Diffusion to cylinder

Diffusion to Cylinders at Lmv Reynolds Numbers Concentration Boundary Layer Equation 63... 

DIFFUSION TO CYLINDERS AT LOW REYNOLDS NUMBERS CONCENTRATION BOUNDARY LAYER EQUATION... 

Diffusion to Cylinders ai Low Reynolds Nionhers Point Particles... 

The mechanism of poisoning automobile exhaust catalysts has been identified (71). Upon combustion in the cylinder tetraethyllead (TEL) produces lead oxide which would accumulate in the combustion chamber except that ethylene dibromide [106-93-4] or other similar haUde compounds were added to the gasoline along with TEL to form volatile lead haUde compounds. Thus lead deposits in the cylinder and on the spark plugs are minimized. Volatile lead hahdes (bromides or chlorides) would then exit the combustion chamber, and such volatile compounds would diffuse to catalyst surfaces by the same mechanisms as do carbon monoxide compounds. When adsorbed on the precious metal catalyst site, lead haUde renders the catalytic site inactive. 

The Cylinder-Plate Procedure. In this procedure the substance being assayed diffuses from cylinders placed upon a uniform thickness of seeded agar, filled or charged with a fixed volume of the analyte, or reference standards or a series of standard solutions. The petri dishes are incubated at a predetermined temperature and the zones of inhibition measured to the nearest 0.1 mm. 

The equivalency found between the behavior of hemisphere and that of disk electrodes also exists between cylinder and band electrodes [29]. Diffusion to a cylinder electrode is linear and described by Equation 12.7, while diffusion to a band is nonlinear. A plane of symmetry passes through the center of the band and normal to its surface, so the nonlinear diffusion process can be broken down into two planar components, one in the direction parallel to the electrode surface, x, and the other in the direction perpendicular to the electrode surface, y. So Fick s second law for a band electrode is... 

Fig. 7.14 Two-dimensional, cylindrical glucose sensor. Glucose diffuses to the sensor only in direction z whereas oxygen can reach the electrode by diffusion through the walls of the cylinder of length L...

Steady-state solutions for diffusion to a cylinder (no flow)... 

We have considered so far only disc-shaped microelectrodes, for which spherical diffusion can be applied, to a good approximation. Other forms have been used, mainly because they might be easier to fabricate. Most noted among these is the linear or strip niicroelec-trode, which is macroscopic in length but microscopic in width. The diffusion field at such electrodes can be approximated. satisfactorily by diffusion to a cylinder. The enhancement of diffusion is less than that... 

The electrode surface was assumed to contain N electroactive metal or metal oxide centers, respectively, which can be not only uniformly but also (mimicking more realistic experimental conditions) randomly distributed an example is the results of atomic force microscopy (AFM) studies on microparticle electrodes [53]. Here, the diffusion domain approach (as described in Section 6.3.2.2.1) has been employed that is, the electrode surface is assumed to be an arrangement of independent diffusion domains of radius Fq. If all particles are of the same radius, rj, but are distributed in a random manner, then a distribution of diffusion domains with different domain radii, ro, follows. The local position-dependent coverage is given by T. The electroactive microparticle flat disks of the radius rj are located in the center of the respective diffusion domain cylinder. The simulated (linear sweep voltammetric) reaction follows a one-electron transfer, and species B is stripped from the electrode surface into the solution, forming A, or ... 

Let us consider diffusion to the surface of a circular cylinder of radius a in a flow with velocity Ui directed along the normal to the cylinder axis. This is a model problem used in chemical engineering for calculating mass transfer to prolate particles it is used even more widely in mechanics of aerosols for analyzing diffusion sedimentation of aerosols on fibrous filters [139,461]. 

Diffusion to an elliptic cylinder in a translational flow at high Peclet numbers was considered in [166]. 

Fixed cylinder. Let us consider diffusion to the surface of a fixed circular cylinder in a steady-state linear shear Stokes (Re - 0) flow in the plane normal to the cylinder axis. The velocity distribution of such a flow remote from the... 

External mass transfer, such as diffusion to particles or to the outside of pipes or cylinders, requires different correlations from those for internal mass transfer, because there is boundary-layer flow over part of the surface, and boundary-layer separation is common. The mass-transfer coefficients can be determined by studying evaporation of liquid from porous wet solids. However, it is not easy to ensure that there is no effect of internal mass-transfer resistance. Complications from diffusion in the solid are eliminated if the solid is made from a slightly soluble substance that dissolves in the liquid or sublimes into a gas. This method also permits measurement of local mass-transfer coefficients for different points on the solid particle or cylinder. 

Smith and Quinn (35) and Hoofd and Kreuzer (46) Independently developed analytical solutions for the facilitation factor which holds over a range In properties and operating conditions. Smith and Quinn obtained their solution by assuming a large excess of carrier. This allowed them to linearize the resulting differential equations. Hoofd and Kreuzer separated their solution into two parts a reaction-limited portion which is valid near the interface and a diffusion-limited portion within the membrane. Both groups obtained the same result for the facilitation factor. Hoofd and Kreuzer ( T) then extended their approach to cylinders and spheres. Recently, Noble et al. (48) developed an analytical solution for F based on flux boundary conditions. This solution allows for external mass transfer resistance and reduces to the Smith and Quinn equation In the limit as the Sherwood number (Sh) becomes very large. 

Cylindrical diffusion is observed, for example, during diffusion to a thin metallic wire or a carbon fiber electrode. Impedance of cylindrical electrodes was studied by Fleischmann et al. [165,166] and Jacobsen and West [167]. The partial differential equation describing diffusion to a cylinder, written for the oscillation concentration of an Ox form, is [144]... 

An argument exactly analogous to that for a spherical electrode, but now considering the accumulation of material in a volume of solution bounded by cylinders at r — dr and r + dr, leads to the basic equation for cylindrical diffusion (i.e. diffusion to a wire of infinite length), that is. 

No serious attempts have been made to interpret adsorption data correctly. Low values of surface areas of this series of porous carbons comes from the inappropriate use of the isotherm of nitrogen adsorption at 77 K. Incidentally, all isotherms should be made available in all publications. The low values are associated with slow-activated diffusion effects in microporosities of dimensions <0.5 nm. High values of surface area ( 1200m g ) result from multilayer adsorption in the wider of the micropores and in porosities of indefinite shape, approximating to cylinders, cones, spheres, etc. Hence, it seems unreasonable to relate such adsorption processes to monolayer adsorption on surfaces of graphitic microcrystallites. 

---