Mass transport, by convection

Glaser, R. W. (1993). Antigen-antibody binding and mass transport by convection and diffusion to a surface a two-dimensional computer model of binding and dissociation kinetics, Anal. Biochem., 213, 152-161. 

We will assume for all of the techniques discussed in this chapter that the analyte solution is quiet (that is, still and unstirred) in order to ensure that mass transport by convection is absent. Furthermore, we will also assume that an excess of ionic electrolyte has been added to the solution to ensure that mass transport by migration is also absent. We see that the only form of mass transport remaining is diffusion, and hence the subtitle to this chapter. 

A simple proof that mass transport by convection is more efficient than movement by diffusion alone can be aflorded by considering a cup of tea we stir sugar into a cup of tea rather than let the sugar move by diffusion atone. 

The two major causes of uneven current distribution are diffusion and ohmic resistance. Nonuniformity due to diffusion originates from variations in the effective thickness of the diffusion layer 8 over the electrode surface as shown in Figure 10.13. It is seen that 8 is larger at recesses than at peaks. Thus, if the mass-transport process controls the rate of deposition, the current density at peaks ip is larger than that at recesses since the rate of mass transport by convective diffusion is given by... 

V/s. The lower limit is determined by the need to maintain the total time of the experiment below 10-50 seconds (i.e., before mass transport by convection becomes important). The upper limit is determined by the double-layer charging current and by the uncompensated solution resistance, as discussed in Section 25.2. 

Glaser, R. W. (1993) Antigen-Antibody Binding and Mass Transport by Convection and Diffusion to a Surface A Two-Dimensional Computer Model of Binding and Dissociation Kinetics. Analytical Biochemistry 213 152-161. 

Above the catalyst surface, substance A will be transported by diffusion, mainly in the x-direction. In a thin layer close to the wall, the diffusion boundary layer, mass transport by convection is negligible, and from (2.338) we obtain the diffusion equation valid for steady one-dimensional diffusion without chemical reaction... 

Phenomena that arise in these materials include conduction processes, mass transport by convection, potential field effects, electron or ion disorder, ion exchange, adsorption, interfacial and colloidal activity, sintering, dendrite growth, wetting, membrane transport, passivity, electrocatalysis, electrokinetic forces, bubble evolution, gaseous discharge (plasma) effects, and many others. 

For the simulation a dynamic ID-model based on mass and energy balances is used.. complete and detailed derivation of the model is beyond the scope of this paper an will be presented elsewhere (Veser and Frauhammer. to be published). The mass-balance equation contains mass transport by convection, dispersion as well as adsorption and desorption from the catalyst surface ... 

Permeable particles containing large pores are used in separation and reaction engineering as adsorbents and catalysts. Perfusion chromatography, developed in 1990 [1] for the separation of proteins, is based on the concept of augmented dif-fusivity by convection [2], which combines the contributions of mass transport by convection and diffusion in adsorbent pores. An example of flow-through particles is given in Fig. 3.4-1 where wide pores are of the order of 7000 A and polymeric microspheres contain small diffusive pores. 

In the case of channel electrodes, the solution containing the electroactive species flows in a channel such as that shown in Figure 8.3 where a rectangular electrode of length Xe and width w is placed on the channel floor. The mass transport by convection can be controlled through the channel design, the electrode size and the flow rate. Moreover, this setup enables the incorporation of electrochemical measurements to flow systems as well as its use in spectroelectrochemistry and photoelectrochemistry [4]. 

By using the length of the band electrode, x, as the characteristic dimension and the Peclet number, Pe, that reflects the relative influence of the mass transport by convection and diffusion... 

Electrochemical timescales are of importance when one desires to measure the kinetics of an electrochemical process. Changing the rate of mass transport by convection, the shape or size of the electrode, and scan rate can vary the timescale. There is a quadratic dependence of the timescale upon the radius of the electrode, favoring microelectrodes, therefore, for rapid kinetic measurements. A timescale as short as 10 ps can be accessed using a microjet electrode. The reader is referred to an excellent analysis by Bond and co-workers. ... 

So far we considered mass transport by convection and diffusion, neglecting a possible influence of potential gradients present in the electrolyte. The equations presented in the preceding sections therefore are strictly applicable only to neutral species, or to minor ionic species present in a supporting electrolyte. The effect of potential gradients on the rate of transport of ionic species is particularly pronounced in solutions where concentration gradients are absent or when two types of ions are present in comparable quantities. We therefore need to have a closer look at the transport mechanisms in electrolytes in presence of a potential gradient. 

As discussed in Sect. 5.6, the Peclet number in the diffusion Pep denotes the ratio of the mass transported by convection relative to the mass transported by diffusion. In the HA for the pure smectitic bentonite, the normalized length L of (5.142) is... 

For an ideally mixed batch reactor, the equation for mass transport by convection is not needed but, apart from this exception, we have to account for convection and in many cases also for diffusion. 

To overcome the mass transport limitation of ligands (e.g., O2, H2O2) or substrates from solution to reach cyt P450 molecules present on an electrode surface, the electrode is rotated at certain speeds (usually in the range 1000-3000 rpm) in electrocatalytic reactions to obtain steady-sate currents. Stirring the electrolyte solution has also been shown to facilitate mass transport by convection. The rotation rate-dependent catalytic currents is governed by the Levich equation, which relates the rates of interfacial electron exchange, enzyme kinetics, and substrate mass transport to steady-state catalytic currents [48-50]. 

Mass transported by convection Mass transported by diffusion... 

In (Bortels et al., 1997 Van den Bossche et al., 1995 2002 Van Parys et al., 2010) a numerical approach is developed in order to define the underlying reaction mechanism. By using the MITReM (Multiple Ion Transport and Reaction Model) model, mass transport by convection, diffusion and migration but also the presence of homogeneous reactions in the electrolyte, are accoxmted for. The related model parameters such as diffusion coefficients, rate constants and transfer coefficients are adjusted in order to improve the agreement between experimental and simulated polarization curves. Thus, the best parameter values, corresponding to the best simulated curve, are selected by a chi-by-eye approach, without a statistical evaluation. 

As already mentioned, the solution to be electrolyzed has to contain an excess (usually a concentration two order of magnitude higher than that of the examined electroactive species) of supporting electrolyte (usually as a salt) to minimize the solution resistance (Ohmic drop, see above). The presence of the supporting electrolyte also enables that the electroactive species transport occurs by diffusion and not by migration under the action of the applied electric field. Furthermore, the solution has to be unstirred to avoid mass transport by convection. 

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