Dispersion flow-induced

Katz and Scott used equation (7) to calculate diffusivity data from measurements made on a specially arranged open tube. The equation that explicitly relates dispersion in an open tube to diffusivity (the Golay function) is only valid under condition of perfect Newtonian flow. That is, there must be no radial flow induced in the tube to enhance diffusion and, thus, the tube must be perfectly straight. This necessity, from a practical point of view, limits the length of tube that can be employed. 

The sample was a solution of polystyrene (PS) dissolved in dioctyl phthalate (DOP). This system has a theta temperature of approximately 22°C [183] and has been the subject of most of the studies investigating flow-induced phase transitions in polymer solutions. The particular sample used here had a molecular weight for PS of 2 million, a poly-dispersity of MW/MN = 1.06, and a concentration of 6%. This results in a semidilute... 

The addition of a very small amount of styrene-isoprene-styrene (SIS) triblock compatibilizer, introduced as a compounded pellet with PS 685, suppresses the shear flow-induced coalescence appreciably, as seen by comparing Fig. 11.35 with Fig. 11.37. On the other hand, there is no effect of this very small amount of SIS on the dispersion rate. 

Blends 3 (a,b,c) Rheologically Robust Matrix and Weak Dispersed Components Since PE 1409 is a low viscosity nearly Newtonian polymer melt, its dispersive behavior is uncomplicated and more Newtonian like. Blend 3a forms a small (3-5-pm) droplet dispersion morphology, and Blend 3b is even finer (1-2 pm), becoming, only below 2% concentration, less subject to flow-induced coalescence. The TSMEE-obtained dispersions are finer than those from the TSMEE, with a variety of kneading elements (126). What is noteworthy about these blends is the early stages of the dispersion process, shown on Fig. 11.44, obtained with Blend 3a using the TSMEE at 180°C and 120 rpm. 

To manipulate and control ultimate properties of processed materials (for example, the strength, electrical, or optical properties of suspensions or polymeric liquids can be modified via flow-induced orientation, dispersion or crystallization) ... 

The resolution of groundwater dating (e.g., by 14C) in through-flow systems is reduced by dispersion and other flow-induced disturbances, such as deviation from piston flow. In this respect stagnant systems are advantageous because they carry the age signal of the time of burial with no further dispersion effects. 

Woodburn55 showed thai, for Re], 650, the correlations proposed by DeMaria and White, J Sater and Levenspiel,43 and Dunn et al.16 could correlate his data. However, for 650 < ReL < 1,500, the axial dispersion in the gas phase was independent of the liquid rate. Under these liquid flow conditions, the reverse gas flow induced by the counterflowing liquid was measured. Thus, he concluded that an additional dispersive mechanism associated with reverse gas flow becomes operative at ReL 650. 

The models of flow dispersion are based on the plug flow model. However, in comparison with the PF model, the dispersion flow model considers various perturbation modes of the piston distribution in the flow velocity. If the forward and backward perturbations present random components with respect to the global flow direction, then we have the case of an axial dispersion flow (ADF). In addition, the axial and radial dispersion flow is introduced when the axial flow perturbations are coupled with other perturbations that induce the random fluid movement in the normal direction with respect to the global flow. 

Dispersion Formation, Subdivision, and Coalescence. The ability to create and control dispersions at distances far from the injection well will be critical to the field-use of dispersion-based mobility control. The early studies of Bernard and Holm, followed by more recent work by Hirasaki, Falls, and co-workers, and others showed that the flow properties of surfactant-induced dispersions depend on the presence and composition of oil, volume ratio of the dispersed and continuous phases, capillary pressure, and capillary number (35,37,39-41,52-54,68). However, it is the size of the droplets or bubbles that dominates dispersion flow (39,68). Moreover, early debates on the ratio of droplet (or bubble) size to pore size have been resolved by ample evidence showing that, under commonly employed conditions, droplets are larger than pores (39). Only for very large capillary numbers (i.e., for interfacial tensions of ca. 

Flow induced phase inversion (FIPI) has been observed by the author and applied to intensive materials structuring such as agglomeration, microencapsulation, detergent processing, emulsification, and latex production from polymer melt emulsifica-A diagrammatic illustration of FIPI is shown in Fig. 4. When material A is mixed with material B, in the absence of any significant deformation, the type of dispersion obtained [(A-in-B) or (B-in-A)] is dictated by the thermodynamic state variables (TSVs) (concentration, viscosity of components, surface activity, temperature, and pressure). If the... 

Let us consider the three additional examples just mentioned. First, we need to identify the features, in each case, that define the microstructural state. In the case of the emulsion or blend, the most important microscale feature that can be influenced by the flow is the orientation and shape of the disperse-phase bubbles or drops (the mean drop size and drop-size distribution will also generally be important and can be influenced by flow-induced drop breakup and coalescence events, but we will ignore this extra complication for purposes of our current discussion). At equilibrium, the drops will be spherical and the microstructure isotropic. For polymeric liquids, it is the statistical configuration of the polymer molecules... 

Problem 3-37. Taylor Dispersion with Streamwise Variations of Mean Velocity. We consider steady, pressure-driven axisymmetric flow in the radial direction between two parallel disks that are separated by a distance 2h. We assume that the volumetric flow rate in the radial direction is fixed at a value Q and that the Reynolds number is small enough that the Navier-Stokes equations are dominated by the viscous and pressure-gradient terms. Finally, the flow is ID in the sense that u = [nr(r, z), 0, 0]. In this problem, we consider flow-induced dispersion of a dilute solute. We follow the precedent set by the classical analysis of Taylor for axial dispersion of a solute in flow through a tube by considering only the concentration profile averaged across the gap, ( ) = f h dz. 

In the context of plankton dynamics an interesting development that has some common ideas with the KiSS approach but introduces a new and important element is described in Martin (2000). The idea is that dispersion of a patch is not only controlled by eddy diffusivity, but also by the geometric characteristics of the mean flow. It turns out that if an incompressible fluid flow induces dispersion in one direction it necessarily produces convergence in another, to conserve the fluid volume. This was already exploited in Sect. 2.7.1, and includes the ingredient of advection, in addition to the reaction-diffusion processes which are the subject of this Chapter. Nevertheless, since this case can be analyzed easily and extends the KiSS model, we consider it here. 

Flow-induced coalescence is accelerated by the same factors that favor drop breakup, e.g., higher shear rates, reduced dispersed-phase viscosity, etc. Most theories start with calculation of probabilities for the drops to collide, for the liquid separating them to be squeezed out, and for the new enlarged drop to survive the parallel process of drop breakup. As a result, at dynamic equilibrium, the relations between drop diameter and independent variables can be derived. 

These two equations indicate which factors can be used to enhance either dispersion or coalescence. Clearly, the shear rate is expected to similarly affect coalescence and breakup. However, the flow-induced coalescence is a strong function of concentration whereas the break is not, thus concentration may be used to discriminate between these two processes. Furthermore the rate of break is proportional to d, whereas the coalescence is proportional to 1/d. Thus, coalescence is not expected to play a major role in the beginning of the dispersion process. 

Flow field and cooling condition between injection molding and compression molding are essentially different. In particular, the flow-induced molecular orientation and/or the distorted shape of the dispersed phase have to be considered seriously in the injection molding. This part deals with the relation between morphology and mechanical properties in the injection-molded products for iPP and iPP/EHR blends (65). This is directly important for the industrial application. The characteristics of these samples are summarized in Table 9.5. 

This quite arbitrary method of two-dimensional transport ignores the components of vertical flow and thus underestimates the transversal dispersion thereby induced. On the other hand we tested a simple non-reacting case with the same hydraulic conditions against an analytical solution and found that the longitudinal dispersion is not influenced by numerical dispersion, whereas the numerical solution overestimates the transversal dispersion by approximately 10 %. The influence of the boundary conditions for top and bottom of the aquifer (no gradient, no flux) is more important in terms of an increased transversal dispersion for these cells. All these effects are negligible compared to the influences of inhomogeneities of hydraulic conductivities onto the modelled transversal dispersion. 

The dispersions of sohd particles in viscous fluids can be found in a wide range of natural and industrial applications. There are some interactiOTis determining the microstructure of the suspension, such as interactions arising from Brownian, interpaiticle, and flow-induced forces. In the equilibrium state, there is a balance between Brownian and interparticle forces. Under the influence of flow, hydrodynamic interactions become craisiderable, in comparison with thermal and interparticle forces. 

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