Forced convection mass transport

The third form of mass transport is convection driven by pressure. When forced circulation exists in electrolyte, convection may be the dominant form of mass transport. Thus, in general, a flux Jj (mol/s cm) of species j may occur due to the above three types of mass transport mechanisms. The flux can be described by the Nernst-Planck equation [5]... 

Phenomena that arise in these materials include conduction processes, mass transport by convection, potential field effects, electron or ion disorder, ion exchange, adsorption, interfacial and colloidal activity, sintering, dendrite growth, wetting, membrane transport, passivity, electrocatalysis, electrokinetic forces, bubble evolution, gaseous discharge (plasma) effects, and many others. 

This section describes the balance of these opposing mass transport forces for the geometry of crevice corrosion. Mass transport of species in aqueous solution can occur by three processes migration, diffusion, or convection. In most cases of crevice corrosion, convection can be ignored owing to the restricted geometry involved. 

Loop Tests Loop test installations vary widely in size and complexity, but they may be divided into two major categories (c) thermal-convection loops and (b) forced-convection loops. In both types, the liquid medium flows through a continuous loop or harp mounted vertically, one leg being heated whilst the other is cooled to maintain a constant temperature across the system. In the former type, flow is induced by thermal convection, and the flow rate is dependent on the relative heights of the heated and cooled sections, on the temperature gradient and on the physical properties of the liquid. The principle of the thermal convective loop is illustrated in Fig. 19.26. This method was used by De Van and Sessions to study mass transfer of niobium-based alloys in flowing lithium, and by De Van and Jansen to determine the transport rates of nitrogen and carbon between vanadium alloys and stainless steels in liquid sodium. 

Convection—the transport of mass or energy as a result of streaming in the system produced by the action of external forces. These include mechanical forces (forced convection) or gravitation, if there are density gradients in the system (natural or free convection). 

There are three types of mass transport processes within a microfluidic system convection, diffusion, and immigration. Much more common are mixtures of three types of mass transport. It is essential to design a well-controlled transport scheme for the microsystem. Convection can be generated by different forces, such as capillary effect, thermal difference, gravity, a pressurized air bladder, the centripetal forces in a spinning disk, mechanical and electroosmotic pumps, in the microsystem. The mechanical and electroosmotic pumps are often used for transport in a microfluidic system due to their convenience, and will be further discussed in section 11.5.2. The migration is a direct transport of molecules in response to an electric field. In most cases, the moving... 

The previous models were developed for Brownian particles, i.e. particles that are smaller than about 1 pm. Since most times particles that are industrially codeposited are larger than this, Fransaer developed a model for the codeposition of non-Brownian particles [38, 50], This model is based on a trajectory analysis of particles, including convective mass transport, geometrical interception, and migration under specific forces, coupled to a surface immobilization reaction. The codeposition process was separated in two sub-processes the reduction of metal ions and the concurrent deposition of particles. The rate of metal deposition was obtained from the diffusion... 

Convection (of the electrolyte liquid phase as a whole) can be natural (due to thermal effects or density gradients) or forced (principal mass transport mode in hydrodynamic techniques). Still, however, close to the electrode surface a diffusion layer develops. 

Convection That form of mass transport in which the solution containing electroanalyte is moved natural convection occurs predominantly by heating of solution, while forced convection occurs by careful and deliberate movement of the solution, e.g. at a rotated disc electrode or by the controlled flow of analyte solution over a channel electrode. 

During dissolution, the concentrations of X and AgY2 increase at the phase boundary, the concentration of Y decreases and, as a consequence of the concentration gradient formed, mass transport occurs, as indicated in fig. 3.6. If the electrolyte is not stirred [1,38,39,40], diffusion and natural convection are the only driving forces of transport. 

Clearly, the solution of this equation at forced-convection electrodes will depend on whether the fluid flow is laminar, in the transition regime, or turbulent. Since virtually all kinetic investigations have been performed in the laminar flow region, no further mention will be made of turbulent flow. The reader interested in mass transport under turbulent flow is recommended to consult refs. 14 and 15. 

Chapter 1 serves as an introduction to both volumes and is a survey of the fundamental principles of electrode kinetics. Chapter 2 deals with mass transport — how material gets to and from an electrode. Chapter 3 provides a review of linear sweep and cyclic voltammetry which constitutes an extensively used experimental technique in the field. Chapter 4 discusses a.c. and pulse methods which are a rich source of electrochemical information. Finally, Chapter 5 discusses the use of electrodes in which there is forced convection, the so-called hydrodynamic electrodes . 

CONVECTION. In general, mass motions within a fluid resulting in transport and mixing of the properties of that fluid. Natural convection results from differences in density caused hy temperature differences. Warn air is less dense than cool aid the warm air rises relative to Ihe cool air. and the cool air sinks. Forced convection involves motion caused by pumps, blowers, or other mechanical dev ices. See also lleat Transfer. 

What characterises the different incubation steps is the time required to reach thermodynamic equilibrium between an antibody and an antigen in the standard format of microtitre plates. In fact the volume used in each of the incubation steps has been fixed between 100 and 200 pL to be in contact with a surface area of approx. 1 cm2 where the affinity partner is immobilised. The dimensions of the wells are such that the travel of the molecule from the bulk solution to the wall (where the affinity partner is immobilised) is in the order of 1 mm. It must be taken into account that the generation of forced convection or even of turbulence in the wells of a microtitre plate is rather difficult due to the intrinsic dimensions of the wells [10]. Indeed, even if some temperature or shaking effects can help the mass transport from the solution to the wall, the main mass transport phenomenon in these dimensions is ensured by diffusion. 

The mass transport limiting current is the maximum current (or rate) that the process can achieve. In order to increase its value, an increase of the electrode area, bulk concentration, or mass transport coefficient is needed. In the last case, this means a decrease of the diffusion layer thickness which can be done, for example, by forced convection. 

When a system is operating at the limiting current, rather than at an appreciable fraction of the limiting current, the problem is very much simplified. Such problems can be classified as mass-transport limited. Usually, the limiting current density is correlated with dimensionless numbers. Most forced-convection correlations take the form... 

The second part of the book discusses ways in which information concerning electrode processes can be obtained experimentally, and the analysis of these results. Chapter 7 presents some of the important requirements in setting up electrochemical experiments. In Chapters 8—11, the theory and practice of different types of technique are presented hydrodynamic electrodes, using forced convection to increase mass transport and increase reproducibility linear sweep, step and pulse, and impedance methods respectively. Finally in Chapter 12, we give an idea of the vast range of surface analysis techniques that can be employed to aid in investigating electrode processes, some of which can be used in situ, together with photochemical effects on electrode reactions— photoelectrochemistry. 

Transport to the electrode surface as described in Chapter 5 assumes that this occurs solely and always by diffusion. In hydrodynamic systems, forced convection increases the flux of species that reach a point corresponding to the thickness of the diffusion layer from the electrode. The mass transfer coefficient kd describes the rate of diffusion within the diffusion layer and kc and ka are the rate constants of the electrode reaction for reduction and oxidation respectively. Thus for the simple electrode reaction O + ne-— R, without complications from adsorption,... 

The mass transfer coefficient, K, is defined as the ratio of the mass transport controlled reaction rate to the concentration driving force. The concentration driving force will depend on both turbulent and bulk convection. Bulk convection depends on molecular diffusivity, while the turbulent component depends on eddy diffusivity (4). The mass transfer coefficient considers the combination of the two transport mechanisms, empirically. 

Convective diffusion — The electrochemical - mass transport controlled by both -> convection and - diffusion is called a process by convective diffusion [i]. Convection is caused by externally controlled force or spontaneous force. Convective diffusion has been conventionally used in a strict sense for well-controlled flow such as for -> rotating disk electrodes [ii], - channel elec-... 

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. 

Of course, the current can never be higher than the rate of the most hindered (slowest) step which is either the electron transfer or the mass transport. The problem of reversibility in terms of the relative ratio of ks and km is illustrated in Fig. 1. Two systems with different electron transfer rates (ks( 1) and ks(2)) are considered and the effect of forced convection (the variation of the rotation rate of the electrode (coT)) is presented. The rate... 

Tubular electrode — Working electrode design employing a tube of the electrode material to be studied with (i.e. secondary battery) the electrolyte solution flowing through the orifice of the tube. This way well-defined forced convection of solution can be established. -> Mass transport processes can be treated mathematically. 

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