Layer stagnant-diffuse

A stagnant diffusion layer is often assumed to approximate the effect of aqueous transport resistance. Figure 4 shows a membrane with a diffusion layer on each side. The bulk solutions are assumed to be well mixed and therefore of uniform concentrations cM and cb2. Adjacent to the membrane is a stagnant diffusion layer in which a concentration gradient of the solute may exist between the well-mixed bulk solution and the membrane surface the concentrations change from Cm to c,i for solution 1 and from cb2 to cs2 for solution 2. The membrane surface concentrations are cml and cm2. The membrane has thickness hm, and the aqueous diffusion layers have thickness ht and h2. 

The dependence of the limiting current density on the rate of stirring was first established in 1904 by Nernst (N2) and Brunner (Blla). They interpreted this dependence using the stagnant layer concept first proposed by Noyes and Whitney. The thickness of this layer ( Nernst diffusion layer thickness ) was correlated simply with the speed of the stirring impeller or rotated electrode tip. 

If q is negligibly small a stagnant diffusion layer in aqueous phase is a rate-limiting step. This case is often the most useful from an analytical point of view. The well-known equation for a reversible polarographic wave can be obtained as ... 

When a biocatalyst is immobilized on or within a solid matrix, mass transfer effects may exist because the substrate must diffuse from the bulk solution to the immobilized biocatalyst. If the biocatalyst is attached to non-porous supports there are only external mass transfer effects on the catalytically active outer surface in the reaction solution, the supports are surrounded by a stagnant film and substrate and product are transported across this Nemst layer by diffusion. The driving force for this diffusion is the concentration difference between the surface and the bulk concentration of substrate and product. 

Though there is fluid flow in the bulk of the electrolyte, it is found that there is a layer adjacent to the electrode in which the electrolyte is stationary, or stagnant. Thus the electron acceptors travel by convection from the bulk up to the stagnant layer and then cross the remaining boundary layer by diffusion. This transport by a convection-with-diffusion mechanism has not been taken into account so far. The equations for the time and space variation of concentration [i.e., Eq. (7.178)], for the transition time [Eq. (7.190)], and for the time variation of potential [Eq. (7.192)] have been derived for convection-free conditions, and they break down when convection becomes significant. The first approximation theory given above, therefore, deviates from experiment if the constant current is applied sufficiently long (times on the order of seconds) for convection to be important. 

When fluid is pumped through a cell such as that shown in Fig. 12, transport of dissolved molecules from the cell inlet to the IRE by convection and diffusion is an important issue. The ATR method probes only the volume just above the IRE, which is well within the stagnant boundary layer where diffusion prevails. Figure 13 shows this situation schematically for a diffusion model and a convection-diffusion model (65). The former model assumes that a stagnant boundary layer exists above the IRE, within which mass transport occurs solely by diffusion and that there are no concentration gradients in the convection flow. A more realistic model of the flow-through cell accounts for both convection and diffusion. As a consequence of the relatively narrow gap between the cell walls, the convection leads to a laminar flow profile and consequently to concentration gradients between the cell walls. 

The parameter refers to the thickness of a stagnant diffusion medium layer at the surface of the solid, where the drug concentration reacBgat steady-state dissolution. Indeed, it is preferable to consideCsto be the solubility ofthe drug in the diffusion layer, since it is the maximum concentration possible in that layer that controls the dissolution rate. Nevertheless, on the basis of this equation, it can still be seen that if the solubility in the dissolution medium was increased, the dissolution rate would also increase. 

Another classification involves the number of phases in the reaction system. This classification influences the number and importance of mass and energy transfer processes in the design. Consider a stirred mixture of two liquid reactants A and B, and a catalyst consisting of small particles of a solid added to increase the reaction rate. A mass transfer resistance occurs between the bulk liquid and the surface of the catalyst particles. This is because the small particles tend to move with the liquid. Consequently, there is a layer of stagnant fluid that surrounds each particle. This results in reactants A and B transferring through this layer by diffusion in order to reach the catalyst surface. The diffusion resistance gives a difference in concentration between... 

Every solid catalyst in solution is surrounded by a "stagnant diffusion layer which reactants must cross in order to reach the surface. The resulting concentration profile is sketched in Fig. 6. The rate of the reactant s arrival at the solid/liquid interface is determined by its concentration gradient at that interface, (dc/dx)x=0. The diffusion layer therefore has the same effect on the rate as does the simplified layer shown by the dotted lines [63]. The thickness of this so-called Nernst layer is designated 5. It follows from Fick s first law of diffusion that the number of moles of reactant A, nA, that reach the surface in unit time is given by... 

Peskin [49] used the Galerkin finite-element method to compute current distribution and shape change for electrodeposition into rectangular cavities. A concentration-dependent overpotential expression including both forward and reserve rate terms was used, and a stagnant diffusion layer was assumed. An adaptive finite-element meshing scheme was used to redefine the problem geometry after each time step. 

Figure 11.3 Oscillating concentration profiles for a finite stagnant diffusion layer a) imaginary part b) real part.

Figure 11.6 Oscillating concentration as a function of time with position as a parameter for a finite stagnant diffusion layer.

Plot, on an impedance plane format, the impedance obtained for a Nernst stagnant diffusion layer and the impedance obtained for a rotating disk electrode under assumption of an infinite Schmidt number. Show that, while the behaviors of the two models at high and low frequencies are in agreement, the two models do not agree at intermediate frequencies. Explain. 

A Nemst stagnant-diffusion-layer model was used to accovmt for the diffusion impedance. This model is often used to account for mass transfer in convective systems, even though it is well known that this model caimot ac-coimt accurately for the convective diffusion associated with a rotating disk electrode. 

So, in all configurations we have (1) diffusion steps in aqueous feed and strip stagnant boundary layers, (2) diffusion of the complex solute-carrier in the LM phase and/or interdiffusion in the membrane support pores,... 

The process of equilibration of the atmosphere with the ocean is called gas exchange. Several models are available however, the simplest model for most practical problems is the one-layer stagnant boundary layer model (Fig. 9-18). This model assumes that a well-mixed atmosphere and a weU-mixed surface ocean are separated by a film on the liquid side of the air-water interface through which gas transport is controlled by molecular diffusion. [A similar layer exists on the air side of the interface that can be neglected for most gases. SO2 is a notable exception (Liss and Slater, 1974).]... 

We saw above that the concentration gradient at an electrode will be linear with respect to the spatial coordinate perpendicular to the electrode surface if the anode/cathode cell were operated at a constant current density and if the fluid velocity were zero. In actuality, there will always be some bulk liquid electrolyte stirring during current flow, either an imposed forced convection velocity or a natural convection fluid motion due to changes in the reacting species concentration and fluid density near the electrode surface. In electrochemical systems with fluid flow, the mass transfer and hydrodynamic fluid flow equations are coupled and the solution of the relevant differential equations is often a formidable task, involving complex mathematical and/or numerical solution techniques. The concept of a stagnant diffusion layer or Nemst layer parallel and adjacent to the electrode surface is often used to simplify the analysis of convective mass transfer in... 

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