Diffusion path lengths

Diffnsion finxes develop as a result of these concentration gradients. The layer of electrolyte where the concentration changes occur and within which the substances are transported by diffnsion is called the diffusion layer. Its thickness, 5 (the diffusion path length), depends on cell design features and on the intensity of convechve... 

Tybsre m is the total mass of analyte collected, D the molecular diffusion coefficient, A the area of the diffusion channel, L the diffusion path length, C the analyte concentration in the air, and Tt the sampling time. In deriving equation (8.7) it was assumed t. that the sorbent is effective sink for the analyte and,... 

For hydrophilic and ionic solutes, diffusion mainly takes place via a pore mechanism in the solvent-filled pores. In a simplistic view, the polymer chains in a highly swollen gel can be viewed as obstacles to solute transport. Applying this obstruction model to the diffusion of small ions in a water-swollen resin, Mackie and Meares [56] considered that the effect of the obstruction is to increase the diffusion path length by a tortuosity factor, 0. The diffusion coefficient in the gel, )3,i2, normalized by the diffusivity in free water, DX1, is related to 0 by... 

The tortuosity factor appears as a squared term because it decreases the concentration gradient and increases the diffusive path length. Using a cubic lattice model and inquiring how many steps a diffusing molecule needs to take to get around an obstacle, 0 was derived to be... 

CaC03 precipitation is clearly visible in Figure 14.14, which is a TEM image of halloysite cross-sections. Halloysite has >90% of the tubular form with outer diameter 50 5nm and inner diameter of the lumen 15 nm. The length of the initial halloysite is less than 1 micron, which results in a substantially short diffusion path length. The calculated value of the free inner space indicates the ability to load a maximum 14 3 % of the total volume ofthe halloysite. The entrapment efficiency of 5 % by volume was estimated. 

The development of composite micro/mesoporous materials opens new perspectives for the improvement of zeolytic catalysts. These materials combine the advantages of both zeolites and mesoporous molecular sieves, in particular, strong acidity, high thermal and hydrothermal stability and improved diffusivity of bulky molecules due to reduction of the intracrystalline diffusion path length, resulting from creation of secondary mesoporous structure. It can be expected that the creation of secondary mesoporous structure in zeolitic crystals, on the one hand, will result in the improvement of the effectiveness factor in hydroisomerization process and, on the other hand, will lead to the decrease of the residence time of products and minimization of secondary reactions, such as cracking. This will result in an increase of both the conversion and the selectivity to isomerization products. 

For a flat-plate porous particle of diffusion-path length L (and infinite extent in other directions), and with only one face permeable to diffusing reactant gas A, obtain an expression for tj, the particle effectiveness factor defined by equation 8.5-5, based on the following... 

Thin-layer cell design is based on reduction of diffusion path length the mobile phase is directed along the working electrode surface as a thin film of liquid (see Figure 3-1). 

Porous electrodes may be regarded as a combination of thin-layer and wall-jet design short diffusion path length, strong convective motion due to high liquid velocities in narrow pores. 

Unsteady State Diffusion. The apparatus, experimental procedures, and the computational procedures used to calculate the diffusion parameter D /r (where D is the diffusion coefficient and r is the diffusion path length) have been described in detail previously (6, 8). A differential experimental system was used to avoid errors caused by small temperature fluctuations. In principle, the procedure consisted of charging the sample under consideration with argon to an absolute pressure of 1204 12 torr (an equilibrium time of about 24 hours was allowed) and then measuring the unsteady state release of the gas after suddenly reducing the pressure outside the particles back to atmospheric. 

The spin-lattice relaxation process is usually exponential. Theoretically, the effect of spin-diffusion, characterized by the coefficient D (order of 1(T12 cm2 s 1), has an influence on T, relaxation times when ix > L2/D, where Lis the diffusion path length. NMR studies of model systems f6r rubber networks, based on a styrene-butadiene-styrene block copolymer (SBSy, in which styrene blocks act as a crosslink for polybutadiene rubber segments of known and uniform length, indicate that spin diffusion operating between PS and PB phases causes a lowering of Tg for the PS component in SBS (as compared to the pure PS) and hindering of the motion of the PB component (as compared to the pure PB)51). 

Whereas current-producing reactions occur at the electrode surface, they also occur at considerable depth below the surface in porous electrodes. Porous electrodes offer enhanced performance through increased surface area for the electrode reacdon and through increased mass-transfer rates from shorter diffusion path lengths. The key parameters in determining the reaction distribution include the ratio of the volume conductivity of the electrolyte to the volume conductivity of the electrode matrix, the exchange current, the diffusion characteristics of reactants and products, and the total current flow. The porosity, pore size, and tortuosity of the electrode all play a role. 

Figure 12.4 The pulse scheme of the three-pulse echo sequence to determine Xe diffusion coefficients in polymers and other porous systems. The shaded areas are magnetic field gradient pulses with amplitude g and length 8. The time between the two gradient pulses A determines the time during which the diffusion path length is...

Exploitation of liquid-liquid microreactor in organic synthesis offers attractive advantages, including the reduction of diffusion path lengths to maximize the rate of mass transfer and reaction rates. Despite the advantages, interest in liquid-liquid micro reactors did not take off until recently, perhaps because of the complication of flow pattern manipulation combined with the limited numbers of liquid-liquid reactions. Initial interest focused on the control of parameters responsible for variation in flow patterns to engineer microemulsions or droplets. However, it was soon realized that liquid-liquid microdevices are more than just a tool for controlling flow patterns and further interest developed. 

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