Longitudinal dispersion phenomena

IV. Longitudinal Dispersion Phenomena as Derived from Flow Properties... 

Longitudinal dispersion in the continuous phase (the liquid phase for a bubble column, and the emulsion phase for a fluidized catalyst bed) is closely related to flow properties of the equipment. Here, we wish to describe the longitudinal dispersion phenomena in terms of the fluid-dynamic properties of the equipment. The prime purpose is to test whether the fluid-dynamic analysis developed earlier is sound, but lon-... 

Equations (20.24) and (20.25) were developed for spills of constant volume, constant surface tension, and low viscosity on calm water. The effects of wind and currents on spreading rates are not well studied and are difficult to estimate. Therefore, the quantifiable uncertainty in the spreading rate lies in the estimation of the parameters used in Eqs. (20.24) and (20.25). The transition from a viscous spread, i.e., Eq. (20.25) to a surface tension spread, i.e., Eq. (20.23) occurs rapidly for most spills, and the spreading rate is described by Eq. (20.24). Since the density and viscosity of water can be estimated fairly confidently, most of the uncertainty in the spreading rate lies in the estimation of the net surface tension, specifically in the estimation of the air-oil surface tension and the oil-water surface tension. There is also an uncertainty in the applications of the slick-spreading model to a cross-sectional nonuniform velocity profile, where the nonuniformities would add to the spreading. In this case, the slick would experience a longitudinal dispersion in addition to the water. This phenomenon is not a component of the sensitivity analysis. 

Another approach to determining the viscoelastic properties of dense microemulsions at high frequencies is to conduct ultrasonic absorption experiments. In such experiments it has been found that the percolation process is correlated to a shift of the ultrasonic dynamics from a single relaxation time to a distribution of relaxation times [121]. Other experiments showed an increase in the hypersonic velocity for samples at and beyond the percolation threshold. The complex longitudinal modulus deduced from such experiments is also correlated with the occurrence of the percolation phenomenon, which suggests that the velocity dispersion is clearly correlated with structural transformations [122]. 

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