Diffusion-limited field

Licinio P. and Frezard. F. 2001. Diffusion limited field induced aggregation of magnetic liposomes. Braz. 

Actually, this is not really diffusion-XimiiQd, but rather Laplacian growth, since the macroscopic equation describing the process, apart from fluctuations, is not a diffusion equation but a Laplacian equation. There are some crucial differences, which will become clearer below. In some sense DLA is diffusion-limited aggregation in the limit of zero concentration of the concentration field at infinity. 

Another example is dendritic crystal growth under diffusion-limited conditions accompanied by potential or current oscillations. Wang et al. reported that electrodeposition of Cu and Zn in ultra-thin electrolyte showed electrochemical oscillation, giving beautiful nanostmctured filaments of the deposits [27,28]. Saliba et al. found a potential oscillation in the electrodeposition of Au at a liquid/air interface, in which the Au electrodeposition proceeds specifically along the liquid/air interface, producing thin films with concentric-circle patterns at the interface [29, 30]. Although only two-dimensional ordered structures are formed in these examples because of the quasi-two-dimensional field for electrodeposition, very recently, we found that... 

More than 20 years ago, Matsushita et al. observed macroscopic patterns of electrodeposit at a liquid/air interface [46,47]. Since the morphology of the deposit was quite similar to those generated by a computer model known as diffusion-limited aggregation (D LA) [48], this finding has attracted a lot of attention from the point of view of morphogenesis in Laplacian fields. Normally, thin cells with quasi 2D geometries are used in experiments, instead of the use of liquid/air or liquid/liquid interfaces, in order to reduce the effect of convection. 

Many challenges remain to be addressed in this field. The use of immobilized catalysts can often reduce the activity of a catalyst Reduced reaction rates due to diffusion limitations through a permeable membrane capsule and the ease or practicality of the synthesis of these catalyst scaffolds are issues that may pose problems. In some cases, these issues have been resolved, but this is often at the expense of other properties of the capsule. For example, the use of thin walls to reduce mass transfer limitations can be at the expense of nanocapsule strength and stability. 

The rate of hydration of obsidian, which is diffusion limited, forms the basis for Obsidian Hydration Dating [f]. A date refers to "the time a fresh surface of obsidian was created, either naturally or by man.. ..Laboratory and field studies have confirmed that the time indicated by a hydrated layer is proportional to the thickness squared of the layer. The hydration rate is independent of the relative humidity of the environment, but the chemical composition of the obsidians affect the rate by orders of magnitude. Si02 increases the rate, whereas CaO, MgO, and H20 decrease it. A 6 - 8 °C temperature increase causes doubling of the rate." The method is quite inexpensive, and it is applicable to ages between a few hundred and several million years. 

For macromolecules (or small molecules in viscous solvents at a low temperature) in a high magnetic field, wqTc 3> 1. At this spin-diffusion limit the rotating-frame cross-relaxation rate is twice as fast as in the laboratory frame, and the rates are of the opposite sign, 5 = —1/2 (fig. 1, top). 

In SNF corrosion tests, there has been a tendency to use the release of more soluble species Tc, Cs, and Mo as markers for fuel corrosion (Finn et al. 2002). As none of these elements are present in the U02 matrix, this approach may not reveal the actual fuel matrix corrosion rate. Furthermore, short-term leaching tests may not expose possible diffusion-limited (tl/2) release of gap and grain boundary species and assume excessive rates of reaction based on initial fast release rates. The microstructure, radiation field, and composition will change over time, so that tests carried out on fuel today may not be relevant to fuel behaviour 300 to 1000 years from now, once the high p-,y-field has decayed. 

An approximate model for the rate of boundary motion can be developed if it is assumed that the rate of dislocation climb is diffusion limited [2], Neglecting any effects of the dislocation motion and the local stress fields of the dislocations on... 

Figure 15.2 The mean-field approximation for diffusion-limited coarsening. Each...

For electrodes with total dimensions smaller than VDt, often called micro-voltammetric electrodes (see Chapter 12), roughness is less of an issue compared to mass transport. Such electrodes are typically less than 10 pm in diameter and exhibit radial rather than planar diffusion. In most cases (the exception being fast voltammetry) the diffusion field is thicker than both the electrode diameter and its surface roughness, and the diffusion-limited response is unperturbed by roughness. 

If an external force field acts on the random walker, it has been shown [58, 59] that in the diffusion limit, this broad waiting time process is governed by the fractional Fokker-Planck equation (FFPE) [60]... 

Another illustration of the power of molecular dynamics simulation can be drawn from the sphere of enzyme catalysis. Many enzyme-catalyzed reactions proceed at a rate that depends on the diffusion-limited association of the substrate with the active site. Sharp et al. [28] have carried out Brownian dynamics simulations of the association of superoxide anions with superoxide dismutase (SOD). The active center in SOD is a positively charged copper atom. The distribution of charge over the enzyme is not uniform, and so an electric field is produced. Using their model, Sharp et al. [28] have shown that the electric field enhances the association of the substrate with the enzyme by a factor of 30 or more. Their calculations also predict correctly the response of the association rate to changes in ionic strength and amino... 

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