Diffusion effects velocity constant

So far no account has been taken of the forces between the two species constituting the encounter complex. It can be shown that the effect of a potential energy of interaction at a distance is to multiply the diffusion-controlled velocity constant by a factor q, given by... 

The kinetic conclusions of Obolentsev and Gryazev (3,4), of Ballod et al. (5,6), and of Topchieva and Panchenkov (7) are in doubt because of the method of study used, i.e., variation of space velocity at constant pressure. In addition, as will be shown below, the probability is high that either the rates of reaction observed in their studies were diffusion limited or the cumene used by them contained cumene hydroperoxide. In the study of Corrigan et al. (8) the presence of large diffusion effects has already been demonstrated. 

Incidentally, it must be recalled that into the modulus which determines diffusion effects there enters the velocity constant referred to the unit of volume of the solid. As a consequence, even if specific activity fc. 

It has also been shovm that the diffusion coefficients in a solvent are inversely proportional to its viscosity. The viscosity changes with temperature, composition, and the concentration of the feed. When the column is operated at a constant reduced velocity, v = udp)/Dj, the efficiency constant. The effect of a change of viscosity due to an adjustment in any of the parameters just Hsted will have Ht-tle effect on the pressure required to keep the reduced velocity constant (since the product of the viscosity and the diffusion coefficient remains constant) but it will markedly affect the retention times (which will increase with increasing viscosity) and, in preparative applications, the production rate. Thus, conditions under which the viscosity is low should be preferred. 

Exercise 9.9.4. Show that the distribution function of residence times for laminar flow in a tubular reactor has the form 2z /Zp, where tp is the time of passage of any fluid annulus and the minimum time of passage. Diffusion and entrance effects may be neglected. Hence show that the fractional conversion to be expected in a second order reaction with velocity constant k is 2B[1 + j lnu5/(5 + 1)] where B = akt n and a is the initial concentration of both reactants. (C.U.)... 

Does the rate depend on linear velocity With external diffusion, the rate at constant space velocity increases with linear velocity, at about 1/2 order. Velocity independence is a good indication of the absence of external diffusion effects. 

Inlet Temperature Effect. - Inlet temperature strongly affects the mass transfer coefficient through diffusivity, because diffusivity is proportional to the square of absolute temperature. Therefore, conversion efficiency increases with temperature as shown in Figure 7. Keeping velocity constant, increasing the inlet temperature is very effective in... 

We can determine the value of AiRxn from laboratory experiments that obviate any diffusion effects. What we do not know is A sfd ( S Fiim/f Fiim)- However, we do know that A sfd is constant at a given reactor operating temperature and pressure. Thus only S Fiim/l Fiim responds to changes in the velocity of the bulk fluid over the surface of the catalyst because iSFiim/l Fiim is the ratio of the stagnant film s surface area to its volume therefore, it is inversely proportional to the stagnant film s thickness. Mathematically... 

These three terms represent contributions to the flux from migration, diffusion, and convection, respectively. The bulk fluid velocity is determined from the equations of motion. Equation 25, with the convection term neglected, is frequently referred to as the Nemst-Planck equation. In systems containing charged species, ions experience a force from the electric field. This effect is called migration. The charge number of the ion is Eis Faraday s constant, is the ionic mobiUty, and O is the electric potential. The ionic mobiUty and the diffusion coefficient are related ... 

Although SynChropak GPC supports have excellent efficiencies for small molecules at various flow rates, macromolecules, because of their low diffusion constants, exhibit band spreading when linear velocities are increased. This effect increases with molecular weight, as seen in Fig. 10.11 (4). It should be noted that proteins are usually homogeneous in size and thus yield better efficiencies than polymers, which are usually heterogeneous. For preliminary analy-... 

An electroosmotic flux is formed as a result of the effect of the electric field in the direction normal to the pores in the membrane, delectric diffuse layer in the pore with a charge density p. The charges move in the direction of the x axis (i.e. in the direction of the field), together with the whole solution with velocity v. At steady state... 

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