Stability viscous effects

Next we turn to the stability of Couette flow for parallel rotating cylinders. This is an important flow for various applications, and, though it is a shear flow, the stability is dominated by the centrifugal forces that arise because of centripetal acceleration. This problem is also an important contrast with the first two examples because it is a case in which the flow can actually be stabilized by viscous effects. We first consider the classic case of an inviscid fluid, which leads to the well-known criteria of Rayleigh for the stability of an inviscid fluid. We then analyze the role of viscosity for the case of a narrow gap in which analytic results can be obtained. We show that the flow is stabilized by viscous diffusion effects up to a critical value of the Reynolds number for the problem (here known as the Taylor number). 

A key idea from the preceding analysis, as well as the analysis of capillary instability in section A, is that viscous effects often cannot change the conditions for instability of a rest state, but only moderate the rate of growth or decay of disturbances. In such cases, analysis of the stability (or instability) of the inviscid limit can be extremely useftd in identifying the conditions for instability. In view of the fact that the inviscid analysis is very much simpler, this is an important observation. 

Increased kinematic viscosity v increases the stability of the flow. This role of viscous effects is fundamentally distinct from the preceding examples, in which the inclusion of viscosity was found to modify the growth rates of unstable disturbances, but not to modify the conditions for linear instability. 

There are two possibilities for the role of viscous effects. One is that the system is unstable in the absence of viscous effects, but the latter stabilizes the system whenever the Reynolds number is below some critical value (which depends, of course, on the problem). The second is that the inviscid fluid is stable, but viscous effects act in such a way as to produce instability. 

In the early stages of this simplistic stability theory, the removal of the electro-viscous effect in soluble starch sols was studied These results seemed to draw the analogy between hydrophobic and... 

In the case of inks, where one needs to maximize the pigment content on the surface, the pigments stabilized with short-range interactions would be preferred. Likewise, in the case of paints, to generate the viscous effect in the formulation mainly to counter the settling of the dispersed particles, one would use long-range interactions. 

The general structure of stability Equation 18 remains unchanged when different quasi-steady models are applied for the various shear stresses terms. Moreover, even when the viscous effects are completely ignored, resorting to an inviscid K-H stability type of analysis, the structure of the resulting stability condition. Equation 18, is still maintained while Equation 19 for attains different expression. For instance, the long wave K-H stability analysis on two inviscid layers (rectangular channel) yields ... 

Foams are thermodynamically unstable. To understand how defoamers operate, the various mechanisms that enable foams to persist must first be examined. There are four main explanations for foam stabiUty (/) surface elasticity (2) viscous drainage retardation effects (J) reduced gas diffusion between bubbles and (4) other thin-film stabilization effects from the iateraction of the opposite surfaces of the films. 

Further examples pf fluorescence stabilization and intensity augmentation as a result of treatment of the chromatogram with viscous, lipophilic liquids are listed in Table 22. The alteration of the pH [293] or the addition of organic acids or bases [292] have also been found to be effective. Wintersteiger [291] has also described the effect that the TLC layer itself (binder) can influence the fluorescence intensity. 

Water-in-oil macroemulsions have been proposed as a method for producing viscous drive fluids that can maintain effective mobility control while displacing moderately viscous oils. For example, the use of water-in-oil and oil-in-water macroemulsions have been evaluated as drive fluids to improve oil recovery of viscous oils. Such emulsions have been created by addition of sodium hydroxide to acidic crude oils from Canada and Venezuela. In this study, the emulsions were stabilized by soap films created by saponification of acidic hydrocarbon components in the crude oil by sodium hydroxide. These soap films reduced the oil/water interfacial tension, acting as surfactants to stabilize the water-in-oil emulsion. It is well known, therefore, that the stability of such emulsions substantially depends on the use of sodium hydroxide (i.e., caustic) for producing a soap film to reduce the oil/water interfacial tension. 

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