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## Smoluchowski Equation (smoluchowski + equation)
## Selected Abstracts## Part 1: Kinetics and mechanism of the crystallization process CRYSTAL RESEARCH AND TECHNOLOGY, Issue 1 2006Oleg D. LinnikovAbstract The kinetics of spontaneous crystallization of sodium chloride from aqueous-ethanol solutions were studied. During the crystallization the electrical conductance and optical transmission of the supersaturated solutions were measured automatically. For monitoring of the total surface of growing potassium chloride crystals at the crystallization the turbidimetric method was used. The growth rate and activation energy were determined. The crystal growth rate was proportional to supersaturation. When the volume fraction of ethanol in solution increased from 14.85 to 29.72%, the activation energy of the growth process did not change and was about 50 kJ· mol -1. Aggregation of the crystals was found. The aggregation kinetics of the crystals may be described approximately by the famous Smoluchowski equation for coagulation of colloidal particles. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Cation-Enhanced Deprotonation of Water by a Strong Photobase ISRAEL JOURNAL OF CHEMISTRY, Issue 2 2009Noga MunitzWe have used picosecond fluorescence spectroscopy to study the proton-dissociation dynamics of bulk water and H2O molecules solvating Mg2+ ions in aqueous solutions. We have analyzed the photo-initiated proton-transfer reaction to a photobase 6-aminoquinoline by the Collins-Kimball approach and have modeled the ensuing bimolecular reaction dynamics by the Smoluchowski equation with radiation boundary conditions. We have found the on-contact proton transfer rate to follow the Marcus free-energy relation for proton transfer and estimate by this rate-equilibrium correlation the considerable enhancement in the acidity of the water molecules solvating the Mg2+ ion. Our findings may be used in the study of metallo-enzymes such as carbonic anhydrases (CAs), which catalyze the reversible addition reaction of OH, to CO2 by increasing the reactivity of the zinc-bound water molecules by means of stabilizing the product of water dissociation, the OH, anion. [source] ## Diffusion through ordered force fields in nanopores represented by Smoluchowski equation AICHE JOURNAL, Issue 6 2009Fu Yang WangAbstract The classical Einstein or Fick diffusion equation was developed in random force fields. When the equation is applied to gas transport through coal, significant discrepancies are observed between experimental and simulation results. The explanation may be that the random force field assumption is violated. In this article, we analyze molecular transport driven by both random and ordered (directional) forces in nanopores. When applied to CO2 transport through cone-shaped carbon nano-tubes (CNTs) and Li+ doped graphite pores, computational results show that directional force fields may significantly affect porous media flow. Directional forces may be generated by potential gradients arising from a range of non-uniform characteristics, such as variations in the pore-sizes and in local surface compositions. On the basis of the simulation and experimental results, the Smoluchowski and Fokker-Planck equations, which account for the directional force fields, are recommended for diffusion through ordered force fields in nanopores. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] ## Approach to self-similarity in Smoluchowski's coagulation equations COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 9 2004Govind MenonWe consider the approach to self-similarity (or dynamical scaling) in Smoluchowski's equations of coagulation for the solvable kernels K(x, y) = 2, x + y and xy. In addition to the known self-similar solutions with exponential tails, there are one-parameter families of solutions with algebraic decay, whose form is related to heavy-tailed distributions well-known in probability theory. For K = 2 the size distribution is Mittag-Leffler, and for K = x + y and K = xy it is a power-law rescaling of a maximally skewed ,-stable Lévy distribution. We characterize completely the domains of attraction of all self-similar solutions under weak convergence of measures. Our results are analogous to the classical characterization of stable distributions in probability theory. The proofs are simple, relying on the Laplace transform and a fundamental rigidity lemma for scaling limits. © 2003 Wiley Periodicals, Inc. [source] |