Molecular flux

As a result of the diffusional process, there is no net overall molecular flux arising from diffusion in a binary mixture, the two components being transferred at equal and opposite rates. In the process of equimolecular counterdiffusion which occurs, for example, in a distillation column when the two components have equal molar latent heats, the diffusional velocities are the same as the velocities of the molecular species relative to the walls of the equipment or the phase boundary. 

In most cases, the term expressing the divergence of the molecular flux in Equation (40) (DV c,) can be neglected compared to the other two transport terms. Important excep-... 

Analysis of thermal decomposition of molecules on hot surfaces of solids is of considerable interest not only for investigation of mechanisms of heterogeneous decomposition of molecules into fragments which interact actively with solid surfaces. It is of importance also for clarifying the role of the chemical nature of a solid in this process. Furthermore, pyrolysis of molecules on hot filaments made of noble metals, tungsten, tantalum, etc., is a convenient experimental method for producing active particles. Note that it allows continuous adjustment of the intensity of the molecular flux by varying the temperature of the filament [8]. 

Fig. 1. Model of subarachnoidal space, CSF flow, and molecular flux (N1). After CSF production in choroid plexus of the ventricles (1,2,3), CSF passes the aperture (4,5), reaches the cistemae (6-9), and divides into a cortical and a lumbar branch of the subarachnoidal space. Finally, CSF drains through the arachnoid villi into venous blood. The illustration represents an idealized cross section through the subarachnoid space. Molecules diffuse from serum with a concentration C(ser) flu ough tissue along the diffusion path x into the subarachnoid space with a concentration C(csF)- Th molecular flux J depends on the local gradient Ac/Ax or dddx and the diffusion constant D. The CSF concentration increases with decreasing volume exchange, i.e., decreasing CSF volume bulk flow (F= 500 ml/day). The flow rate of a molecule in CSF is r= FIA, where A is the varying cross section of the subarachnoid space.

The blood-CSF barrier for proteins is defined functionally by nonlinear interaction of the molecular flux and CSF flow rate. 

In order to evaluate this expression, we need to know the force v / that is responsible for producing the molecular flux. It could be an external force such as an electric field acting on ions. Then evaluation of Eq. 18-48 would lead to the relationship between electric conductivity, viscosity, and diflusivity known as the Nernst-Einstein relation. 

Equation 15 can be used only for substrates that have their normal to the surface coincident with the direction of the molecular beam. When the normal to the surface element is at an angle 3 to the molecular beam, the molecular flux at an angle 4 from the center line and at an angle of incidence (3 onto the surface decreases by a factor of cos ((3), and the incident molecular flux, r(i), is given by ... 

Turner, S. M. Stable isotopes, mass spectrometry, and molecular fluxes Applications to toxicology. J. Pharmacol. Toxicol. Methods 53, 75-85, 2006. 

The factor r] accounts for the number of emitted Balmer-a photons per molecule, which involves the type of dissociation process, t] = 1 holds for dissociative excitation with the products D°(n = 3)+D° (Is), i.e., only one atom will directly emit Balmer-a radiation whereas the other is set free already as a proton. In the worst case of a pure molecular flux the total deuterium flux would be underestimated by a factor of 2 by determining it from the Balmer-line emissions solely. More details concerning the energies of the dissociated atoms and accompanying heating mechanisms can be found in [46] and below. 

In order to convert the photons into molecular fluxes the D/XB-value for the Fulcher-a band is needed. For this purpose a collisional-radiative model (CRM) has been set up which includes all levels that could contribute to the population of the 3p 3f7u state. Figure 6.12 shows that under the conditions of the TEXTOR scrape-off layer the levels 2p 3flu and 2s 3X+ also contribute to... 

In these equations, tt is the molecular flux of momentum and g and F are gravitational acceleration and external body forces, respectively. The physical interpretation of the various terms appearing in these equations again follows similar lines the first term is the rate of increase in momentum per unit volume the second term represents... 

Kaczmarski et al. used a similar model for the calculation of the band profiles of the enantiomers of 1-indanol on a chiral phase in HPLC [29,57]. These authors ignored the external mass transfer and assumed that local equilibrium takes place for each component between the pore surface and the stagnant fluid phase in the macropores (infinite fast kinetics of adsorption-desorption). They also assumed that surface diffusion contribution is much faster than pore diffusion and neglected pore diffusion entirely. Instead of the single file Maxwell-Stefan diffusion, these authors used the generalized Maxwell-Stefan diffusion (see Chapter 5).The calculation (see below) requires first the selection of equations to calculate the surface molecular flux [29,57,58],... 

The first argument is based on the spatial separation between the molecules. The molecular flux at an average speed of 200 m/s is about 3 x 109 cm 2.s 1 at the plane of the detector. This flux corresponds to an average molecular density of 1.7 x 1011 m-3 or an average molecular distance of 200 pm. This is three orders of magnitude wider than any realistic range of molecular (van der Waals) forces, which are typically confined to below 100 nm. 

Flynn GL, Roseman TJ. Membrane diffusion. II. Influence of physical adsorption on molecular flux through heterogeneous dimethylpolysiloxane barriers. J Pharm Sci 1971 60(12) 1788-1796. 

The molecular fluxes can be extended to systems containing gradients in the other two space dimensions as well, denoting a complete three dimensional flux formulation. 

The molecular flux models are still not closed as the mean free path I and the molecular speed quantities ([C[)m are not determined yet. A frequently used closure is examined in the next paragraph. 

Averaging the product of the absolute value of the gradient and the fluxes gives as the result the average contributory effect of mass and molecular fluxes at the interfaces over the whole domain of integration [67]. Drew [54] defined the averaged interfacial area per unit volume by ... 

Desorption was monitored with mass spectroscopy. The cracking patterns of 2-propanol, acetone, and propene were individually determined ( ). For quantitative analysis, masses 45, 45, 41, 18, and 2 were used for 2-propanol, acetone, propene, water, and hydrogen, respectively, after correction for cracking in a similar procedure as described (52 ) The mass spectrometer sensitivities were determined to be 5.26, 7 88, 5.07, 4 74, and 5.20 amp/torr, and the pumping speeds were 9.5, 15.1, 51.0, 1.7, 56.9 L sec"", respectively for the five species. These two latter quantities were used to convert the mass spectrometer readings into molecular fluxes. 

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