Hydrodynamic interaction interfacial viscosity

The last term in Eq. 19 is the non-dissipative part of the stress tensor, representing the hydrodynamic interactions. The parameter C is estimated as jly- flaMr], where the interfacial tension y and aM is the diffusivity. For a fluid with high viscosity, one has C -C 1, which implies that the hydrodynamic interactions can be neglected. The parameter IT (nondimensional pressure) mathematically acts like a Lagrange multiplier, which generates the incompressibility condition V V = 0. The boundary conditions on p and / are as follows (where n represents a normal direction to the boundary surface) ... 

It is encouraging that substantial progress has been made in analyzing the hydrodynamics of droplet interactions in dispersions from fundamental considerations. Effects of flow field, viscosity, holdup fraction, and interfacial surface tension are somewhat delineated. With appropriate models of coalescence and breakage functions coupled with the drop population balance equations, a priori prediction of dynamics and steady behavior of liquid-liquid dispersions should be possible. Presently, one universal model is not available. The droplet interaction processes (and... 

The dynamic mechanical properties of a filled system, in the absence of interaction between components, can be described on the basis of a mechanical model proposed by Takayanagi for non-interacting polymer mixtures. This model is very useful for describing properties of filled systems with interfacial layers. Based on hydrodynamic considerations, an equation was proposed (analogous to the Einstein equation for viscosity of suspension) to calculate the modulus of composite, Ec ... 

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