Convective systems hydrodynamic methods

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]. 

A reciprocal proportionality exists between the square root of the characteristic flow rate, t/A, and the thickness of the effective hydrodynamic boundary layer, <5Hl- Moreover, f)HL depends on the diffusion coefficient D, characteristic length L, and kinematic viscosity v of the fluid. Based on Levich s convective diffusion theory the combination model ( Kombi-nations-Modell ) was derived to describe the dissolution of particles and solid formulations exposed to agitated systems [(10), Chapter 5.2]. In contrast to the rotating disc method, the combination model is intended to serve as an approximation describing the dissolution in hydrodynamic systems where the solid solvendum is not necessarily fixed but is likely to move within the dissolution medium. Introducing the term... 

Electrochemical systems can be studied with methods based on impedance measurements. These methods involve the application of a small perturbation, whereas in the methods based on linear sweep or potential step the system is perturbed far from equilibrium. This small imposed perturbation can be of applied potential, of applied current or, with hydrodynamic electrodes, of convection rate. The fact that the perturbation is small brings advantages in terms of the solution of the relevant mathematical equations, since it is possible to use limiting forms of these equations, which are normally linear (e.g. the first term in the expansion of exponentials). 

Graphical methods can be used to extract information concerning mass transfer if the data are collected under well-controlled hydrodynamic conditions. The systems described in Chapter 11 that are imiformly accessible with respect to convective diffusion would be appropriate. The analysis would apply to data collected on a rotating disk electrode as a function of disk rotation speed, or an impinging jet as a function of jet velocity. 

Numerical simulations of styrene free-radical polymerization in micro-flow systems have been reported. The simulations were carried out for three model devices, namely, an interdigital multilamination micromixer, a Superfocus interdigital micromixer, and a simple T-junction. The simulation method used allows the simultaneous solving of partial differential equations resulting from the hydrodynamics, and thermal and mass transfer (convection, diffusion and chemical reaction). 

Currently, analytical approaches are still the most preferred tools for model reduction in microfluidic research community. While it is impossible to enumerate all of them in this chapter, we will discuss one particular technique - the Method of Moments, which has been systematically investigated for species dispersion modeling [9, 10]. The Method of Moments was originally proposed to study Taylor dispersion in a circular tube under hydrodynamic flow. Later it was successfully applied to investigate the analyte band dispersion in microfluidic chips (in particular electrophoresis chip). Essentially, the Method of Moments is employed to reduce the transient convection-diffusion equation that contains non-uniform transverse species velocity into a system of simple PDEs governing the spatial moments of the species concentration. Such moments are capable of describing typical characteristics of the species band (such as transverse mass distribution, skew, and variance). 

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