viscosity and density was also derived [Doi and Ohta, 1991]. The derivation considered time evolution of the area and orientation of the interface in flow, as well as the interfacial tension effects. The relation predicted scaling behavior for the stress and the velocity gradient tensors ... 

Interfacial tension gradient effects are represented as apparent dilational viscosity effects. 

The tangential bulk-phase stress component evaluated at the interface combines an elastic (interfacial tension gradient) effect, e, and an apparent viscous effect, rxj + tIj) -I- e 7o). One of the most convenient methods of measuring capillary waves is to use light scattering (29), which can yield information on both the tension and dilational modulus of the interface. 

We may now define an external effectiveness factor >jex as the ratio of the rate with external chffusion resistance to the rate without interfacial gradients ... 

The interfacial pressure difference effect and the combined interfacial shear and time fraction gradient effect are treated in the same manner as suggested discussing the... 

A high modulus gradient at the interface is also be avoided in materials Joined as a result of the interdiffusion of materials to form a fractal surface [32]. The effect is to produce an interfacial composite region. This strengthens the interface and leads to a more gradual change in modulus and avoids the sharp concentrations of stress which would occur at a smooth interface. 

The effectiveness of a crude oil demulsifier is correlated with the lowering of the shear viscosity and the dynamic tension gradient of the oil-water interface. The interfacial tension relaxation occurs faster with an effective demulsifier [1714]. Short relaxation times imply that interfacial tension gradients at slow film thinning are suppressed. Electron spin resonance experiments with labeled demulsifiers indicate that the demulsifiers form reverse micellelike clusters in the bulk oil [1275]. The slow unclustering of the demulsifier at the interface appears to be the rate-determining step in the tension relaxation process. 

A study on a commonly used demulsifier, namely, a phenol-formaldehyde resin, elucidated how various parameters such as interfacial tension, interfacial shear viscosity, dynamic interfacial-tension gradient, dilatational elasticity, and demulsifier clustering affect the demulsification effectiveness [1275]. 

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