Non-equilibrium gas-liquid transition model

A new rigorous mathematical model for evaporation/condensation, including boiling, has been proposed. A problem of phase transition and in particular evaporation/condensation is one of the most acute problems of modern technology with numerous applications in industry, such as: in refrigeration, distillation in chemical industry. It is very common to use equilibrium evaporation model, which assumes that concentrations of species in the gas phase is always at saturated condition. Such kind of approach can lead to significant errors, resulting in negative concentrations in complex computer simulations. In this work two analytical solution of simplified differential-algebraic system have been obtained. One of them was deduced using assumption that the process is isothermal and gas volume fraction is constant. In the second solution the assumption about gas volume fraction has been removed. The code for numerical solution of differential-algebraic system, using conservative scheme, has been developed. It was designed to solve both systems of equations with boiling and without. Numerical calculations of ammonia-water system with various initial conditions, which correspond to evaporation and/or condensation of both components, have been performed. It has been shown that, although system quickly evolves to quasi equilibrium state (the differences between current and equilibrium concentrations are small) it is necessary to use non-equilibrium evaporation model, to calculate accurately evaporation/condensation rates, and consequently all other dependent variables

A Greatly Under-Appreciated Fundamental Principle of Physical Organic Chemistry

If a species does not have a finite lifetime in the reaction medium, it cannot be a mechanistic intermediate. This principle was first enunciated by Jencks, as the concept of an enforced mechanism. For instance, neither primary nor secondary carbocations have long enough lifetimes to exist in an aqueous medium, so SN1 reactions involving these substrates are not possible, and an SN2 mechanism is enforced. Only tertiary carbocations and those stabilized by resonance (benzyl cations, acylium ions) are stable enough to be reaction intermediates. More importantly, it is now known that neither H3O+ nor HO− exist as such in dilute aqueous solution. Several recent high-level calculations on large proton clusters are unable to localize the positive charge; it is found to be simply “on the cluster” as a whole. The lifetime of any ionized water species is exceedingly short, a few molecular vibrations at most; the best experimental study, using modern IR instrumentation, has the most probable hydrated proton structure as H13O6+, but only an estimated quarter of the protons are present even in this form at any given instant. Thanks to the Grotthuss mechanism of chain transfer along hydrogen bonds, in reality a proton or a hydroxide ion is simply instantly available anywhere it is needed for reaction. Important mechanistic consequences result. Any charged oxygen species (e.g., a tetrahedral intermediate) is also not going to exist long enough to be a reaction intermediate, unless the charge is stabilized in some way, usually by resonance. General acid catalysis is the rule in reactions in concentrated aqueous acids. The Grotthuss mechanism also means that reactions involving neutral water are favored; the solvent is already highly structured, so the entropy involved in bringing several solvent molecules to the reaction center is unimportant. Examples are given

Modelling of group combustion of droplets in a spray fuel cloud

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Modelling of group combustion of droplets in a spray fuel cloud

Release and combustion of a spray cloud in an atmosphere is a phenomenon encountered in a wide range of applications. For solution of a set of problems which is connected with ecology, theory of combustion and explosion, engine design, fire safety, etc. the knowledge of spray combustion behaviour is required. To investigate the influence of a variety in density and transport coefficients and flame front structure, combustion of pure gas cloud is studied numerically. Combustion of a small-scale spherical pocket of fuel droplets in a calm environment may be considered as a model enabling the transient combustion process to be studied conveniently in one-dimensional geometry. Apart from pure academic interest, such a study provides useful estimations of burning spray cloud characteristics which can be applied for the analysis of more complicated situations. An analytical approach is used to find quasi-steady state distributions of gas temperature and fuel mass fraction for both pure evaporating and burning clouds. This approach is quite fruitful, it gives important qualitative analytical relationships, which help to comprehend the complex process of evaporation or combustion of spray the cloud. Numerical method is used to solve the problem of spray cloud combustion using more common unsteady statement. Two types of ignition are used at the centre or from penphery of cloud. Two types of flames (premixed and diffusion flames) are observed in the numerical simulations. Distributions of all components and temperature are obtained at different moments of time for both types of ignition. The diffusion burning time and total evaporation time are estimated using numerical results