Diffusion coefficient polar coordinates

Figure 4. The following data were used leak radius r0 (40 micron), leak conductance F = 1 cc. sec.-1, gas pressure (air) p (20 torr), diffusion coefficient (26) for ions Di — 2 sq. cm. sec.-"1, for electrons De = 2000 sq. cm. sec.-1 (at 20 torr air). The flow velocities were assumed independent of 6 and (spherical polar coordinates). The spherically symmetrical flow pattern, which obviously overestimates the flow velocity for large values of 6 was chosen because of its simplicity. The velocity of the radially directed flow at a distance r is v = F/2irr2. The time re-...

For reasons of simplicity, the Thiele modulus will be defined and calculated for a catalyst plate with pore access at both ends of the plate and not at the bottom or top. Note that for most cases in real-life applications the assumptions have to be modified using polar coordinates for the calculations. The Thiele modulus q> is therefore defined as the product of the length of the catalyst pore, /, and the square root of the quotient of the constant of the speed of the reaction, k. divided by the effective diffusion coefficient DeS ... 

Reactions in solution proceed in a similar manner, by elementary steps, to those in the gas phase. Many of the concepts, such as reaction coordinates and energy barriers, are the same. The two theories for elementary reactions have also been extended to liquid-phase reactions. The TST naturally extends to the liquid phase, since the transition state is treated as a thermodynamic entity. Features not present in gas-phase reactions, such as solvent effects and activity coefficients of ionic species in polar media, are treated as for stable species. Molecules in a liquid are in an almost constant state of collision so that the collision-based rate theories require modification to be used quantitatively. The energy distributions in the jostling motion in a liquid are similar to those in gas-phase collisions, but any reaction trajectory is modified by interaction with neighboring molecules. Furthermore, the frequency with which reaction partners approach each other is governed by diffusion rather than by random collisions, and, once together, multiple encounters between a reactant pair occur in this molecular traffic jam. This can modify the rate constants for individual reaction steps significantly. Thus, several aspects of reaction in a condensed phase differ from those in the gas phase ... 

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