Diffusion-convection particles

Figure 11.10. Schematic diagram of a hyper-diffusive (gel-fiUed gigaporous) particle (left), tentacle ion-exchanger interacting with a globular protein (middle), and a perftisive (diffusion-convection) particle (right).

This chapter provides analytical solutions to mass transfer problems in situations commonly encountered in the pharmaceutical sciences. It deals with diffusion, convection, and generalized mass balance equations that are presented in typical coordinate systems to permit a wide range of problems to be formulated and solved. Typical pharmaceutical problems such as membrane diffusion, drug particle dissolution, and intrinsic dissolution evaluation by rotating disks are used as examples to illustrate the uses of mass transfer equations. 

There are, in principle, three ways in which material may be transported to the electrode surface diffusion, convection and migration. Of these, perhaps the most straightforward is migration, which simply consists of the movement of a charged particle under the influence of an electric field. Experimentally, it is well established that after an extremely short time an ion in solution in an electric field will behave as if it had acquired a steady velocity in the direction of the field. The reason why a steady velocity is established rather... 

The objective of the present research is to predict the rate of deposition of Brownian particles by considering the effects of diffusion, convection, and interaction forces between particle and collector. It will be shown that, when the repulsion due to the double-layer is sufficiently large, the interaction forces can be incorporated into a boundary condition for the convective-diffusion equation. This boundary condition takes the form of a virtual first-order chemical reaction which occurs on the surface of the collector. 

Fig. 3- Cose 1. Sherwood numbers computed for the convective-diffusion of particles of finite sine to the surface of a spherical collector by neglecting interaction forces. The dashed line is the Levich-LighthilJ equation (19) which is valid when a diffusion boundary-layer exists and the particles are infinitesimal.

Compared to small molecules the description of convective diffusion of particles of finite size in a fluid near a solid boundary has to account for both the interaction forces between particles and collector (such as van der Waals and double-layer forces) and for the hydrodynamic interactions between particles and fluid. The effect of the London-van der Waals forces and doublelayer attractive forces is important if the range over which they act is comparable to the thickness over which the convective diffusion affects the transport of the particles. If, however, because of the competition between the double-layer repulsive forces and London attractive forces, a potential barrier is generated, then the effect of the interaction forces is important even when they act over distances much shorter than the thickness of the diffusion boundary layer. For... 

That sufficient convection occurred to exclude the diffusion of particles to and from the interface as a rate-determining factor. 

At high velocity and with gases of low diffusivity, convective dispersion in the bed will be the dominating factor for particularly with relatively large catalyst particles. 

Due to the high number of particles in a packed bed, the model for a single particle hes to be simple. Here, an one dimensional approach has been chosen as compromise between accuracy and computing time. The change of a scalar in time within the particle is influenced by diffusion, convection and source terms. Thus, the energy and species distribution over the particle can be described by the general transport equation... 

Blending is a reshuffling process involving the random movement of individual and groups of particles. Three mechanisms by which blending processes can occur are diffusion, convection, and shear (Fig. 1) (1,2). Diffusion is the redistribution of individual particles by their random movement relative to one another. It is often referred to as micro mixing in the literature, because it addresses the blending process on an individual particle basis. Examples of where diffusion can occur include ... 

The success of the analysis in correlating experimental data for clean filters offers convincing support for the theory of convective diffusion of particles of finite diameter to surfaces. As particles accumulate in the filter, both the efficiency of removal and the pressure drop increase, and the analysis no longer holds. Some data on this effect are available in the literature. Care must be taken in the practical application of these results because of pinhole leaks in the filters or leaks iU ound the frames. 

Buyevich, Yu. A., On convective diffusion toward particles of a condensed polydis-perse cloud of solid spheres, J. Eng. Phys. Thermophys., Vol. 23, No. 4, 1972. 

On the other hand the analysis by a detailed diffusion/convection model leads to a mass-balance equation in a slab adsorbent particle which includes terms relating to diffusive flux, convective flux and accumulation ... 

The solution of problems on convective diffusion toward particles at finite Re and Pep numbers, was well as for boundary conditions more general than (6.93), can be found in work [13]. 

The maps shown in Fig. 4 demonstrate that, with convective flows alone (no diffusion), a particle can be made to visit any location within the droplet if the switching period is long enough. Mixing is quantified by tracking an initial swarm of particles whose population moments are... 

A diffusion-convection-reaction problem in a catalytic particle... 

Our second example is a problem from chemical engineering concerning diffusion-convection and reaction in a catalytic particle. The model equation described by Quinta-Ferreira (1988) and Sereno (1989) is given by ... 

The fluid velocity field v is quite important in convective diffusion of particles occurring in filters and scruhhers used for gas cleaning. Knowledge of v in the separator is essential in predicting particle separation. 

Therefore, the governing equation for convective diffusion of particle density function n(rp) of size tp becomes... 

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