Mass transport convection

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... 

Diflfiision, convection and migration are the fonns of mass transport that contribute to the essential supply and removal of material to and from the electrode surface [1, 2, 3 and 4],... 

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... 

Concentration gradients for the analyte in the absence of convection, showing the time-dependent change in diffusion as a method of mass transport. 

The shape of a voltammogram is determined by several experimental factors, the most important of which are how the current is measured and whether convection is included as a means of mass transport. Despite an abundance of different voltam-metric techniques, several of which are discussed in this chapter, only three shapes are common for voltammograms (figure 11.33). 

Concentration gradient for the analyte showing the effects of diffusion and convection as methods of mass transport. 

Analysis of a method of maximizing the usefiilness of smaH pilot units in achieving similitude is described in Reference 67. The pilot unit should be designed to produce fully developed large bubbles or slugs as rapidly as possible above the inlet. UsuaHy, the basic reaction conditions of feed composition, temperature, pressure, and catalyst activity are kept constant. Constant catalyst activity usuaHy requires use of the same particle size distribution and therefore constant minimum fluidization velocity which is usuaHy much less than the superficial gas velocity. Mass transport from the bubble by diffusion may be less than by convective exchange between the bubble and the surrounding emulsion phase. 

The liquid-liquid extraction process is based on the specific distribution of dissolved components between two immiscible fluids, for instance, between aqueous and organic liquids. The process refers to a mass exchange processes in which the mass transport of component (j) from phase (1) to phase (2) by means of convection or molecular diffusion acts to achieve the chemical potential (p) equilibrium (134) ... 

Both share more or less the same merits but also the same disadvantages. The beneficial properties are high OCV (2.12 and 1.85 V respectively) flexibility in design (because the active chemicals are mainly stored in tanks outside the (usually bipolar) cell stack) no problems with zinc deposition in the charging cycle because it works under nearly ideal conditions (perfect mass transport by electrolyte convection, carbon substrates [52]) self-discharge by chemical attack of the acid on the deposited zinc may be ignored because the stack runs dry in the standby mode and use of relatively cheap construction materials (polymers) and reactants. 

Overall, the RDE provides an efficient and reproducible mass transport and hence the analytical measurement can be made with high sensitivity and precision. Such well-defined behavior greatly simplifies the interpretation of the measurement. The convective nature of the electrode results also in very short response tunes. The detection limits can be lowered via periodic changes in the rotation speed and isolation of small mass transport-dependent currents from simultaneously flowing surface-controlled background currents. Sinusoidal or square-wave modulations of the rotation speed are particularly attractive for this task. The rotation-speed dependence of the limiting current (equation 4-5) can also be used for calculating the diffusion coefficient or the surface area. Further details on the RDE can be found in Adam s book (17). 

The governing equation for mass transport in the case of an incompressible flow field is easily derived from the general convection-diffusion equation Eq. (32) with... 

Under realistic conditions a balance is secured during current flow because of additional mechanisms of mass transport in the electrolyte diffusion and convection. The initial inbalance between the rates of migration and reaction brings about a change in component concentrations next to the electrode surfaces, and thus gives rise to concentration gradients. As a result, a diffusion flux develops for each component. Moreover, in liquid electrolytes, hydrodynamic flows bringing about convective fluxes Ji j of the dissolved reaction components will almost always arise. 

It was shown in Section 1.8 that in addition to ion migration, diffusion and convection fluxes are a substantial part of mass transport during current flow through electrolyte solutions, securing a mass balance in the system. In the present chapter these processes are discussed in more detail. 

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