Моделирование сорбционных процессов на твердофазных ионообменниках

Объектом исследования являются характеристики ионообменных материалов, влияющие на процессы очистки технологических растворов от растворенных в них соединений. Цель работы – определить влияние селективных свойств ионообменного материала, кинетических характеристик, а также метода осуществления процесса на эффективность разделения ионов щелочных и щелочноземельных элементов В процессе выполнения работы изучались физико-химические характеристики ионообменного материала, определялись кинетические, гидравлические и селективные свойства сорбентов. В результате исследования определены коэффициенты селективности, высота эквивалентной теоретической ступени для непрерывной и ступенчатой подачи ионита в колонну, получены параметрические модели, адекватно описывающее зависимость перепада давления через слой ионообменного материала и величины расширения ионообменного слоя от скорости потока и температуры.The object of the study are the characteristics of ion-exchange materials, which influence the processes of purification of process solutions from the diluted compounds. The aim of this work was to determine the impact of the selective properties of ion-exchange material, kinetic characteristics, and a method of implementing the process on the efficiency of the separation of ions of alkali and alkaline earth elements In the process of doing the work studied physico-chemical characteristics of ion-exchange material was determined in a kinetic, hydraulic and selective properties of the sorbents. The study identified the factors of selectivity, the height equivalent to theoretical stages for continuous and stepped feed of an ion exchanger in a column, adequately describing the dependence of the pressure drop through the layer of ion exchange material and the value of the expansion of the ion exchange layer from the flow rate and temperature

Semi-discrete finite difference multiscale scheme for a concrete corrosion model: approximation estimates and convergence

We propose a semi-discrete finite difference multiscale scheme for a concrete corrosion model consisting of a system of two-scale reaction-diffusion equations coupled with an ode. We prove energy and regularity estimates and use them to get the necessary compactness of the approximation estimates. Finally, we illustrate numerically the behavior of the two-scale finite difference approximation of the weak solution.Comment: 22 pages, 1 figure, submitted to Japan Journal of Industrial and Applied Mathematic

Estimation of critical dislocation distances

This paper describes in detail quantitative studies of the spiral mode of crystal growth, particularly focussing on the critical dislocation distance between two spirals rotating in opposite direction using the model derived in (Cont. Mech. Thermodynamics 17, 373 (2006)) from the classical BCF model presented in (Philos. Trans. R. Soc. London Ser. A 243, 299 (1951)). Based on our numerical studies we can show that the critical dislocation distance is a function of the diffusion coefficient and the temperature coupling constant as well as a function of the desorption rate. However, it is not a function of the flux rate

A new model for fungal hyphae growth using the thin viscous sheet equations

In this paper, we model the growth of single nonbranching fungal hypha cell. The growth proceeds as an elongating expansion in a single direction. Modelling of hyphae growth consists out of two parts: transport of cell wall building material to the cell wall and growth of the cell wall as new cell wall building material arrives. In this paper we present a new model for hyphae growth using the work of Barnicki-Garcia et al. (1989), which assumes that cell wall building material is transported in straight lines by an isotropic point source, and the work of Campas and Mahadevan (2009), which assumes that the cell wall is a thin viscous sheet. Furthermore, we include a novel equation which models the hardening of the cell wall with age. We show numerically that these governing equations have solutions corresponding to hyphae growth. We also compute asymptotic expansions near the apex and the base of the cell

Unfolding-based corrector estimates for a reaction-diffusion system predicting concrete corrosion

We use the periodic unfolding technique to derive corrector estimates for a reaction-diffusion system describing concrete corrosion penetration in the sewer pipes. The system, defined in a periodically-perforated domain, is semi-linear, partially dissipative, and coupled via a non-linear ordinary differential equation posed on the solid-water interface at the pore level. After discussing the solvability of the pore scale model, we apply the periodic unfolding techniques (adapted to treat the presence of perforations) not only to get upscaled model equations, but also to prepare a proper framework for getting a convergence rate (corrector estimates) of the averaging procedure.Comment: 23 pages, one figur