Mathematical model of deep-bed filtration of a two-component suspension through a porous medium

2017 ◽  
Vol 52 (2) ◽  
pp. 299-308 ◽  
Author(s):  
Zh. M. Makhmudov ◽  
U. Zh. Saidullaev ◽  
B. Kh. Khuzhayorov
2021 ◽  
Vol 1 (1 (109)) ◽  
pp. 68-76
Author(s):  
Fazil Veliev

Cotton mass is considered as a compressible porous two-component medium, consisting of a mixture of cotton fibres and air included in the porous medium, which is essential in dynamic treatment processes and requires consideration when planning technological modes. It was found that the speed of sound in multicomponent media significantly decreases with an increase in the content of the gaseous component. With a certain content of components, it can become less than in each of the components separately. This is due to the fact that with an increase in the content of the gaseous component, the density of the medium increases insignificantly, and the compressibility of air sharply decreases in the pores. As a result of the research, it was found that the value of the dynamic change in the density of cotton raw materials can significantly exceed its density during static compression. This kind of influence can have both adverse and desirable effects on the primary stage of cotton processing. The dynamic characteristics of raw cotton as an object of mechanical technology were studied. The values of the speed of sound as a function of the density of cotton raw materials were determined on the basis of the theory of a two-component porous medium. The types of the dynamic compression curve of raw cotton have been established. Experimental studies on the compressibility of raw cotton are generalized. From the analysis of the cleaning processing of fibres and seeds on cleaning machines, it follows that when assigning a technological processing mode, it is necessary to comply it with the value of the sound speed for a given density of raw materials. It is necessary to avoid such rates of penetration of the working bodies into raw materials that are commensurate with the speed of sound at a given raw material density. This local dramatic increase in cotton media characteristics is a significant cause of fibre damage


2018 ◽  
Vol 769 ◽  
pp. 329-335
Author(s):  
Andrey Petrov ◽  
Leonid A. Igumnov

The problem of the effect of a normal harmonic force on a porous beam in a 3D formulation is solved using the boundary-element method. A homogeneous fully saturated elastic porous medium is described using Biot’s mathematical model. The effect of the porosity and permeability parameters on the deflection of the beam and the distribution of pore pressure over the beam thickness is investigated. The comparison of the boundary-element solution with a 2D numerical-analytical one is given.


Processes ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 185 ◽  
Author(s):  
Zhenzhen Jia ◽  
Qing Ye ◽  
Haizhen Wang ◽  
He Li ◽  
Shiliang Shi

Porous medium burners are characterized by high efficiency and good stability. In this study, a new burner was proposed based on the combustion mechanism of the methane-air mixture in the porous medium and the preheating effect. The new burner is a two-section and double-deck porous medium with gas inlets at both ends. A mathematical model for the gas mixture combustion in the porous medium was established. The combustion performance of the burner was simulated under different equivalence ratios and inlet velocities of premixed gas. The methane combustion degree, as well as the temperature and pressure distribution, was estimated. In addition, the concentrations of emissions of NOx for different equivalence ratios were investigated. The results show that the new burner can not only realize sufficient combustion but also save energy. Furthermore, the emission concentration of NOx is very low. This study provides new insights into the industrial development and application of porous medium combustion devices.


2001 ◽  
Vol 12 (5) ◽  
pp. 557-569 ◽  
Author(s):  
J. CHADAM ◽  
P. ORTOLEVA ◽  
Y. QIN ◽  
R. STAMICAR

The shape stability of the reaction interface for reactive flow in a porous medium is investigated. Previous work showed that the Reaction-Infiltration Instability could cause the reaction zone to lose stability when the Peclet number exceeded a critical value. The new feature of this study is to include a velocity-dependent hydrodynamic dispersion. A mathematical model for this phenomenon is given in the form of a moving free-boundary problem. The spectrum of the linearized problem is obtained, and the related analysis and numerical calculations show that the onset of the instability is not eliminated by the new dispersive terms. The details of analysis show that the instability is reduced especially by the transverse dispersion.


2018 ◽  
Vol 196 ◽  
pp. 04003 ◽  
Author(s):  
Liudmila Kuzmina ◽  
Yuri Osipov

A one-dimensional model for the deep bed filtration of a monodisperse suspension in a porous medium with variable porosity and permeability and multiple pore-blocking mechanisms is considered. It is assumed that the small pores are clogged by separate particles; pores of medium size, exceeding the diameter of the particles, can be blocked by arched bridges, forming stable structures at the pore throats. These pore-blocking mechanisms - size-exclusion and different types of bridging act simultaneously. Exact solutions are obtained for constant coefficients, on the concentrations front and at the porous medium inlet.


mSphere ◽  
2018 ◽  
Vol 3 (3) ◽  
Author(s):  
Gaurav D. Sankhe ◽  
Narendra M. Dixit ◽  
Deepak K. Saini

ABSTRACT Two-component signaling systems (TCSs) are central to bacterial adaptation. However, the mechanisms underlying the reactions involving TCS proteins and their reaction rates are largely undetermined. Here, we employed a combined experimental and theoretical approach to elucidate the kinetics of autophosphorylation of three histidine kinases (HKs) of Mycobacterium tuberculosis , viz. , MtrB, PrrB, and PhoR, all known to play a role in regulating its virulence. Using wild-type and mutant proteins, we performed dimerization assays, thermophoretic-affinity measurements, and competition-based phosphorylation assays to establish that for HK, MtrB autophosphorylation occurs in cis , similar to what has been proposed for the PhoR and PrrB HKs. Next, to determine the kinetics of cis autophosphorylation, we used a quantitative high-throughput assay and identified a two-step mechanism of HK activation, involving (i) the reversible association of HK with ATP, followed by (ii) its phosphorylation. We developed a mathematical model based on this two-step cis mechanism that captured the experimental data. Best-fit parameter values yielded estimates of the extent of HK-ATP association and the rates of HK autophosphorylation, allowing quantification of the propensity of HK autophosphorylation. Our combined experimental and theoretical approach presents a facile, scalable tool to quantify reactions involving bacterial TCS proteins, useful in antibacterial drug development strategies. IMPORTANCE Two-component systems consisting of an input-sensing histidine kinase (HK) and an output-generating response regulator (RR) are one of the key apparatuses utilized by bacteria for adapting to the extracellular milieu. HK autophosphorylation is shown to occur primarily in trans (intermolecular) and more recently shown to occur in cis (intramolecular). Although the catalysis of HK activation remains universal, the reaction scheme for evaluation of the kinetic parameter differs between these designs and cis mode largely remains unexplored. We combined experimental and theoretical approach to unravel two-step mechanism of activation of three cis mode HKs of M. tuberculosis . The new mathematical model yields best-fit parameters to estimate the rates of HK-ATP association and HK autophosphorylation.


2009 ◽  
Vol 247 (9) ◽  
pp. 2455-2484 ◽  
Author(s):  
Ján Filo ◽  
Volker Pluschke

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