Fluid motion dispersion

Fluid mixing is a unit operation carried out to homogenize fluids in terms of concentration of components, physical properties, and temperature, and create dispersions of mutually insoluble phases. It is frequently encountered in the process industry using various physical operations and mass-transfer/reaction systems (Table 1). These industries include petroleum (qv), chemical, food, pharmaceutical, paper (qv), and mining. The fundamental mechanism of this most common industrial operation involves physical movement of material between various parts of the whole mass (see Supplement). This is achieved by transmitting mechanical energy to force the fluid motion. 

Both Fig. 37 and Fig. 39 show solid particles highly dispersed as a dilute phase in the oscillating fluid, either gas or liquid, without evidence of any bubbles. When a packed bed of solid particles was subjected to the action of an oscillating liquid, however, only the upstroke portion of the periodic fluid motion was capable of dispersing the solid particles against the action of gravity, while during downstroke they fell back onto the distributor plate. 

The three-stage rotating disk reactor is illustrated in Fig. 30. Each stage consists of one cylindrical and two conical elements and is connected to the next stage by another cylindrical element with a relatively small diameter. Fluid motion and gas dispersion are achieved by a rotating flat plate that contains holes at its outer edge to generate gas bubbles. The reactor can be used for cocurrent and countercurrent flow of gas and liquid or slurry. 

The application of the chemical schemes to atmospheric phenomena requires a diffusion formulation that reflects time-dependence and spatial variability of meteorological conditions. An attempt has been made to keep the mathematical description near the level of detail and precision of the observational data. This has resulted in a Lagrangian air parcel formulation with finite-rate vertical diffusion. The approach avoids the artificial numerical diffusion because it uses natural (or intrinsic) coordinates that are aligned with fluid motion. This allows us simultaneously to include upward dispersion and chemical change. Figure 1 schematically illustrates the main features of the formulation. Highspeed memory requirements are limited by allowing sequential point-by-point output of the history of the air parcel. 

This non-Fickian behavior arises from the fact that the range of fluid motions responsible for dispersion of a tracer depends on the size of the tracer patch in relation to the spectrum of fluid motions occurring, and the distinction between stirring and mixing (e.g., see Csanady, 1972 Rhines and Young, 1983 Young et al., 1982). 

Roger WA, Trice VG, and Rushton JH. Effect of fluid motion on interfacial area of dispersions. Chem Eng Prog 1956 52 515-520. 

There are two transport processes associated with fluid motion through porous media advection and dispersion. The former can be attributed to the bulk motion of the fluid, and the latter can be attributed, in general, to variations in concentration and velocity. 

It is apparent from equations 3.2.4-3.2.7 that the determination of the concentration field is dependent on the values of the Gaussian dispersion parameters a, (or Oy in the fully coupled puff model). Drawing on the fundamental result provided by Taylor (1923), it would be expected that these parameters would relate directly to the statistics of the components of the fluctuating element of the flow velocity. In a neutral atmosphere, the factors affecting these components can be explored by considering the fundamental equations of fluid motion in an incompressible fluid (for airflows less than 70% of the speed of sound, airflows can reasonably be modeled as incompressible) when the temperature of the atmosphere varies with elevation, the fluid must be modeled as compressible (in other words, the density is treated as a variable). The set of equations governing the flow of an incompressible Newtonian fluid at any point at any instant is as follows ... 

Rushton J.H., Effect of fluid motion on inteifacial area of dispersions, Chem. Eng. Progr. 52 (1956) 12, p. 515-520... 

A tank reactor and separator (Fig. 12-6) are used to study the heterogeneous reaction between pure liquid A (phase 1) and reactant B dissolved in phase 2 (also liquid). The solvent in phase 2, reactant B, and the products of reactior are all insoluble in liquid A. No reaction occurs in the separator. The reactor operates isothermally at 25°C, and at this temperature A has a limited solubility in phase 2, the value being 2.7 x 10 g mole/liter. Phase 2 is dispersed aj bubbles in continuous phase 1, which is recycled. There is excellent stirring in the reactor, but the fluid motion within the bubbles of phase 2 is insufficien to prevent some mass-transfer resistance. From independent measurements it is estimated that at average conditions the reaction resistance within the bubbles is 75% of the total resistance (mass-transfer plus reaction resistance) (n) Derive a relationship between the concentration of reactant B entering the reactor in phase 2 and the concentration leaving the separator. 

Let us now discuss in some detail the peculiarities of particle motion during electrophoresis and some other electrical properties of free disperse systems. Electrophoresis usually takes place in a stationary liquid. In a moving fluid the motion of particles occurs only in thin flat gaps and capillaries (microelectrophoresis), where the fluid motion is caused by electroosmosis. If fairly large non-conducting particles are dispersed in a rather dilute electrolyte solution, the ratio of particle radius to the double layer thickness may be substantially greater than 1, i.e., r/8 = kt 1. The streamlines of outer electric field surround the particle and are parallel to most of its surface, as shown in Fig. V-9. In this case the particle velocity, v0, can be with good precision described by Helmholtz-Smoluchowski equation. 

In a circular bed, the effective dispersion tensor is anisotropic and is composed of the longitudinal and lateral dispersion coefficients D Jff and Djjf, respectively. The longitudinal dispersion coincides with the direction of the mean fluid flow with the lateral dispersion normal to this direction. At high Peclet numbers, the longitudinal dispersion is large in comparison with the lateral dispersion, since the component of the fluid velocity parallel to the mean flow direction has the largest gradients. The lateral dispersion D if is associated with the weaker lateral fluid motion, whence D fj. 

A sol (Section 9.2.1) is a fluid colloidal dispersion with free particles, subject to Brownian motion. Siliceous earths are stable, concentrated aqueous suspensions of non-aggregated particles of silica produced by the in situ growth of silica microcrystals. Particles of different sizes are obtained by controlling their growth. They are byproducts of the glass industry. 

The induced surface flow also gives rise to secondary bulk fluid motion, in the same way that bulk meridional vortices are generated in a fluid trapped between rotating and stationary disks in Batchelor flows [19], as depicted in Fig. 12. In this flow recirculation mode, particles dispersed in the flow are convected to the bottom by the bulk meridional recirculation. However, due to the inward radial velocity in the Ekman boundary layer (see Fig. 13), the particles begin to swirl in a helical-like manner toward the center of the base [19]. Although the flow recirculates back up a central spinal coluirm, the gravitational... 

Radial dispersion contributes more significantly to the peak profile (dilution of the sample plug) than does axial dispersion. This type of fluid motion results in a washout effect accounting for the small carry-over between successively injected samples. This advantageous phenomenon in turn is a result of the use of low flow rates and small tubing bores, and leads to decreased peak widths and hence increased sample throughputs. 

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