Film diffusion particle size

The emission of a pheromone from a controlled-release formulation can depend on the diffusion through holes in the matrix or on the penetration of the compound through a wall or membrane by absorption, solution and diffusion (8). Thus variation in the parameters of the formulations, such as film thickness, particle size, solvent, pore dimensions, etc., alters the release rate. The design of the formulation must therefore take into account the effect of each variable on the emission rate in order to develop a system that is effective during the appropriate cycle of the target insect. 

More advanced insulations are also under development. These insulations, sometimes called superinsulations, have R that exceed 20 fthh-°F/Btu-m. This can be accomplished with encapsulated fine powders in an evacuated space. Superinsulations have been used commercially in the walls of refrigerators and freezers. The encapsulating film, which is usually plastic film, metallized film, or a combination, provides a barrier to the inward diffusion of air and water that would result in loss of the vacuum. The effective life of such insulations depends on the effectiveness of the encapsulating material. A number of powders, including silica, milled perlite, and calcium silicate powder, have been used as filler in evacuated superinsulations. In general, the smaller the particle size, the more effective and durable the insulation packet. Evacuated multilayer reflective insulations have been used in space applications in past years. 

As diffusion to the surface of a polymer is one of the limiting steps in extraction, the particle size or film thickness of a sample is also important [278,333,337-340]. With the typical diffusion coefficients of additives in polymers a particle diameter of about 0.3 mm is required for an extraction time of about 1000 s at 40 °C. An exception to this is the extraction of thin films and foams, for which the shortest dimension is small. It is not surprising that no more than 50 % of antioxidants could be extracted from PP pellets as opposed to 90 % recoveries from the same polymer extruded into film [341]. Grinding of the polymer is usually an essential step before extraction. Care should be taken to avoid loss of volatile additives owing to the heat generated in such processes. Therefore, cryogrind-ing is preferred. 

It is important to differentiate between two terms that are widely used in the literature, namely chemical kinetics and kinetics . Chemical kinetics is defined as the investigation of chemical reaction rates and the molecular processes by which reactions occur where transport (e.g., in the solution phase, film diffusion, and particle diffusion) is not limiting. On the other hand, kinetics is the study of time-dependent processes. Because of the different particle sizes and porosities of soils and sediments, as well as the problem to reduce transport processes in these solid phase components, it is difficult to examine the chemical kinetics processes. Thus, when dealing with solid phase components, usually the kinetics of these reactions are studied. 

Zogorski et al. [125] indicate that external transport is the rate-limiting step in systems having poor mixing, dilute concentration of adsorbate, small particle sizes of adsorbent, and a high affinity of adsorbate for adsorbent. Some experiments conducted at low concentrations have shown that film diffusion solely controls the adsorption kinetics of low molecular weight substances [81,85]. 

High crosslink densities may severely depress polymer reactivity as a result of large decreases in swelling and diffusion rate within the polymer. Diffusion control in a polymer reaction can be detected by the inverse dependence of rate on polymer particle size (radius for spherical particle, thickness for film or sheet) [Imre et al., 1976 Sherrington, 1988]. 

Fixed beds cannot use very small sizes of catalyst because of plugging and high-pressure drop, whereas fluidized beds are well able to use small-size particles. Thus for very fast reactions in which pore and film diffusion may influence the rate, the fluidized bed with its vigorous gas-solid contacting and small particles will allow a much more effective use of the catalyst. 

Particles of constant size Gas film diffusion controls, Eq. 11 Chemical reaction controls, Eq. 23 Ash layer diffusion controls, Eq. 18 Shrinking particles Stokes regime, Eq. 30 Large, turbulent regime, Eq. 31 Reaction controls, Eq. 23... 

Combining Eqs. 14 and 15 and replacing the first term expression with Eqs. 8,10, or 11 for each size of particle, we obtain in turn, for film diffusion controlling,... 

It Is seen from equation (7) that the optimum velocity is, directly proportional to the diffusivity of the solute in the mobile phase. To a lesser extent it also appears to be inversely dependant on the particle diameter of the packing (the particle size is an optional choice) and the film thickness of the stationary phase. The film thickness of the stationary phase is determined by the physical form of the packing, that is, in the case of silica gel, the nature of the surface and in the case of a reverse phase, on the bonding chemistry. 

Another test entails the observation of the dependence of the rate on particle size. For reasons of geometry, the rate is inversely proportional to the particle radius at film diffusion control (proportional to the surface area per unit volume), and is also inversely proportional to the square of the particle radius if the rate is controlled by particle diffusion (the distance to be covered by diffusion being an additional factor). Thus, the rate-controlling step can be found by performing several experiments with particles of different radius. 

In the above equations, H0, //p, and H are the plate-height contributions due to the finite particle size, solid diffusion, and liquid-film diffusion, respectively. CGS units are used in these equations. Obviously, the bigger the height of the plate, the higher the resistance to the diffusion and the lower the uptake rate. 

The fact that ATR-IR spectroscopy uses an evanescent field and therefore probes only the volume very close to the IRE has important consequences for its application in heterogeneous catalysis, in investigations of films of powder catalysts. The catalyst particle size and packing affect the size of the detectable signals from the catalyst and bulk phase. Furthermore, if the catalyst layer is much thicker than the penetration depth of the evanescent field, diffusion of reactants and products may influence the observed signals. In fast reactions, gradients may exist within the catalyst layer, and ATR probes only the slice closest to the IRE. 

Glueckauf, E. Derived first comprehensive equation for relationship between HETP and particle size, particle diffusion, and film diffusion in ion exchange. 

The first detailed study on ion exchange rates, and particularly mechanisms, appeared in the very definitive and elegant studies of Boyd et al. (1947) with zeolites. Working in conjunction with the Manhattan Project, these researchers clearly showed that ion exchange is diffusion-controlled, and that the reaction rate is limited by mass-transfer phenomena that are either film (FD) or particle (PD) diffusion-controlled. Boyd et al. (1947) were also the first to derive rate laws for FD, PD, and CR. Additionally, they demonstrated that particle size had no effect on reaction control, that in FD the rate was inversely proportional to particle size, and that the PD rate was inversely proportional to the square of the particle size. 

Particle Size. Particle size usually affects the type of diffusion that predominates in an ion exchange process (Mortland and Ellis, 1959 Helfferich, 1966). Film diffusion usually predominates with small particles and PD is usually rate-limiting for large particles. 

The two methanation reactions are strongly exothermic. The temperature rise for typical methanator gas compositions in hydrogen plants is about 74°C (133°F) for each 1% of carbon monoxide converted and 60°C (108°F) for each 1% of carbon dioxide converted. At higher temperatures, the intrinsic rates of both methanation reactions can become sufficiently fast for diffusion effects to become important as shown in Figure 5.42. Under these conditions, film diffusion controls the overall rate of reaction. Diffusion limitations can be overcome to some extent by using a catalyst with a smaller particle size (3.1mm diameter by 3.6 mm long compared to regular catalyst dimensions of 5.4 mm by... 

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