Solutal convection

J. Holuigue, O. Bertrand, E. Arquis. Solutal convection in crystal growth effect of interface curvature on flow structuration in a three-dimensional cylindrical configuration. J Cryst Growth 180 591, 1997. 

Solute flux within a pore can be modeled as the sum of hindered convection and hindered diffusion [Deen, AIChE33,1409 (1987)]. Diffusive transport is seen in dialysis and system start-up but is negligible for commercially practical operation. The steady-state solute convective flux in the pore is J, = KJc = where c is the radially... 

We have reviewed today s knowledge of the mechanisms for growth of electrolyte crystals from aqueous solution Convection, diffusion, and adsorption ( ) mechanisms leading to linear rate laws, as well as the surface spiral mechanism (parabolic rate law) and surface nucleation (exponential rate law). All of these mechanisms may be of geochemical importance in different situations. 

A CV voltammogram can be recorded under either a dynamic or a steady state depending on the electrode design and solution convection mode. In a stationary solution with a conventional disk electrode, if the scan rate is sufficiently high to ensure a non-steady state, the current will respond differently to the forward and backward potential scan. Figure 63 shows a typical CV for a reversible reduction.1... 

With macroelectrodes, the duration of an experiment in stationary solutions is determined by the onset of distortion due to solution convection. Even in... 

Comparable or larger errors are introduced by unwanted convective mass transport. Convection is caused by physical motion of the solution, sometimes purposefully introduced for techniques such as rotating electrode voltammetry. When a quiet solution is desired, however, convective errors may arise at longer experiment times (slow scan rates) from mechanical vibrations of the solution. Convection is a particular problem for cells inside inert-atmosphere boxes, on which fans and vacuum pumps may be operative. Convection raises the current... 

The flows and the consequent solute segregation caused by thermo-solutal convection in nondilute alloys is only beginning to be explored by experimental and computational analyses. Recent results are discussed by Brown (5). 

Solution. Convective motion will be assumed to begin when ... 

From time to time we have mentioned that thermal conductivities of materials vary with temperature however, over a temperature range of 100 to 200°C the variation is not great (on the order of 5 to 10 percent) and we are justified in assuming constant values to simplify problem solutions. Convection and radiation boundary conditions are particularly notorious for their nonconstant behavior. Even worse is the fact that for many practical problems the basic uncertainty in our knowledge of convection heat-transfer coefficients may not be better than 20 percent. Uncertainties of surface-radiation properties of 10 percent are not unusual at all. For example, a highly polished aluminum plate, if allowed to oxidize heavily, will absorb as much as 300 percent more radiation than when it was polished. 

The incorporation of solutal convection into morphological stability theory is here illustrated on the basis of a very simple model. It is assumed that the interfacial solute gradient Gc in the liquid is enhanced by a Nusselt number Nu given by... 

Albeit simplified, the convection model proposed here is consistent with the introduced macroscopic interface approach. It implies a reasonable parametrisation of the basic effect of solutal convection the steepening of the solutal gradient at the cellular interface. The corresponding predicted decrease in the plate spacing is in agreement with the available field observations in Figure 3. 

The present model approach has combined three equations to predict the onset of cellular growth during freezing of natural waters (i) constitutional supercooling from morphological stability theory, (ii) an exact diffusive solute redistribution and (iii) an intermittent turbulent solutal convection model. The main results are ... 

Transport with flow of soil solution convection-dispersion... 

Any reactions that occur must occur at the electrode-solution interface and the reacting species must be brought to the electrode surface by diffusion or mass transport through stirring of the solution (convection). The ions in the bulk of the solution are not attracted to the electrodes by potential difference there is no potential gradient in the bulk of the solution. Even when we are interested in the bulk properties of the solution, we are only analyzing an extremely small amount of the solution that is no longer... 

Electrochemical systems where the mass transport of chemical species is due to diffusion and electromigration were studied in previous chapters. In the present chapter, we are going to consider the occurrence of the third mechanism of mass transfer in solution convection. Although the modelling of natural convection has experienced some progress in recent years [1], this is usually avoided in electrochemical measurements. On the other hand, convection applied by an external source forced convection) is employed in valuable and popular electrochemical methods in order to enhance the mass transport of species towards the electrode surface. Some of these hydrodynamic methods are based on electrodes that move with respect to the electroljAic solution, as with rotating electrodes [2], whereas in other hydrodynamic systems the electrolytic solution flows over a static electrode, as in waU-jet [3] and channel electrodes [4]. 

The kinetic study of this process reveals that in the case of individual resins two different situations occur. The first situation takes place when the solution convection levels the concentration in aU points, and the second one happens when there is no convection in the system. 

The central part of the RDE theory and technique is the convection of electrolyte solution. Due to the solution convection, the reactant in the solution will move together with the convection at the same transport rate. Let s first consider the situation where the flow of electrolyte solution from the bottom of the electrode edge upward with a direction parallel to the electrode surface to see how the diffusion— convection layer can be formed and what is its mathematic expression. 

Note that this do (cm) is different from that of diffusion layer thickness because within the diffusion layer, there is no solution convection, hut within this diffusion—convection layer, both diffusion and convection coexist. Based on convection kinetic theory, this diffusion—convection layer thickness can be approximately expressed as Eqn (5.1) ... 

This decrease in current is due to the slow spread of the diffusion layer out into the bulk solution, with a concomitant decrease in the concentration gradient. In practice, this process continues for around 100 s or so, after which time random convection processes in the solution take over, and put an end to the further movement of the diffusion layer. Waiting for nearly two minutes, and relying on chance solution convection for a steady-state current, is not particularly attractive. Accordingly, in amperometric measurements for sensing applications, the spread of this diffusion layer is limited by the use of one or more of the following mechanisms convective diffusion the... 

The separation of a mixture into discrete zones from an initial band of origin is difficult to achieve in free solution. Convection due to gravity... 

A further critical contribution to the crystallization process is played by thermal energy and the way this is delivered in the solution (convective or dielectric heating) basically crystal nuclei can show different crystallographic phases, however their stability is firmly dependent on the temperature. It can happen that a solid material shows one crystalline phase at high temperatures and another one at lower. For instance, relatively to CdS elongated nanostructures Jun et al. reported a temperature-mediated phase control of the initial seeds finally producing nanorods for temperatures as high as 300°C and branched architectures for temperatures below 180°C [38, 39]. 

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