Fluid hydrodynamics

Tubular Modules. Tubular modules are generally limited to ultrafiltration appHcations, for which the benefit of resistance to membrane fouling because of good fluid hydrodynamics overcomes the problem of their high capital cost. Typically, the tubes consist of a porous paper or fiber glass support with the membrane formed on the inside of the tubes, as shown in Figure 24. 

The phenomenon of concentration polarization, which is observed frequently in membrane separation processes, can be described in mathematical terms, as shown in Figure 30 (71). The usual model, which is weU founded in fluid hydrodynamics, assumes the bulk solution to be turbulent, but adjacent to the membrane surface there exists a stagnant laminar boundary layer of thickness (5) typically 50—200 p.m, in which there is no turbulent mixing. The concentration of the macromolecules in the bulk solution concentration is c,. and the concentration of macromolecules at the membrane surface is c. 

In Spite of the existence of numerous experimental and theoretical investigations, a number of principal problems related to micro-fluid hydrodynamics are not well-studied. There are contradictory data on the drag in micro-channels, transition from laminar to turbulent flow, etc. That leads to difficulties in understanding the essence of this phenomenon and is a basis for questionable discoveries of special microeffects (Duncan and Peterson 1994 Ho and Tai 1998 Plam 2000 Herwig 2000 Herwig and Hausner 2003 Gad-el-Hak 2003). The latter were revealed by comparison of experimental data with predictions of a conventional theory based on the Navier-Stokes equations. The discrepancy between these data was interpreted as a display of new effects of flow in micro-channels. It should be noted that actual conditions of several experiments were often not identical to conditions that were used in the theoretical models. For this reason, the analysis of sources of disparity between the theory and experiment is of significance. 

Microreactor scale-up is built upon the premise of numbering up channels. Figure 11.1. A single channel is demonstrated with the same geometry and fluid hydrodynamics as a full-scale reactor. Numbering up rehes on creating a massively... 

The motion of a particle in the flow field can be described in the Lagrangian coordinate with the origin placed at the center of the moving particle. There are two modes of particle motion, translation and rotation. Interparticle collisions result in both the translational and the rotational movement, while the fluid hydrodynamic forces cause particle translation. Assuming that the force acting on a particle can be determined exclusively from its interaction with the surrounding liquid and gas, the motion of a single particle without collision with another particle can be described by Newton s second law as... 

Weissburg, M. J. and R. K. Zimmer-Faust. Life and death in moving fluids Hydrodynamic effects on chemosensory-mediated predation. Ecology 74, 1428-1443 (1993). 

Boundary layers also contribute to the effect of intestinal fluid hydrodynamics on drug absorption by both diffusional- and carrier-mediated processes. In a well-defined isolated in situ model such as perfused intestine of the rat, a good estimate of the gut wall permeability, which is the vector of convective diffusive mass transfer, passive diffusion and carrier-mediated transport, can be accomplished [99,100]. 

The second approach to concentration polarization, and the one used in this chapter, is to model the phenomenon by assuming that a thin layer of unmixed fluid, thickness S, exists between the membrane surface and the well-mixed bulk solution. The concentration gradients that control concentration polarization form in this layer. This boundary layer film model oversimplifies the fluid hydrodynamics occurring in membrane modules and still contains one adjustable parameter,... 

The theoretical description of translational diffusion in a lipid bilayer depends on the size of the diffusing particle. Theoretical descriptions based on fluid hydrodynamic theory (51, 52) have been shown to be applicable to particles whose radius in the plane of the bilayer is significantly larger than the radius of the lipid molecules that constitute the bilayer, in which case the diffusion coefficient may be given by ... 

Progress in the physics of disordered media—that is, in the physics of media with a random distribution of microheterogeneity—is mainly made via the solution of problems involving the connection between the microscopic structure and the macroscopic behavior. This problem properly belongs to the realm of the kinetic theory of matter and is analogous to the problem of locking in the theory of fluids, hydrodynamic turbulence, the theory of phase transitions, and so on. 

Membrane Fouling. Pretreatment of the membrane or feed solution prior to filtration may be desirable within allowable limits. The various treatment options are discussed in Sec. 6.3. At the start of a filtration run, the solute or solids concentration is relatively small and progressively builds as the permeate is removed from the system. If a substantial flux decline is observed at low solids concentration, membrane fouling aspects are believed to be important. A flux decrease with an increase in solids concentration is largely due to concentration polarization and can be minimized through efficient fluid hydrodynamics and/or backpulsing. PH221123)... 

The analysis of mass transfer in electrochemical cells requires the use of equations that describe the condition of electroneutrality (which applies for the entire elecnolyte outside the double layer at an electrode), species fluxes, mass conservation, current density, and fluid hydrodynamics. Often, mass transport events are rate limiting, as compared to kinetics processes at the electrode surface, in which case the overall electrode reaction rate is solely dependent on species mass transfer (e.g., during high-rate electroplating of some metals and for those elecnochemical reactions where the concentration of reactant in solution is low). 

The fluid hydrodynamics and geometric configuration of the electrochemical reactor are key to understand the mixed processes that occur in a system. Though the specific geometry of the electrocatalysts is important, the mass transfer can be determined solely by fluid hydrodynamics [1],... 

Formulation. In this section, we will summarize the procedure for calculating dynamic mechanical properties of dilute polymer solutions by applying statistical mechanics to the model mentioned above. Basic equations of the theory consist of equations of motion for the polymer elements, an equation of motion for the fluid (hydrodynamics), a diffusion equation to describe the statistical nature of the problem and an equation of stress. 

Cellular and diffusion models are usually used for estimation of longitudinal mixing (turbulence) in reaction zone and consequently for evaluation of deviation degree of fluids hydrodynamic structure from ideal displacement and mixing regimes [3, 7, 19-21]. 

Attou A, Ferschneider G. A two-fluid hydrodynamic model for the transition between trickle and pulse flow in a cocurrent gas-liquid packed-bed reactor. Chem. Eng. Sd. 2000 55 491. 

The parameters and consequently the efficiency of PV strongly depends on the properties of the membrane material. Common membrane materials are various dense polymers and microporous inorganic membranes (zeolithes, silica,. ..) either with hydrophilic or organophilic character. Furthermore composite membranes offer the possibility to combine different materials for the dense active layer and the porous support layer. Besides membrane material fluid hydrodynamics influences the efficiency of separation. The pressure drop especially on the permeate side reduces the driving force of the most permeating components. 

Based on the available open Hterature, industrial technologists have not generally reported the development of state-of-the-art reactor models that combine intrinsic reaction kinetics, transport effects, and fluid hydrodynamics across the required range of temporal and length scales. If available, they have been kept as company confidential for business reasons. However, Shin and coworkers (2007) describe a hybrid model for a multitubular reactor used in terephthaldehyde manufacture that couples a commercial CFD... 

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