Transport internal diffusive

In coulometry these exchange membranes are often used to prevent the electrolyte around the counter electrode from entering the titration compartment (see coulometry, Section 3.5). However, with membrane electrodes the ion-exchange activity is confined to the membrane surfaces in direct contact with the solutions on both sides, whilst the internal region must remain impermeable to the solution and its ions, which excludes a diffusion potential nevertheless, the material must facilitate some ionic charge transport internally in order to permit measurement of the total potential across the membrane. The specific way in which all these requirements are fulfilled in practice depends on the type of membrane electrode under consideration. 

At catalytically active centers in the center of carrier particles, external mass transfer (film diffusion) and/or internal mass transfer (pore diffusion) can alter or even dominate the observed reaction rate. External mass transfer limitations occur if the rate of diffusive transport of relevant solutes through the stagnating layer at a macroscopic surface becomes rate-limiting. Internal mass transfer limitations in porous carriers indicate that transport of solutes from the surface of the particle towards the active site in the interior is the slowest step. 

Attainable internal vapor pressure for a heptane-octane droplet with internal diffusive transport (56)... 

General Discussion. We have shown that for the vaporization of practical, multicomponent droplets, qualitatively different vaporization behavior results when extreme internal transport rates are assumed. Since diffusive transport is always present during the transient, it is the... 

Figure 2.8 shows the dependence of the cadmium transport internal driving force coefficients, external driving force coefficients, K, and overall mass-transfer coefficients, K, on feed flow rate (Fig. 2.8A) or strip flow rate (Fig. 2.8B) variations. It is clearly seen that the resistivity to the diffusion of protons is much lower than that of cadmium species themselves. 

However, the two-sink model as well as other existing adsorption (sink) models do not seem to be able to describe the strong asymmetry between the adsorption/desorption of VOCs on/from indoor surface materials (the desorption process is much slower than the adsorption process). Diffusion combined with internal adsorption is assumed to be capable of explaining the observed asymmetry. Diffusion mechanisms have been considered to play a role in interactions of VOCs with indoor sinks. Dunn and Chen (1993) proposed and tested three unified, diffusion-limited mathematical models to account for such interactions. The phrase unified relates to the ability of the model to predict both the ad/absorption and desorption phases. This is a very important aspect of modeling test chamber kinetics because in actual applications of chamber studies to indoor air quality (lAQ), we will never be able to predict when we will be in an accumulation or decay phase, so that the same model must apply to both. Development of such models is underway by different research groups. An excellent reference, in which the theoretical bases of most of the recently developed sorption models are reviewed, is the paper by Axley and Lorenzetti (1993). The authors proposed four generic families of models formulated as mass transport modules that can be combined with existing lAQ models. These models include processes such as equilibrium adsorption, boundary layer diffusion, porous adsorbent diffusion transport, and conveetion-diffusion transport. In their paper, the authors present applications of these models and propose criteria for selection of models that are based on the boundary layer/conduction heat transfer problem. 

The low solubility of methane in water limits its diffusive transport in the flooded soil, and most methane is oxidized to carbon dioxide. The aerenchyma of plants mediates the transport of air (oxygen) to the roots and methane from the anaerobic soil to the atmosphere. The flux of gases in the aerenchyma depends on concentration and total pressure gradients and internal structure, including openings of the aerenchyma (see Chapter 7 for details). 

Pfennig, A., Mulhcomponent diffusion, in International Workshop on Transport in Fluid Multiphase Systems From Experimental Data to Mechanistic Models, Aachen, 2004. 

In this model the momentum transport in the ejections will be reduced by damping the axial flow component. Moreover the dissipation is reduced due to a reduction of the internal shear by a vorticiy diffusion process. Finally the vortex core increases in width and the axial momentum is smeered over larger areas. Therefore it is thinkable that the competition between vorticity diffusion and the cascade process, which both are not dissipative processes, would result in a reduction of the energy transport since the diffusion transports the energy in the opposite direction than the cascade process This means towards vortices of larger scale. 

The infinitesimal control volume is a hollow cylinder of length dz and with a thickness dr, located inside the internal fluid and co-axial with the axis of the fiber (Fig. 22.11). Oxygen enters this volume by convective transport with the liquid stream flowing along the fiber at z position and by diffusive transport through the cylinder lateral surface with radius (r + dr). Then, O2... 

Figure 5. Pellet intruded at Sbara. Once the alloy is able to pass through pores at the pellet surface, it floods through the pellet. The large macroporous voids act as conduits for flow throughout the pellet. The pellet thus appears to have good internal diffusion transport properties.

Transport phenomena often accompany processes conducted in reactors with a catalyst bed. Included are internal and external diffusion, and internal and external energy transfer. Chemical reactions taking place on the surface of non-porous catalyst grains usually meet a resistance in a form of an external mass or energy transfer, whereas the internal mass transfer and an external energy transfer most often accompany non-isodiermal processes in porous grains. 

On the other hand, the rates of electrochemical reaction should be distributed uniformly over the entire thickness of the electrode, requiring high rates of transport of reactants and products via diffusion paths. In the limits of fast reactant diffusion, the internal electrode surface would be utilized uniformly for current conversion, resulting in a simple proportionality of the current density, a J SecsaIcl- This proportionality is only valid for electrodes with thickness Ice where 8cl is the... 

As outlined in Chapter 4, the thermal conductivity in the dilute-gas limit, is related to a number of effective cross sections, which are associated with the transport of translational and internal energy, and with their interaction. In principle, a similar analysis as given for nitrogen in Section 14.2 can be performed for polyatomic molecules. In practice, such an analysis is often hampered by a lack of experimental information and insufficient knowledge of the behavior of cross sections describing the diffusion of internal energy at high temperatures. 

Modeling supercritical extraction of solid material is based on the mass balances that are relevant for the internal diffusive transport of the extract within the solid matter and the external convective transport of the extract from the solid surface to the solvent fluid. 

The Sherwood number can be viewed as describing the rabo of convective to diffusive transport and finds its counterpart in heat transfer in the form of the Nusselt number. It is high ( 1) when flow is turbulent or the boundary layer "film" is very thin. The Biot number has the same form as the Sherwood number but refers to two adjacent phases or media. In one of these, which we term internal, transport is usually by diffusion. This can be in a gas bubble, a liquid drop, a porous solid parbcle, or some other enbty. The adjacent ("external") phase is a liquid or a gas in relative motion to the particle and has an attendant "film resistance." Like the Sherwood number, Bi is high ( 1) when the external phase is in turbulent motion (caused, for example, by stirring) or the boxmdary layer is very thin. We will have more to say about it in Illustration 5.1. 

In Chapter 4, two different transport regimes were identified transport inside the particles and transport between the bulk fluid and the surface of the catalyst particles. Transport inside the catalyst particles is known as internal or intraparticle transport, or as pore diffusion. Transport between the bulk fluid stream and the external surface of the catalyst particles is known as external or interparticle transport. The mechanisms of transport are different fiar these two regimes, and the rates of transport are influenced by different variables. Internal transport will be treated first, followed by extmial tranqiort. These discussions will be preceded by a brief overview iff the physical nature of heterogeneous catalysts. 

Physical properties affecting catalyst perfoniiance include tlie surface area, pore volume and pore size distribution (section B1.26). These properties regulate tlie tradeoff between tlie rate of tlie catalytic reaction on tlie internal surface and tlie rate of transport (e.g., by diffusion) of tlie reactant molecules into tlie pores and tlie product molecules out of tlie pores tlie higher tlie internal area of tlie catalytic material per unit volume, tlie higher the rate of tlie reaction... 

The transport of particles in the plasma is diffusive or convective for the neutrals, whereas the charge carriers move under the influence of the external and internal electric and magnetic fields. The drift velocityv of the charged particles is proportional to the electric field E ... 

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