Natural convection mass transport

The sweep rate should be v > 10 mV s, chosen so as to limit errors due to natural convective mass transport ... 

The usual specific flow-rates for extraction are very small. In terms of space velocities, these are about 5 to 15 kg/h per litre of extractor volume, with superficial velocities in the range of 0.5 to 10 mm/s. With these small velocities, natural convection mass transfer is the favoured mechanism of transport. Gas densities are in the range of 500 to 800 kg/m3, and viscosities are about 5 x 10 7 kg/(m s), thus giving kinematic viscosities of about 10 9 m2/s, which is a very small value for a fluid. For example, the kinematic viscosity of water is 10"7 m2/s and that of ambient air is 2 x 10 5 m2/s. This makes free convection a principal mechanism for mass-transfer in high pressure gases. 

Equation 61 demonstrates that the corrosion rate for this class of systems is controlled uniquely by the by the rate of mass transport. Comparing Equation 61 with Equation 53 reveals that the corrosion potential is defined by the natures of the anodic and cathodic partial processes for Equation 53 while, in the case at hand, the corrosion potential is influenced by the magnitude of the mass transfer coefficient - a property of the convective mass transport condition. 

Electrode reactions are heterogeneous processes, so that their rates will be influenced (a) by the concentration of the reactant at the surface which is related to the bulk concentration by an adsorption isotherm, (b) by the presence of any intermediates and/or products which are adsorbed on the surface, and (c) by the nature of the electrode material and solvent, also, (d) depending on concentration and/or solution agitation or flow rate, by diffusional or convective mass transport of reagents and/or products to or... 

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). 

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). 

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. 

A major fallacy is made when observations obeying a known physical law are subjected to trend-oriented tests, but without allowing for a specific behaviour predicted by the law in certain sub-domains of the observation set. This can be seen in Table 11 where a partial set of classical cathode polarization data has been reconstructed from a current versus total polarization graph [28], If all data pairs were equally treated, rank distribution analysis would lead to an erroneous conclusion, inasmuch as the (admittedly short) limiting-current plateau for cupric ion discharge, albeit included in the data, would be ignored. Along this plateau, the independence of current from polarization potential follows directly from the theory of natural convection at a flat plate, with ample empirical support from electrochemical mass transport experiments. 

Convective crystal dissolution means that crystal dissolution is controlled by convection, which requires (i) a high interface reaction rate so that crystal dissolution is controlled by mass transport (see previous section), and (ii) that mass transport be controlled by convection. In nature, convective crystal dissolution is common. In aqueous solutions, the dissolution of a falling crystal with high solubility (Figure 1-12) is convective. In a basaltic melt, the dissolution of most minerals is likely convection-controlled. 

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. 

By introduction of a typical value for D0, 10 r> cm2 s 1, it is seen that the value of 8 after, for example, 5 seconds amounts to 0.1 mm. At times larger than 10-20 seconds, natural convection begins to interfere and the assumption of linear diffusion as the only means of mass transport is no longer strictly valid. At times larger than approximately 1 minute, the deviations from pure diffusion are so serious and unpredictable that the current observed experimentally cannot be related to a practical theoretical model. 

The density differences leading to natural convection most often have a thermal origin. The lofting of warm air masses at the earth s surface and their replacement by cooler and denser masses from above is an example of convective flow (thermal convection) that profoundly affects our atmosphere. Likewise, heated fluid elements in a separation chamber will rise convectively while cooler elements descend. The resulting transport of solute can profoundly affect separations. 

When the S becomes larger than a few tenths of a millimeter, natural convection begins to interfere and the assumption of diffusion as the only means of mass transport is no longer... 

Here, T is the appropriate state variable conjugate to the flux J and X, and depends on the thermodynamic state of the system. These linear, phenomenological laws are fundamental to all processes involving the transfer of mass, momentum or energy but, in many practical circumstances encountered in industry, the fundamental transport mechanisms arise in parallel with other means of transport such as advection or natural convection. In those circumstances, the overall transport process is far from simple and linear. However, the description of such complex processes is often rendered tractable by the use of transfer equations, which are expressed in the form of linear laws such as... 

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