Transport phenomena, hydrodynamic

For displacements shorter than the mean pore dimension, (z2) < a, where flow velocities tend to be spatially constant and homogeneously distributed, Brownian diffusion is the only incoherent transport phenomenon that contributes to the hydrodynamic dispersion coefficient. As a direct consequence, the dispersion coefficient approaches the ordinary Brownian diffusion coefficient,... 

Ary given catalytic material can be abstracted based on the same underlying similar architecture — for ease of comparison, we describe the catalytic material as a porous network with the active centers responsible for the conversion of educts to products distributed on the internal surface of the pores and the external surface area. Generally, the conversion of any given educt by the aid of the catalytic material is divided into a number of consecutive steps. Figure 11.13 illustrates these different steps. The governing transport phenomenon outside the catalyst responsible for mass transport is the convective fluid flow. This changes dramatically close to the catalyst surface from a certain boundary onwards, named the hydrodynamic boundary layer, mass transport toward and from the catalyst surface only takes place... 

A critical review of emulsion flow in porous media has been presented. An attempt has been made to identify the various factors that affect the flow of OAV and W/O emulsions in the reservoir. The present methods of investigation are only the beginning of an effort to try to develop an understanding of the transport behavior of emulsions in porous media. The work toward this end has been difficult because of the complex nature of emulsions themselves and their flow in a complex medium. Presently there are only qualitative descriptions and hypotheses available as to the mechanisms involved. A comprehensive model that would describe the transport phenomenon of emulsions in porous media should take into account emulsion and porous medium characteristics, hydrodynamics, as well as the complex fluid-rock interactions. To implement such a study will require a number of experi-... 

Advective transport alone does not account for all observed transport behavior. Transport observations in porous media exhibit characteristics indicative of a phenomenon beyond that described by advection only, such as breakthrough prior to and tailing after the advective front. This additional transport phenomenon is attributed to hydrodynamic dispersion, which is the sum of diffusive and mechanical dispersive processes. The former is attributed to concentration gradients, and the latter is attributed to variations in velocity at both micro and macro spatial scales. 

Unfortunately, despite these advances in comprehension, technical tools to control transport phenomena at the appropriate scales were not systematically available at that time. The local operating conditions at the scales of interest could only be controlled by external actions applied at the reactor or unit-operation scale flow rate, inlet or jacket temperature, pressure, mechanical energy provided to a stirrer, etc. The propagation of the consequences of these external actions from the unit-operation scale down to the transport-phenomenon scale could not be directly controlled and was only indirectly transmitted by non-selective dissipative hydrodynamics and physical processes. 

Let us take an example of mixing fluorescein with water (D = 3x 10" cm /s). For a microsystem with / 100 pm and 17 30 pm/s, the Peclet number is equal to 10. Thus, td> ra, which is contrary to equation 1.33. This indicates that diffusion phenomenon is much slower than hydrodynamic transport phenomenon, which is contrary to what was suggested based on the scaling analysis. Hence, the scaling laws cannot be used blindly. It provides an estimate of the process, which need to be verified from the exact analysis. 

The rate of agitation, stirring, or flow of solvent, if the dissolution is transport-controlled, but not when the dissolution is reaction-con-trolled. Increasing the agitation rate corresponds to an increased hydrodynamic flow rate and to an increased Reynolds number [104, 117] and results in a reduction in the thickness of the diffusion layer in Eqs. (43), (45), (46), (49), and (50) for transport control. Therefore, an increased agitation rate will increase the dissolution rate, if the dissolution is transport-controlled (Eqs. (41 16,49,51,52), but will have no effect if the dissolution is reaction-controlled. Turbulent flow (which occurs at Reynolds numbers exceeding 1000 to 2000 and which is a chaotic phenomenon) may cause irreproducible and/or unpredictable dissolution rates [104,117] and should therefore be avoided. 

In this section we studied the phenomenon of enhanced (hydrodynamic) transport, induced by population growth in reaction-diffusion systems. Based on our Fisher theorem approach, we have shown that the expressions for the emerging hydrodynamic speeds have a simple physical interpretation They are proportional to space specific fitness functions, which express the ability of a population to fill out space. Based on our approach, we came up with simple rules for solving inverse problems in geographical population genetics. 

There are approximately 200 cilia on each ciliated cell. They are packed at a density of 6-8 cilia per m2 and cannot move without affecting neighbouring cilia. In order to perform an unhindered beat cycle the movement of each cilium is slightly out of phase with that of its neighbor, leading to a phenomenon termed ciliary metachrony . Metachrony results solely from hydrodynamic coupling between adjacent cilia and provides the necessary cooperation within a field of cilia to permit them to transport mucus. 

First, and most important, nonlinear dynamics provides an intellectual framework to pursue the consequences of nonlinear behavior of transport systems, which is simply not possible in an intellectual environment that is based upon a linear mentality, characterized by well-behaved, regular solutions of idealized problems. One example that illustrates the point is the phenomenon of hydrodynamic dispersion in creeping flows of nondilute suspensions. It is well known that Stokes flows are exactly reversible in the sense that the particle trajectories are precisely retraced when the direction of the mean flow is reversed. Nevertheless, the lack of reversibility that characterizes hydrodynamic dispersion in such suspensions has been recently measured experimentally [17] and simulated numerically [18], Although this was initially attributed to the influence of nonhydrodynamic interactions among the particles [17], the numerical simulation [18] specifically excludes such effects. A more general view is that the dispersion observed is a consequence of (1) deterministic chaos that causes infinitesimal uncertainties in particle position (due to arbitrarily weak disturbances of any kind—... 

There are some special cases in FFF related to the two extreme limits of the cross-field driving forces. In the first case, the cross-field force is zero, and no transverse solute migration is caused by outer fields. However, because of the shear forces, transverse movements may occur even under conditions of laminar flow. This phenomenon is called the tubular pinch effect . In this case, these shear forces lead to axial separation of various solutes. Small [63] made use of this phenomenon and named it hydrodynamic chromatography (HC). If thin capillaries are used for flow transport, this technique is also called capillary hydrodynamic fractionation (CHDF). A simple interpretation of the ability to separate is that the centers of the solute particles cannot approach the channel walls closer than their lateral dimensions. This means that just by their size larger particles are located in streamlines of higher flow velocities than smaller ones and are eluted first (opposite to the solution sequence in the classical FFF mode). For details on hydrodynamic chromatography,see [64-66]. 

The electrodes with bubbles evolving seem to lead in the confined electrochemical cell to a hydrodynamic puffing phenomenon , clearly three dimensional and unsteady in the cell. Then all the coupled phenomena, transports and reactions are affected and should actually be three dimensional and unsteady. 

This phenomenon is denoted feed-side concentration polarization and, in practice, affects mainly the fluxes of compounds of high sorption coefficient, even under turbulent hydrodynamic conditions over the membrane, as their permeability (and hence flux across the membrane) is high. It should at this point be emphasized that contrary to the non-ideal transport phenomena discussed earlier, feed-side concentration polarization is not a membrane-intrinsic phenomenon, but stems from poor design of the upstream flow conditions in practice it may in fact not be overcome owing to module design limitations (Baker et ah, 1997). 

In thermally non-homogeneous supercritical fluids, very intense convective motion can occur [Ij. Moreovei thermal transport measurements report a very fast heat transport although the heat diffusivity is extremely small. In 1985, experiments were performed in a sounding rocket in which the bulk temperature followed the wall temperature with a very short time delay [11]. This implies that instead of a critical slowing down of heat transport, an adiabatic critical speeding up was observed, although this was not interpreted as such at that time. In 1990 the thermo-compressive nature of this phenomenon was explained in a pure thermodynamic approach in which the phenomenon has been called adiabatic effect [12]. Based on a semi-hydrodynamic method [13] and numerically solved Navier-Stokes equations for a Van der Waals fluid [14], the speeding effect is called the piston effecf. The piston effect can be observed in the very close vicinity of the critical point and has some remarkable properties [1, 15] ... 

The concentration polarization is a phenomenon, which influences the pervaporation efficiency. The boundary-layer resistance to the solute transport was reported by Psaume et al. [9] for the recovery of trichloroethylene in aqueous solutions. They showed that under certain operating conditions, transport through the membrane was determined by the hydrodynamic conditions in the feed-side, and thus the resistance of the membrane becomes relatively negligible. Colman et al. [77] showed that resistance to the transfer of the boundary layer is a limiting factor of the dehydration of isopropanol by pervaporation. Various others studies [16,78,79] highlighted the importance of the hydrodynamics on resistance to the solute mass transport in pervaporation. 

It was shown that for certain system parameters given by a critical Reynolds number, there is a possibility of propagation of the specific flow structures inside the liquid layer. The convection cells, which can appear, are similar to those observed in the Ryleigh-Benard experiment [9]. Such phenomenon can be very important for some air-water-phospholipid systems such as the pulmonary surfactant present in the natural mass exchanger - the lungs. The hydrodynamic system described in the piq er can be a very useful tool for explanation of convective diffusion-reaction transport process in case of interaction of allergens with pulmonary epithelium, causing atopy. 

Although the phenomenon of polarisation has been illusuated by considering cation transport through cation-selective membranes, the same description applies to anions. However, the mobility of anions with the same valence in the boundary layer is a little greater than that of cations. This implies that under similar hydrodynamic conditions (equal thickness of the boundary layer, same cell construction) for the anion and cation, the limiting current densitj will be attained faster at a cation-exchange membrane than at an anion-exchange membrane. 

When the phase containing the electroactive species is moving relatively to the reaction interface, convection (or hydrodynamic transport) occurs. This phenomenon is less frequently encountered with the solid electrolytes than with the liquid ones, and... 

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