Forced convective mass transport

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. 

Convective mass transport is caused by the movement of the solution as a whole. The driving force in this case is external energy, usually in the form of mechanical energy of stirring the solution, rotating the... 

RRDE is significantly simpler than with conventional cyclic voltammetry data in quiescent solutions [88, 89]. As such, these forced convection systems have been widely used in the study of electrocatalysis in general. Of special interest are situations where the rate determining step is chemical (a) or electrochemical (B) (Scheme 3.7) [60], In particular, for an RDE at steady state, the rate at which the reactant is depleted at the interface must be equal to the rate at which it is replenished from the solution via convective mass transport. For a reaction first order in dioxygen this relationship reads ... 

Convective mass transport around an electrode may arise from forced or free convection. Solution of Eq. (108) requires coupling with the corresponding equations of motion for forced or free convection (408, 409). For instance, laminar free convection on a vertically oriented electrocatalyst gives variation of the surface rate along the electrode with an average rate (407-410)... 

At low Re, the viscous effects dominate inertial effects and a completely laminar flow occurs. In the laminar flow system, fluid streams flow parallel to each other and the velocity at any location within the fluid stream is invariant with time when boundary conditions are constant. This implies that convective mass transfer occurs only in the direction of the fluid flow, and mixing can be achieved only by molecular diffusion [37]. By contrast, at high Re the opposite is true. The flow is dominated by inertial forces and characterized by a turbulent flow. In a turbulent flow, the fluid exhibits motion that is random in both space and time, and there are convective mass transports in all directions [38]. 

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... 

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. 

Dne to the macroporons strnctnre of monolithic stationary phases (flow channels), the solvent is forced to pass the entire polymer, leading to faster convective mass transfer (compared to diffnsion), which provides for analyte transport into and out of the stagnant pore liqnid, present in the case of microparticulate columns. 

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... 

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