Transport phenomena molecular diffusion

Bulk or forced flow of the Hagan-Poiseuille type does not in general contribute significantly to the mass transport process in porous catalysts. For fast reactions where there is a change in the number of moles on reaction, significant pressure differentials can arise between the interior and the exterior of the catalyst pellets. This phenomenon occurs because there is insufficient driving force for effective mass transfer by forced flow. Molecular diffusion occurs much more rapidly than forced flow in most porous catalysts. 

Dispersion is a band-spreading or mixing phenomenon that results from the coupling of fluid flow with molecular diffusion. Diffusion is mass transport due to a concentration gradient. 

Small particles in a temperature gradient are driven from the high- to low-temperature regions. This effect was first observed in the nineteenth century when it was discovered that a dust-free or dark space surrounded a hot body, suitably illuminated. Particle transport in a temperature gradient has been given the name thermophoresis, which means being carried by heat." Thermophoresis is closely related to the molecular phenomenon thermal diffusion, transport produced by a temperature gradient in a multicomponent system. 

Concerning membranes, new separation capabilities are expected for these materials. The molecular sieving effect caused by connected nanopores can be applied to the separation of molecules with molecular weights smaller than 1000. The key properties of such membranes are based on the preponderant effect of activated diffusion in nanopores, however. This phase transport phenomenon derives from the nanophased ceramic concept and classes these membranes among those materials expected to be crucial in the areas of modem technology, such as environmental protection, biotechnology, and the production of effect chemical. 

Equation 7.2.a-5 implicitly assumes perfectly ordered flow in that V (pyD Vx ) is specific for molecular diffusion. Deviations from perfectly ordered flow, as encountered with turbulent flow, lead to a flux that is also expressed as if it arose from a diffusion-like phenomenon, in order to avoid too complex mathematical equations. The proportionality factor between the flux and the concentration gradient is then called the turbulent or eddy diffusivity. Since this transport mechanism is considered to have the same driving force as molecular diffusion, the two mechanisms are summed and the resulting proportionality factor is called effective diffusivity, D,. In highly turbulent flow the contribution of... 

In the mid-1800s. Pick [3,4] introduced two differential equations that provide a mathematical framework to describe the otherwise random phenomenon of molecular diffusion. The flow of mass by diffusion across a plane was proportional to the concentration gradient of the diffnsant across it. The components in a mixture are transported by a driving force dnring diffusion. The molecnlar motion is Brownian. The ability of... 

In these expressions, molecular diffusion has been neglected relative to turbulent diffusion. When the reactor is sufficiently long, (Dr L ), the distance after which the spot has dispersed laterally and the flow has become uniform over the available flow section is small compared to the length of the reactor, and the main process observed inside the reactor is the transport of the spot inside the reactor and its gradual expansion along the axial direction. It is this phenomenon that we model by employing the concept of turbulent dispersion introduced in Chapter 8. For this reactor, the mean residence time is related simply to velocity U of the mean flow ... 

At this point, the variables C and u are now used to connote the average (macroscopic) tracer concentration and velocity, respectively, and the overbar is dropped for convenience. Implicit in this formulation is the belief that fundamentally Lagrangian (particle) dispersion can be modeled as a continuum Eulerian phenomenon in a fashion analogous to the Fickian formulation of molecular transport by Brownian motion. This is a useful fiction for simple modeling exercises, but must be used with caution (see the next section on isopycnal diffusion). 

Q phases are already one of the most promising, research-intensive LLC-based drug delivery systems because of the superior diffusion and access characteristics afforded by their 3-D interconnected nanopore systems [129, 151-154]. Initial results have also shown that Q-phase LLC materials also possess superior transport and access properties in membrane applications compared to L and Hu phases [170]. This phenomenon could translate into the design of superior LLC-based heterogeneous catalysts or bulk sorbents, as the interconnected nanochannels may provide more open pathways for better accessibility and selective molecular and/or ion diffusion. However, designing functional amphiphiles that can readily form useful Q-phase materials is not a straightforward task. To date, less than a handful of LLC monomers are known in the literature that can be polymerized in Q phases [172-175]. 

The transfer of heat in a fluid may be brought about by conduction, convection, diffusion, and radiation. In this section we shall consider the transfer of heat in fluids by conduction alone. The transfer of heat by convection does not give rise to any new transport property. It is discussed in Section 3.2 in connection with the equations of change and, in particular, in connection with the energy transport in a system resulting from work and heat added to the fluid system. Heat transfer can also take place because of the interdiffusion of various species. As with convection this phenomenon does not introduce any new transport property. It is present only in mixtures of fluids and is therefore properly discussed in connection with mass diffusion in multicomponent mixtures. The transport of heat by radiation may be ascribed to a photon gas, and a close analogy exists between such radiative transfer processes and molecular transport of heat, particularly in optically dense media. However, our primary concern is with liquid flows, so we do not consider radiative transfer because of its limited role in such systems. 

The objectives of the present research were (i) to develop a solvent transport model accounting for diffusional and relaxational mechanisms, in addition to effects of the viscoelastic properties of the polymer on the dissolution behavior (ii) to perform a molecular analysis of the polymer chain disentanglement mechanism, and study the influence of various molecular parameters like the reptation diffusion coefficient, the disentanglement rate and die gel layer thickness on the phenomenon and (iii) to experimentally characterize the dissolution phenomenon by measuring the temporal evolution of the various fronts in the problem. 

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