Interfacial instability analysis

Interfacial instabilities in microsystems are complex phenomena and may be promoted by many different means. Future work requires a further development of experimental models and expansion of computational simulations to better understand the criteria under which instabilities develop. In addition, specific applications using interfacial instabilities for fluid manipulation, analysis, and material production should be continued to be explored. 

Interface stability in co-extrusion has been the subject of extensive analysis. There is an elastic driving force for encapsulation caused by the second normal stress difference (56), but this is probably not an important mechanism in most coprocessing instabilities. Linear growth of interfacial disturbances followed by dramatic breaking wave patterns is observed experimentally. Interfacial instabilities in creeping multilayer flows have been studied for several simple constitutive equations (57-59). Instability modes can be traced to differences in viscosity and normal stresses across the interface, and relative layer thickness is important. 

The equations developed in the last section can also be used to estimate the onset of an interfacial flow instability which leads to a rippled interface. According to Schrenk and co-workers (1976, 1978) this instability is due to slip at the interface between the polymers when a critical interfacial shear stress is exceeded. This critical stress will vary for various polymer types, but for the system of acrylonitrile-butadiene-styrene copolymer, ABS, and styron 470, this critical stress was 5.0 x lO Pa. The analysis developed in Section 7.6.2 can be used to assess the conditions under which we might expect an interfacial instability to arise. 

However, it seems that this instability may be more complicated than just a failure of adhesion between layers in shear flow. In many cases the region of fully developed shear flow is small or nonexistent and the analysis developed in Section 7.6.2 may not be applicable. The origin of the interfacial instability could be at the die exit where large stresses arise as the velocity profile undergoes a rapid rearrangement. It could also be associated with converging flow upstream of the die lips. In other words, differences in the extensional viscosity of the two polymers as well as differences in the relaxation behavior could lead to interfacial instability. 

Theoretical aspects of emulsion formation in porous media were addressed by Raghavan and Marsden (51-53). They considered the stability of immiscible liquids in porous media under the action of viscous and surface forces and concluded that interfacial tension and viscosity ratio of the immiscible liquids played a dominant role in the emulsification of these liquids in porous media. A mechanism was proposed whereby the disruption of the bulk interface between the two liquids led to the initial formation of the dispersed phase. The analysis is based on the classical Raleigh-Taylor and Kelvin-Helmholz instabilities. 

Reichenbach, J. and Linde, H., Linear perturbation analysis of surface-tension-driven convection at a plane interface (Marangoni instability), J. Colloid Interface Sci., 84, 433 143, 1981. Nepomnyashchy, A.A., Velarde, M.G., and Colinet, R, Interfacial Phenomena and Convection, CRC Press/Chapman Hall, London, 2002. 

The early work on modeling electrohydrodynamic instabilities performed a linear stability analysis of the electric and fluid interfacial boundary conditions using the transfer relations developed by Melcher [1]. Melcher developed... 

The underlying idea behind the stability analysis is that all possible initial perturbations z(x) consistent with system boundary conditions may occur. If all of these perturbations diminish in amplitude with time, the system is stable. But if any permrbation grows, instability occurs and the interface never remms to its initial flat configuration. It is clear from Equation 5.2 that if the system is stable with respect to all initial interfacial deformations having the forms Zia and Z2a of individual Fourier components, it is stable with respect to a general deformation. But if it is unstable with respect to even one Fourier component, interfacial deformation can be expected to increase continuously with time, and there is no return to the initial state. 

In the examples of interfacial stability considered thus far, the systems have been at rest in their initial states. Hence the predictions of when instability can be expected are, in fact, conditions for thermodynamic stability. We have chosen not to emphasize this point and to carry out the analyses in terms of perturbations of the general equations of change because we obtain in this way not only the stability condition but also the rates of growth of unstable perturbations and the appropriate frequencies of oscillation and damping factors for stable perturbations. Also, the basic method of analysis used above is applicable to systems not initially in equilibrium, as we shall see later in this chapter and in Chapter 6. 

For the case of a solute that lowers interfacial tension, we have seen already that instability occurs when transport is from the phase of lower diffusivity to one of higher diffusivity. With the general analysis we can draw the following conclusions ... 

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