Viscous instability

When the mobility ratio is greater than one, viscous instability ensues during displacements in i stems of sufficient width OlO cm) to permit the formation and propagation of viscous fingers. These... 

Examples of miscible displacement are the intrusion of saltwater into fresh groundwater or a step change in feed composition in a chemical reactor. In one sense, miscible displacements are simpler processes than immiscible displacements because issues such as interfacial behavior and phase trapping are not relevant. However, they are complicated by hydrodynamic dispersion (which tends to smear the displacement front), and they are subject to similar viscous instabilities as those described earlier. 

Water and gas coning to producing oil wells are forms of viscous instabilities and they lead to sudden declines in oil production rate. 

A smaller channel has a smaller flow characteristic length and time. Thus, Re is smaller and it is difficult to have inertia/viscous flow instability. Conversely, De becomes larger and it is easier to have elastic/viscous instability. The relative dominance of elastic to inertial effects is typified by the Elasticity number, El, i.e., the ratio of fluid elasticity to fluid inertia. El is expressed as... 

When immiscible fluid streams are contacted at the inlet section of a microchannel network, the ultimate flow regime depends on the geometry of the microchannel, the flow rates and instabilities that occur at the fluid-fluid interface. In microfluidic systems, flow instabilities provide a passive means for co-flowing fluid streams to increase the interfacial area between them and form, e.g. by an unstable fluid interface that disintegrates into droplets or bubbles. Because of the low Reynolds numbers involved, viscous instabilities are very important At very high flow rates, however, inertial forces become influential as well. In the following, we discuss different instabilities that either lead to drop/bubble breakup or at least deform an initially flat fluid-fluid interface. Many important phenomena relate to classical work on the stability of unbounded viscous flows (see e.g. the textbooks by Drazin and Reid[56]and Chandrasekhar [57]). We will see, however, that flow confinement provides a number of new effects that are not yet fully understood and remain active research topics. 

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