Mass convection/diffusion mechanism

Referring to Figure 9.1, we will assume that the species of interest is transported from the blood vessel lumen, where its bulk concentration is Q, to the blood vessel surface, where its concentration is Cs, by a convective-diffusive mechanism which depends on the local fluid mechanics and can be characterized by a fluid-phase mass transfer coefficient ki (see Reference 6 for further background). The species flux in the blood phase is given by... 

There are three types of mass transport processes within a microfluidic system convection, diffusion, and immigration. Much more common are mixtures of three types of mass transport. It is essential to design a well-controlled transport scheme for the microsystem. Convection can be generated by different forces, such as capillary effect, thermal difference, gravity, a pressurized air bladder, the centripetal forces in a spinning disk, mechanical and electroosmotic pumps, in the microsystem. The mechanical and electroosmotic pumps are often used for transport in a microfluidic system due to their convenience, and will be further discussed in section 11.5.2. The migration is a direct transport of molecules in response to an electric field. In most cases, the moving... 

The scope of kinetics includes (i) the rates and mechanisms of homogeneous chemical reactions (reactions that occur in one single phase, such as ionic and molecular reactions in aqueous solutions, radioactive decay, many reactions in silicate melts, and cation distribution reactions in minerals), (ii) diffusion (owing to random motion of particles) and convection (both are parts of mass transport diffusion is often referred to as kinetics and convection and other motions are often referred to as dynamics), and (iii) the kinetics of phase transformations and heterogeneous reactions (including nucleation, crystal growth, crystal dissolution, and bubble growth). 

The transfer of mass from one point to the other may take place by two different modes, namely, diffusion and convection. The basic mechanisms for these modes of mass transfer are similar to those for heat transfer discussed in 4.2 and 4.3. Specifically, the mechanism for mass convection is analogous to heat convection and that for mass diffusion is analogous to heat conduction. 

M 44a] [P 40] Numerical errors which are due to discretization of the convective terms in the transport equation of the concentration fields introduce an additional, unphysical diffusion mechanism [37]. Especially for liquid-liquid mixing with characteristic diffusion constants of the order of 1CT9 m2 s 1 this so-called numerical diffusion (ND) is likely to dominate diffusive mass transfer on computational grids. 

Mass transport by diffusion can be regarded as the last resort. When movement of the electroactive species is not promoted by the input of external energy, either electrical (migration) or mechanical (convection), diffusion takes over. The driving force in this case is the... 

The Peclet number means the ratio of the mass transfer rate by convection mechanism into the pore to the mass transport rate by a diffusion mechanism. At... 

Basically, three mechanisms are responsible for mass transport inside an electrochemical cell diffusion, migration, and convection. Diffusion is mass transport because of concentration gradients, i.e., variations in the concentration of a species with position. Diffusion occurs mainly near the electrode surface because of gradients created by the consumption of species that undergo redox reactions and are incorporated into the deposit. This incorporation process depletes the deposition species near the electrode, generating the concentration gradient. 

The LSW theory dealing with Ostwald ripening [50,51] is, strictly speaking, valid for the case of immobile oil droplets when the molecular diffusion is the only mechanism of mass transfer. Under these circumstances, the contributions of molecular and convective diffusion are related by the Peclet number (Npe) ... 

We have previously written an expression for j n in Eq. (2-150), but this expression is in terms of the local bulk concentration evaluated at the interface, c, and thus to determine c we would need to solve bulk-phase transport equations. We will not pursue that subject here. However, when we use this material to solve flow problems, we will consider several cases for which it is not necessary to solve the full convection-diffusion equation for c. We will see that the concentration of surfactant tends to become nonuniform in the presence of flow -i.e., when u n and u v are nonzero at the interface. This tendency is counteracted by surface diffusion. When mass transfer of surfactant to and from the bulk fluids is added, this will often tend to act as an additional mechanism for maintenance of a uniform concentration T. This is because the rate of desorption from the interface will tend to be largest where T is largest, and the rate of adsorption largest where T is smallest. 

Solid particles. The problem of convective diffusion to a chain of solid reacting particles was studied in [168, 350], The retardation mechanism (shielding) of mass exchange in a chain of solid particles and the quantitative behavior of such a system are the same as for chains of drops. 

We now consider forced convection. We have seen that the diffusion layer thickness (5) is a crucial parameter in the diffusion equations. It is a fitting parameter in fact, a thickness from the electrode surface within which no hydrodynamic motion of the solution is assumed, i.e., the mass transport occurs by molecular mechanism, mostly by diffusion. The exact solution of the respective convective-diffusion equations is very complicated therefore, only the essential features are surveyed for two cases stirring of the solution and rotating disc electrode (RDE). 

The mass balance equations are written for aU the species included in the detailed kinetic mechanism and for every lumped reactor in the network. CFD calculations are used to provide the initial guesses for the composition. Each reactor, whether lumped or not, is assumed to be perfectly mixed. The steady-state mass balance of each species k accounts for convection, diffusion, and chemical reaction terms ... 

While mass convection, laminar convection and diffusion contribute to the distribution in the system, desagglomeration and destruction are the principal dispersive mechanisms. In practice, some of these mechanisms are acting together. 

For the high current density range, mass transport of reactants and products becomes a limiting factor. So the oxidant and fuel concentration is significantly reduced at high current densities, and they cause fuel cell voltage losses. The mass transport mechanisms within the fuel cell include convection, diffusion, and/or convectimi. Simplification of (17.1) for simple concentration polarization is shown in (17.4). Thus,7ii , can be also defined as current density, where the... 

This approach may become possible as CFD codes become better able to solve the convective diffusion equations for heat and mass transfer in the presence of a chemical reaction and in addition to their more established but not completely perfect role in the prediction of the fluid mechanics. At the moment, this procedure lacks validation even for single-phase stirred-tank reactors. 

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