A review of chemical diffusion: Criticism and limits of simplified methods for diffusion coefficient calculation

A review of the physics and modelling of mass diffusion involving different gaseous chemical species is firstly proposed. Both accurate and simplified models for mass diffusion involve the calculation of individual species diffusion coefficients. Since these are computationally expensive, in CFD they are commonly estimated by assuming constant Lewis or Schmidt numbers for each chemical species. The constant Lewis number assumption is particularly used. As a matter of fact, these assumptions have never been theoretically justified nor verified in practical flames. The only published information are the first observations by Smooke and Giovangigli about the Lewis number against temperature distributions in methane–air premixed and counterflow diffusion one-dimensional flames. The aim of this work is to verify these assumptions. Functional dependences of molecular properties appearing in these numbers are made explicit to show that while Sc _i depends only on composition, Le _i depends also on temperature and therefore it certainly cannot be assumed constant in a flame. Then, accurately calculating molecular properties, distributions of these characteristic numbers against temperature are obtained a posteriori from numerical simulations of different flames, premixed and non-premixed, and burning different fuels. For non-premixed flames, individual species Lewis number distributions are broad for most of the species considered in this article, whilst they are tight for premixed flames. Some attention is focused on the particular shape of Lewis distributions in non-premixed flames: they are characterized by four or five (when extinction is experienced) branches associated to precise regions in the flame (basically, lean, rich and stoichiometric combusting zones). Instead, the Schmidt distributions are always tighter, also when extinctions take place: for many species they can be approximatively assumed constant. Finally, a simplified procedure to estimate individual species diffusion coefficients is suggested, assuming the median of non-premixed flame Schmidt distributions has a constant value for each chemical species.     

Discretized diffusion processes

We study the properties of the "rigid Laplacian" operator; that is we consider solutions of the Laplacian equation in the presence of fixed truncation errors. The dynamics of convergence to the correct analytical solution displays the presence of a metastable set of numerical solutions, whose presence can be related to granularity. We provide some scaling analysis in order to determine the value of the exponents characterizing the process. We believe that this prototype model is also suitable to provide an explanation of the widespread presence of power law in a social and economic system where information and decision diffuse, with errors and delay from agent to agent.     

Kinetics of isothermal homogeneous-condensation processes

Isothermal condensation of supersaturated vapors of various substances and formation of lampblack particles by isothermal decomposition of hydrocarbon (acetylene) molecules is investigated by analytic methods. Expressions that differ generally from the classical ones are obtained, on the basis of the quasichemical model of cluster particles, for the quasi-equilibrium and stationary distribution functions of the cluster sizes, as well as for the rates of formation of clusters having critical dimensions. Analytic expressions describing the time evolution of the degree of supersaturation and of the size distribution function of condensed cluster particles are obtained for the case when the system goes over from the supersaturated state to thermodynamic equilibrium. Equations for the principal characteristics of lampblack formation, viz., the characteristic time and the average size and density of the lampblack particles, are obtained with allowance for the properties of the formation and dissociation (evaporation) of small lampblack cluster particles.Translated from Trudy Ordena Lenina Fizicheskogo Instituta im. P. N. Lebedeva AN SSSR, Vol. 145, pp. 189–219, 1984.     

Kinetics of particle coarsening processes

A nonequilibrium statistical mechanical theory for particle coarsening processes is presented. In this theory, the rate of change of a given particle is determined by both a deterministic and a fluctuation terms, and the particle size distribution (PSD) satisfies Fokker-Planck-type equation. We use a time scaling technique and find the PSD scaled by average particle size as well as the power laws of time dependence of some quantities. The asymptotic scaled PSD is independent of initial condition but does depend on the equilibrium volume fraction. We show that the average radius grows att ^1/3 and the density of particles decays ast ^?1.     

Theory of diffusion controlled growth

We present a new theoretical framework for diffusion limited aggregation and associated dielectric breakdown models in two dimensions. Key steps are understanding how these models interrelate when the ultraviolet cutoff strategy is changed, the analogy with turbulence and the use of logarithmic field variables. Within the simplest, Gaussian, truncation of mode-mode coupling, all properties can be calculated. The agreement with prior knowledge from simulations is encouraging, and a new superuniversality of the tip scaling exponent is both predicted and confirmed.