Interfacial instability values

Schrenk et al. (66) were among the first to report and study this interfacial instability, which they attributed to exceeding a critical value of interfacial shear stress. This criterion... 

Interfacial Instability, Fig. 1 Images of the peaking instability of different ferrofluids with applied magnetic fields above the critical values needed for instability (Images taken from Amin et al. [7])... 

Appropriate concentrations of microemulsifiers are necessary in an extracting emulsion to lower the interfacial tension. Figure 9 compares the dependence of the coefficient for cholesterol extraction by an emulsion (curve 1) and the interfacial tension in a two-phase, non-emulsion system (curves 2-4) on the ethanol to diethyl ether molar ratio. There is a maximum on the cholesterol extraction curve which corresponds to minima in the interfacial tension curves. At this composition the greatest interfacial instability due to diffusion of ethanol and diethyl ether takes place. Consequently the nanodispersion formation is the greatest at the same composition for which the cholesterol extraction coefficient has a maximal value. 

The wavelength X increases with an increase in the kinematic viscosity of silicone oil. The analytical equation for A (8.30) agrees with the measured values of A for vi = 2 mm /s, but overestimates A as vi exceeds lOmm /s. The amplitude of the interfacial instability is also measured. 

Recently [7] we constructed an example showing that interfacial flexibility can cause instability of the uniform state. Two elastic capacitors, C and C2, were connected in parallel. The total charge was fixed, but it was allowed to redistribute between C and C2. It was shown that if the interface was absolutely soft , i.e., contraction of the two gaps was not coupled, the uniform distribution became unstable at precisely the point where the dimensionless charge density s reached the critical value, = (2/3). In other words, the uniform distribution became unstable at the point where, under a control,... 

FIGURE 1.8. (a) Schematic representation of the device used to study capillary surface instabilities. A polymer-air bilayer of thicknesses /ip and /ia, respectively, is formed by two planar silicon wafer held at a separation d by spacers. A capillary instability with wavelength k = 27t/q is observed upon applying a voltage U or a temperature difference AT. (b) Dispersion relation (prediction of Eq. (1.6)). While all modes are damped (r < 0) in the absence of an interfacial pressure pei, the application of an interfacial force gradient leads to the amplification of a range of k-values, with /.m the maximally amplified mode. 

Monodisperse melts appear to exhibit a plateau region in the stress vs shear rate flow curve [51,62,65]. The capillary flow behavior actually closely resembles the oscillatory shear behavior in the sense that the flow curve essentially overlaps on the absolute value of complex modulus G vs the oscillation frequency (0 [62]. Thus.it appears that the transition-like capillary flow behavior of highly entangled monodisperse melts reflects constitutive bulk properties of the melts and is not interfacial in origin. It remains to be explored whether this plateau indeed manifests a real constitutive instability, i.e., whether it is double-valued. 

Stemling and Scriven wrote the interfacial boundary conditions on nonsteady flows with free boundary and they analyzed the conditions for hydrodynamic instability when some surface-active solute transfer occurs across the interface. In particular, they predicted that oscillatory instability demands suitable conditions cmcially dependent on the ratio of viscous and other (heat or mass) transport coefficients at adjacent phases. This was the starting point of numerous theoretical and experimental studies on interfacial hydrodynamics (see Reference 4, and references therein). Instability of the interfacial motion is decided by the value of the Marangoni number, Ma, defined as the ratio of the interfacial convective mass flux and the total mass flux from the bulk phases evaluated at the interface. When diffusion is the limiting step to the solute interfacial transfer, it is given by... 

In the rotary annular contactor [D2, L2, T2] shown schematically in Fig. 4.27 [T2], the organic and aqueous phases flow countercurrently by gravity in the annular space between a rotating itmer cylinder and a stationary outer cylinder. Taylor-instability vortices generated in the annulus promote dispersion and interfacial area. This is one of the simplest of the mechanically a tated contactors, and it has been developed for possible application to fuel reprocessing. In laboratory extractions of uranium from nitric add with TBP in kerosene, Davis [D2] obtained values as low as 7.5 cm for the column hei t equivalent to a theoretical stage. The rotor speed varied from 1200 to 2000 r/min, with annular widths of 0,1 to 0.35 cm and a stator diameter of 2.2 cm. The residence time per theoretical stage was 10 s or less. 

A more elaborated theoretical model based on interfacial Taylor instability triggering the surface wave was developed by Peskin and Raco [39]. A thin layer of a liquid, wetting the surface of a solid resonator wbch vibrates to its plane, forms a chessboard-like pattern of stationary capillary waves. This phenomenon occurs when the vibration amplibde exceeds a threshold value. Further on, ligament breakup of the liquid occurs and droplets are hurled from the crests of the capillary waves. Together with the wavelength, they introduced wave amplibde and the sheet thickness as parameters to determine the droplet size [39]. 

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