Diffusion limited

Rice S A 1985 Diffusion-limited reactions Oomprehensive Ohemical Kinetics vol 25, ed C H Bamford, C F H Tipper and R G Compton (Amsterdam Elsevier)... 

Meakin P 1983 Formation of fractal clusters and networks by irreversible diffusion-limited aggregation Phys. Rev. Lett. 51 1119-22... 

In a homogeneous system, tire rate of mixing is governed by Smoluchowski s equations [77], according to which tire diffusion-limited association rate of S and L (equation (C2.14.13)), supposed uncharged, equals tliat of tire flux and is... 

A common feature of biopolymer adsorjition is that its rate is usually one to tliree orders of magnitude smaller than the diffusion-limited rate to a perfect sink ... 

An appropriate value of 7 for a system modeled by the simple Langevin equation can also be determined so as to reproduce observed experimental translation diffusion constants, Dt in the diffusive limit, Dt is related to y hy Dt = kgTmy. See [22, 36], for example. 

There is no doubt that the coefficient of the third term on the right hand side of this equation is much larger than the coefficient of the second term at the bulk diffusion limit, and this justifies our original form (5,29). However, on constructing from and using equation (5,32) and its... 

It remains to check Chat our supposedly general equations (11.20) -(11.23) reduce to the previously obtained limiting forms at the extremes of bulk diffusion and Knudsen diffusion. The bulk diffusion limit is easily obtained by letting — and assuming that for all r, s,... 

Effective diffusion coefficient, in porous medium at bulk diffusion limit, 14... 

Examination of oven-aged samples has demonstrated that substantial degradation is limited to the outer surface (34), ie, the oxidation process is diffusion limited. Consistent with this conclusion is the observation that oxidation rates are dependent on sample thickness (32). Impact property measurements by high speed puncture tests have shown that the critical thickness of the degraded layer at which surface fracture changes from ductile to brittle is about 0.2 mm. Removal of the degraded layer restores ductiHty (34). Effects of embrittled surface thickness on impact have been studied using ABS coated with styrene—acrylonitrile copolymer (35). 

The rate-limiting step typically occurs at the air—Hquid interface and, for biological species without diffusion limitations, the overall relationship can be simply written at steady state as... 

Polymerization Processes. Free-radical polymerization is carried out in a variety of ways. One of the practical problems that must be dealt with is mnaway reactions which can result from auto acceleration, an increase in rate of polymerization caused by diffusion-limited termination (reduced... 

Catalyst Effectiveness. Even at steady-state, isothermal conditions, consideration must be given to the possible loss in catalyst activity resulting from gradients. The loss is usually calculated based on the effectiveness factor, which is the diffusion-limited reaction rate within catalyst pores divided by the reaction rate at catalyst surface conditions (50). The effectiveness factor E, in turn, is related to the Thiele modulus,

first-order rate constant, a the internal surface area, and the effective diffusivity. It is desirable for E to be as close as possible to its maximum value of unity. Various formulas have been developed for E, which are particularly usehil for analyzing reactors that are potentially subject to thermal instabilities, such as hot spots and temperature mnaways (1,48,51). 

The former usually involves process temperature or isolation. Sohds surface characteristics are important in that they control the extent to which an operation is diffusion-limited, i.e., diffusion into and out of the pores of a given sohds particle, not through the voids among separate particles. The size of the solids parti(des, the surface-to-mass ratio, is also important in the evaluation of surface characteristics and the diffusion problem. 

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