Diffusion effects through particle

Particles migrate to the wall region by means of particle-particle collisions and diffusion, and through particle-wall collision effects which tend to widen the particle velocity distribution in the radial direction. 

The effective diffusivity is obtained from D, but must also take into account the two features that (1) only a portion of the catalyst particle is permeable, and (2) the diffusion path through the particle is random and tortuous. These are allowed for by the particle voidage or porosity, p, and the tortuosity, rp, respectively. The former must also be measured, and is usually provided by the manufacturer for a commercial catalyst. For a straight cylinder, rp = 1, but for most catalysts, the value lies between 3 and 7 typical values are given by Satterfield. 

Taylor (T4, T6), in two other articles, used the dispersed plug-flow model for turbulent flow, and Aris s treatment also included this case. Taylor and Aris both conclude that an effective axial-dispersion coefficient Dzf can again be used and that this coefficient is now a function of the well known Fanning friction factor. Tichacek et al. (T8) also considered turbulent flow, and found that Dl was quite sensitive to variations in the velocity profile. Aris further used the method for dispersion in a two-phase system with transfer between phases (All), for dispersion in flow through a tube with stagnant pockets (AlO), and for flow with a pulsating velocity (A12). Hawthorn (H7) considered the temperature effect of viscosity on dispersion coefficients he found that they can be altered by a factor of two in laminar flow, but that there is little effect for fully developed turbulent flow. Elder (E4) has considered open-channel flow and diffusion of discrete particles. Bischoff and Levenspiel (B14) extended Aris s theory to include a linear rate process, and used the results to construct comprehensive correlations of dispersion coefficients. 

No experiments with variation in particle size of the silica gel have been done to study intraparticle diffusion effects. In silica gel such diffusion would be only through the pores (analogous to the macropores of a polystyrene) since the active sites lie on the internal surface. The silica gel used by Tundo had a surface area of 500 m2/g and average pore diameter of 60 A.116). Phosphonium ion catalyst 28 gave rates of iodide displacements that decreased as the 1-bromoalkane chain length increased from C4 to Cg to C16, The selectivity of 28 was slightly less than that observed with soluble catalyst hexadecyltri-n-butylphosphonium bromide U8). Consequently the selectivity cannot be attributed to intraparticle diffusional limitations. 

Test of Uptake Model Based on a Slow Surface Reaction Combined with Diffusion within the Particle. Since the simple diffusion model is inadequate to describe the uptake behavior of the molybdenum and tellurium oxide vapors by the clay loam particles, a more complex model is required, in which the effects of a slow surface reaction and of diffusion of the condensed vapor into the particle are combined. Consider the condensation of a vapor at the surface of a substrate (of any geometry) and the passage by diffusion of the condensed vapor through a thin surface layer into the body of the substrate. The change in concentration of solute per unit volume in the surface layer caused by vapor condensa-... 

The diffusion of small particles depends upon many factors. In addition to Brownian motion, we must consider the effect of gravity and the motion of the fluid in which the particles reside. Ordinary diffusion as understood in colloid chemistry must be modified considerably when we deal with turbulence. However, we still retain the usual definition of diffusion, namely that it is the number or mass of particles passing a unit cross section of the fluid in unit-time and unit-concentration gradient. That is, if dw particles (or mass) move through an area / in time dt and dC/dx is the concentration increase in the jc-directior then... 

The positive effect of velocity on the permeate flux is a result of enhanced hydrodynamic effects at the membrane surface, since high velocities lead to high shear and turbulent flow, which results in the formation of vortices and eddies that minimize the concentration polarization effects and the development of a fouling layer. The bigger the thickness of this layer, the higher its flow resistance and the smaller the permeate flux through the membrane becomes. Under turbulent flow conditions, shear effects induce hydrodynamic diffusion of the particles from the boundary layer back into the bulk, with a positive effect on the permeate flux. 

An interesting technique for the measurement of intraparticle diffusivity as well as longitudinal diffusion in the particle bed has been described by Deisler and Wilhelm (21). It deviates from all other techniques mentioned in that it is based on a dynamic flow study, analyzing the effect of the particles on the propagation of a sinusoidal variation of composition of a binary gas mixture passed through the catalyst bed. The authors have demonstrated the versatility of their general technique for determination of diffusion properties, as well as adsorption equilibria between the solids and the gas composition employed. If this general technique were modified to measure specifically the particle diffusivity, a very convenient and accurate method may result. 

Adsorption of molecules proceeds by successive steps (1) penetration inside a particle (2) diffusion inside the particle (3) adsorption (4) desorption and (5) diffusion out of the particle. In general, the rates of adsorption and desorption in porous adsorbents are controlled by the rate of transport within the pore network rather than by the intrinsic kinetics of sorption at the surface of the adsorbent. Pore diffusion may take place through several different mechanisms that usually coexist. The rates of these mechanisms depend on the pore size, the pore tortuosity and constriction, the cormectivity of the pore network, the solute concentration, and other conditions. Four main, distinct mechanisms have been identified molecular diffusion, Knudsen diffusion, Poiseiulle flow, and surface diffusion. The effective pore diffusivity measured experimentally often includes contributions for more than one mechanism. It is often difficult to predict accurately the effective diffusivity since it depends so strongly on the details of the pore structure. 

The effects of particle size and temperature clearly demonstrated that the reaction was controlled by intraparticle diffusion resistance. Thus, the initial rates were plotted against dp (inverse of particle diameter) to find that a straight line passing through origin was obtained (Fig.7). This confirms that the reaction was intraparticle diffusion limited". 

The kinetic profile was thus interpreted by a burst effect coupled with a drug diffusion process through the particle modelled as a homogeneous sphere. The drug diffusion coefficient was considerably reduced when entrapped in the carrier DVE = 1.1 10-20 cm2 s 1 compare to DVE = 10 9 m2 s-1 in solution. The encapsulation of different drugs into nanospheres showed that carriers had... 

---