Molecular transport phenomena

Fig. 1. The MR Toolkit MR techniques yield infonnation about chemical and physical processes over length scales of A to cm. Imaging pulse sequences may be integrated with spectroscopy and molecular diffusion measurements providing maps of chemical composition and molecular transport phenomena at spatial resolutions of 30-500 pm.

One of the advantages of PPG NMR is its ability to provide direct information about the entirety of molecular transport phenomena in pelletized adsorbents and catalysts (316). As an example, Table I presents the transport parameters for methane in granulated zeolite NaCaA (16,53). 

This table consists of three columns giving for each discipline (thermodynamics, chemical kinetics, molecular transport phenomena, laboratory reactors) the numbers of... 

Membrane modelling has been considered from both the nano/microscopic and the macroscopic viewpoints, but little has been done to bridge these two limits. The breadth of microscopic modelling work for PEMs encompasses molecular dynamics simulations [17] and statistical mechanics modelling [18-21]. Most applications have focused on Nafion, and interestingly, some models even apply macroscopic transport relations to the microscopic transport within a pore of a membrane [41]. While the focus of this Chapter is on macroscopic models required for computational simulations of complete fuel cells [12,13,15], the proposed modelling framework is based on fundamental relations describing molecular transport phenomena. 

In very viscous liquids there is normally no turbulence, so that transport of both matter and heat depends on molecular transport phenomena, i.e. diffusion and heat conduction. For viscous liquids the thermal diffusivity, i.e. the conductivity of the liquid divided by its specific heat per unit volume, is usually much greater than the molar diffusivity (e.g. by a factor of around 10 Yet local temperature gradients may exist within the striations. These may be estimated as follows ... 

A cell consists in a natural sophisticated laboratory, where thousands of reactions take place every second. When compared with a standard lab-on-a-chip, a lab-on-a-cell has some advantages a cell performs much more functions than the ones that could be integrated into a lab-on-a-chip device all the reactions are ruled by diffusion and molecular transport phenomena and occur at a millisecond timescale the cells reactions are specific and produce pure and active compounds (Le Gac and van den Berg, 2010). 

Kerkhof and Geboers in their paper Toward a Unified Theory of Isotropic Molecular Transport Phenomena (AIChE Journal (2005), 51, 81) give the following equation ... 

The permeation of gases and vapors through thin films is dependent on the molecular size, shape, wettability and soundness of the fabricated membrane. Since permeation in well-made products is a molecular transport phenomenon, it is affected by orientation, degree of crystallinity and temperature. Attempts have been made to relate permeation rates through thin films to absorption of thicker films, sheets, pipe, etc. This has been generally unsuccessful. Thicker films and sheets represent an average set of properties obtainable firom many thin films produced under a variety of conditions. To produce a thin film representative of this average is not practical. 

Another mechanism that may affect the velocity profile in a microchannel is thermal creep. It is a molecular transport phenomenon that occurs when two isopressure containers at different temperatures are connected by a channel whose diameter is close to the gaseous mean free path. Under this condition, gaseous molecules start to flow from the cooler... 

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). 

One of the innovative applications of scanning probe microscopy for nanolithography is dip pen nanolithography (DPN). In this special technique the water meniscus formed between the tip and the substrate acts as a medium for molecular transport. The technique depends on the key phenomenon that the molecule to be deposited on the substrate (which is referred as the ink ) can be transported in a controlled way from the tip (which is initially coated with the ink) to the substrate. The molecule (the ink) to be deposited on the substrate should interact with the substrate to form a chemical bond, leading to a stable structure [82]. 

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. 

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. 

Thermal conduction is the molecular transport of heat energy caused by a temperature gradient. The heat is transported from regions of high temperature towards those at lower temperatures, i.e. in the opposite direction to the temperature gradient. The corresponding law is FOURIER S law. The same phenomenon of transport of energy... 

Microscale thermal transport phenomenon involves complex transfer mechanism of free electrons and phonons. The molecular dynamics and processes are not significant in most of the microscopic engineering applications. However, scale effects become extremely important in system with sudden high heat flux irradiation by laser pulses and some other dimensionally space- and time-governed problems. Anisimov etal. (1974) proposed the first two-step model for microscale conduction as... 

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. 

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