Dispersion fluid flow

Diffusion The movement of dissolved materials in fluids because of a concentration gradient that is, dissolved materials diffuse from areas of higher concentration to areas of lower concentration. Unlike dispersion, fluid flow is not involved with diffusion. 

Detailed mathematical models in these models a comprehensive investigation into the effect of various dyeing parameters, including both bulk and dispersive fluid flow, is carried out. These parameters are then related to the physicochemical laws of the dyeing process. Therefore complex differential equations are derived. Major simplifications to the model would be required in order to solve these equations explicitly, and therefore numerical solutions are used. 

Laminae of clay and clay drapes act as vertical or horizontal baffles or barriers to fluid flow and pressure communication. Dispersed days occupy pore space-which in a clean sand would be available for hydrocarbons. They may also obstruct pore throats, thus impeding fluid flow. Reservoir evaluation, is often complicated by the presence of clays. This is particularly true for the estimation of hydrocarbon saturation. 

Internal Flow. Depending on the atomizer type and operating conditions, the internal fluid flow can involve compHcated phenomena such as flow separation, boundary layer growth, cavitation, turbulence, vortex formation, and two-phase flow. The internal flow regime is often considered one of the most important stages of Hquid a tomiza tion because it determines the initial Hquid disturbances and conditions that affect the subsequent Hquid breakup and droplet dispersion. 

Figure 8-32. Correlation for the dispersion of fluids flowing in pipes. (Source Levenspiel, 0., Ind. Eng. Chem., 50, 343, 1958.)...

Due to the very low volumetric concentration of the dispersed particles involved in the fluid flow for most cyclones, the presence of the particles does not have a significant effect on the fluid flow itself. In these circumstances, the fluid and the particle flows may be considered separately in the numerical simulation. A common approach is to first solve the fluid flow equations without considering the presence of particles, and then simulate the particle flow based on the solution of the fluid flow to compute the drag and other interactive forces that act on the particles. 

Theoretical representation of the behaviour of a hydrocyclone requires adequate analysis of three distinct physical phenomenon taking place in these devices, viz. the understanding of fluid flow, its interactions with the dispersed solid phase and the quantification of shear induced attrition of crystals. Simplified analytical solutions to conservation of mass and momentum equations derived from the Navier-Stokes equation can be used to quantify fluid flow in the hydrocyclone. For dilute slurries, once bulk flow has been quantified in terms of spatial components of velocity, crystal motion can then be traced by balancing forces on the crystals themselves to map out their trajectories. The trajectories for different sizes can then be used to develop a separation efficiency curve, which quantifies performance of the vessel (Bloor and Ingham, 1987). In principle, population balances can be included for crystal attrition in the above description for developing a thorough mathematical model. 

Glaser and Litt (G4) have proposed, in an extension of the above study, a model for gas-liquid flow through a b d of porous particles. The bed is assumed to consist of two basic structures which influence the fluid flow patterns (1) Void channels external to the packing, with which are associated dead-ended pockets that can hold stagnant pools of liquid and (2) pore channels and pockets, i.e., continuous and dead-ended pockets in the interior of the particles. On this basis, a theoretical model of liquid-phase dispersion in mixed-phase flow is developed. The model uses three bed parameters for the description of axial dispersion (1) Dispersion due to the mixing of streams from various channels of different residence times (2) dispersion from axial diffusion in the void channels and (3) dispersion from diffusion into the pores. The model is not applicable to turbulent flow nor to such low flow rates that molecular diffusion is comparable to Taylor diffusion. The latter region is unlikely to be of practical interest. The model predicts that the reciprocal Peclet number should be directly proportional to nominal liquid velocity, a prediction that has been confirmed by a few determinations of residence-time distribution for a wax desulfurization pilot reactor of 1-in. diameter packed with 10-14 mesh particles. 

The energy of fast fluid flow can be utihzed to intensify processes in chemical reactors and there are two basic ways of doing it by purposefully creating the cavitation conditions in the reacting liquid or by using a supersonic shockwave for fine phase dispersion. 

The form of the effective mobility tensor remains unchanged as in Eq. (125), which imphes that the fluid flow does not affect the mobility terms. This is reasonable for an uncharged medium, where there is no interaction between the electric field and the convective flow field. However, the hydrodynamic term, Eq. (128), is affected by the electric field, since electroconvective flux at the boundary between the two phases causes solute to transport from one phase to the other, which can change the mean effective velocity through the system. One can also note that even if no electric field is applied, the mean velocity is affected by the diffusive transport into the stationary phase. Paine et al. [285] developed expressions to show that reversible adsorption and heterogeneous reaction affected the effective dispersion terms for flow in a capillary tube the present problem shows how partitioning, driven both by electrophoresis and diffusion, into the second phase will affect the overall dispersion and mean velocity terms. 

Laux, H. Modeling of dilute and dense dispersed fluid-particle flow, PhD Thesis, NTNU Trondheim, Norway (1998). 

In PF, the transport of material through a vessel is by convective or bulk flow. All elements of fluid, at a particular axial position in the direction of flow, have the same concentration and axial velocity (no radial variation). We can imagine this ideal flow being blurred or dispersed by backmixing of material as a result of local disturbances (eddies, vortices, etc.). This can be treated as a diffusive flow superimposed on the convective flow. If the disturbances are essentially axial in direction and not radial, we refer to this as axial dispersion, and the flow as dispersed plug flow (DPF). (Radial dispersion may also be significant, but we consider only axial dispersion here.)... 

Figure 13.15 Correlation for the dispersion of fluids flowing in pipes, adapted from Levenspiel (1958b).

Figure 13.17 Experimental findings on dispersion of fluids flowing with mean axial velocity u in packed beds prepared in part from Bischoff (1961).

An injected slug of tracer material flows with its carrier fluid down a long, straight pipe in dispersed plug flow. At point A in the pipe the spread of tracer is 16 m. At point B, 1 kilometer downstream from A, its spread is 32 m. What do you estimate its spread to be at a point C, which is 2 kilometers downstream from point A ... 

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