Hydrodynamic transport regime

The solution flow is nomially maintained under laminar conditions and the velocity profile across the chaimel is therefore parabolic with a maximum velocity occurring at the chaimel centre. Thanks to the well defined hydrodynamic flow regime and to the accurately detemiinable dimensions of the cell, the system lends itself well to theoretical modelling. The convective-diffiision equation for mass transport within the rectangular duct may be described by... 

The hydrodynamic, transport and mixing characteristics in this flow regime are reasonably well understood. 

Finally, it has to be emphasized that both the hydrodynamic parameters and the concentrations of the species involved simultaneously determine whether the transport regime is of kinetic, diffusional, or mixed diffixsional-kinetic type. Therefore, it is not surprising that different investigators, who studied the same transport system in different hydrodynamic and concentration... 

The hydrodynamics of a circulating fluidized bed is further complicated by the existence of significant variations in solids concentration and velocity in the radial direction. A more uniform distribution can be achieved at conditions of lower solids concentrations under higher gas flow conditions. In the dilute transport regime, the solids concentration is very low and both gas and solids have short residence times. 

Chemical mass is redistributed within a groundwater flow regime as a result of three principal transport processes advection, hydrodynamic dispersion, and molecular diffusion (e.g., Bear, 1972 Freeze and Cherry, 1979). Collectively, they are referred to as mass transport. The nature of these processes and how each can be accommodated within a transport model for a multicomponent chemical system are described in the following sections. 

Regime of transport limitation, here

diffusion through the hydrodynamic boundary layer. The apparent activation energy under these conditions gets close to zero. Every educt molecule reacts instantaneously on the outer catalyst surface, no educt diffusion inside the catalyst particle takes place. 

It is also demonstrated that the simultaneous numerical solution by a difference scheme of both the transport and hydrodynamic mechanisms is probably impossible, but that the separate considerations of these two regimes, which is possible, can be connected in a physically reasonable manner... 

To understand and ultimately to forecast the performance of a reactor, it is essential to study the coupling of "true" (intrinsic) kinetics with mass and energy transport, and to determine the flow regimes of the three phases (hydrodynamics). Modelling... 

Hydrodynamic electrodes1 are electrodes which function in a regime of forced convection. The advantage of these electrodes is increased transport of electroactive species to the electrode, leading to higher currents and thence a greater sensitivity and reproducibility. Most of the applications of these electrodes are in steady-state conditions, i.e. constant forced convection and constant applied potential or current. In this case dc/dt = 0, which simplifies the solution of the convective diffusion equation (Section 5.6)... 

Hydrodynamic electrodes — are electrodes where a forced convection ensures a -> steady state -> mass transport to the electrode surface, and a -> finite diffusion (subentry of -> diffusion) regime applies. The most frequently used hydrodynamic electrodes are the -> rotating disk electrode, -> rotating ring disk electrode, -> wall-jet electrode, wall-tube electrode, channel electrode, etc. See also - flow-cells, -> hydrodynamic voltammetry, -> detectors. 

Rivers transport material in several phases dissolved, suspended particulate and bed load. Physical and chemical processes within an estuary infiuence the transportation and transformation of this material, thereby affecting the net supply of material to the oceans. Several definitions and geomorphologic classifications of estuaries have been reviewed by Pe-rillo (1995). From a chemical perspective, an estuary is most simply described as the mixing zone between river water and seawater characterised by sharp gradients in the ionic strength and chemical composition. Geographic distinctions can be made between drowned river valleys, fjords and bar-built estuaries. They can alternatively be classified in terms of the hydrodynamic regime as ... 

The potential profile associated with hydrodynamic techniques usually takes the form of a linear sweep between two potentials in which the oxidation or reduction processes of interest occur. As for cyclic voltammetry, the gradient of the ramp represents the scan rate. However, for steady-state techniques, the scan rate used must be sufficiently slow to ensure that the steady state is attained at every potential during the course of the voltammetric scan. The upper value of the scan rate that may be used under the steady-state regime is therefore restricted by the rate of convective mass transport of material to the electrode surface. The faster the rate of convective mass transport the faster the scan rate that may be used consistent with the existence of steady-state conditions. 

The modeling and design of a three-phase reactor requires the knowledge of several hydrodynamic (e.g., flow regime, pressure drop, holdups of various phases, etc.) and transport (e.g., degree of backmixing in each phase, gas-liquid, liquid-solid mass transfer, fluid-reactor wall heat transfer, etc.) parameters. During the past decade, extensive research efforts have been made in order to improve our know-how in these areas. Chapters 6 to 8 present a unified review of the reported studies on these aspects for a variety of fixed bed columns (i.e., co-current downflow, co-current upflow, and counter-current flow). Chapter 9 presents a similar survey for three-phase fluidized columns. 

Gas-liquid systems are encountered very frequently in a variety of industrial applications. For example, the production of crude oil and natural gas involves the transportation of a gas and a liquid phase in pipes. Although very significant efforts have been made to arrive at a fundamental description and subsequent CFD modeling of these type of flows, unfortunately the progress is still very limited and the engineer, faced with the solution of practical problems, very often has to resort to semiempirical methods. This state of the art is mainly due to the fact that numerous flow regimes, with their specific hydrodynamic characteristics, can prevail. 

Gas-liquid Reasonable Turbulence modeling -1- modeling of interfacial transport phenomena -1- prediction of flow regime transition -1- interaction of hydrodynamics with chemical transformation processes... 

---