Continuum description of quasi-static intrusion of non-wetting liquid into a porous body

Cieszko, M.; Czapla, E.; Kempiński, M.

doi:10.1007/s00161-014-0340-2

Cited by 3 publications

(5 citation statements)

References 20 publications

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“…The most important challenge is integration of the current data into a unified model of the brain as a single multilevel model. We need to explore, verify, and apply experiences from many various areas of science: from modeling of severe illnesses [17] and traditional neuronal networks [50,51], through liquid state machines [63,64] to liquid and gas distribution in porous materials [7][8][9].…”

Section: Results Of Other Scientistsmentioning

confidence: 99%

OFN-Based Brain Function Modeling

Prokopowicz

Mikołajewski

2017

Theory and Applications of Ordered Fuzzy Numbers

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A modeling approach may significantly help to explore the problem of weak understanding of the physiological and pathological central nervous system function in the most noninvasive and comprehensive way. The aim of this chapter is to assess and discuss the extent to which possible opportunities concerning computational brain models based on fuzzy logic techniques may be exploited. IntroductionStructured networks and functional connections of interacting neural populations underlying both physiological and pathological central nervous system (CNS) function are still poorly understood. Interdisciplinarity and independence of research provide a variety of scientific approaches, used tools, and wide coverage and even overlapping of the research fields, especially as regards human research, including neuroscience [1]. The modeling approach may significantly help to explore the aforementioned problem in the most noninvasive way. The aim of this chapter is to assess and discuss the extent to which possible opportunities concerning computational brain models based on fuzzy logic techniques may be exploited.

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Section: Results Of Other Scientistsmentioning

confidence: 99%

OFN-Based Brain Function Modeling

Prokopowicz

Mikołajewski

2017

Theory and Applications of Ordered Fuzzy Numbers

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“…A non-standard approach to the problem of macroscopic description of such processes is presented in the paper (Cieszko et al 2015), where balance equations and constitutive relations have been formulated analysing the process of liquid intrusion in the pressurespace continuum, and menisci motion, as a process of diffusive transport in this continuum. In this model, there are parameters and functions describing pore size distributions in the boundary conditions and in the coefficients characterizing diffusive transport of menisci in the pressure-space continuum.…”

Section: Introductionmentioning

confidence: 99%

Limit Models of Pore Space Structure of Porous Materials for Determination of Limit Pore Size Distributions Based on Mercury Intrusion Data

2018

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This paper proposes the application of capillary and chain random models of pore space structure for determination of limit pore diameter distributions of porous materials, based on the mercury intrusion curves. Both distributions determine the range in which the pore diameter distribution of the investigated material occurs and defines the degree of inaccuracy of the method based on the mercury intrusion data caused by the indeterminacy of the sample shape and its pore space architecture. We derived equations describing the quasi-static process of mercury intrusion into the porous layer and porous ball with a random chain pore space structure and analysed the influence of the model parameters on the mercury intrusion curves. It was shown that the distribution of link length in the chain model of the pore space, random location of chain capillaries in the sample and the length distribution of the capillaries do not influence significantly the intrusion process. Therefore, a simple model of the mercury intrusion into the layer is proposed in which chain links of the pore space have random diameters and constant length. This model is used as a basic model of the intrusion process into a sample of any shape and size and with homogeneous and isotropic chain pore space architecture. The thickness of the layer then represents the mean length of chain capillaries in the sample. It was also proved that the capillary and chain models of pore space architecture are limit models of the network model identified in this paper with the pore architecture of the investigated sample. This justifies the application of both models for determination of limit cumulative distributions of pore diameters in porous materials based on the mercury intrusion data. Keywords Mercury porosimetry • Capillary potential curve • Chain and capillary models of pore structure • Limit pore diameter distributions B M.

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“…The form of this dependence extends the dimensionality of processes taking place in unsaturated porous materials. It is explicitly visible already in description of a relatively simple problem of quasi-static intrusion of non-wetting liquid into a porous body, considered in paper [15] as a process taking place in the pore spacepressure continuum. This additional dimensionality determines the complexity of processes of capillary transport in unsaturated porous materials.…”

Section: Partial and Phase Densities Of The Constituentsmentioning

confidence: 99%

“…This concern, among others, the description of quasi-static intrusion of mercury into porous materials and description of liquid or gas flow through unsaturated porous material. In the first case, the equations have a form characteristic for nonstationary processes in which, instead of time as the independent variable, the mercury pressure is present, [15]. In the second case, for example, even the geometrically very simple problem of liquid flow through a layer of unsaturated porous material is described by a system of three coupled, nonlinear equations for distributions of saturation, the fluid pressure and its flow velocity in the layer.…”

Section: Conclusion and Final Remarksmentioning

confidence: 99%

“…The situation here is unusual for hydrostatics, where in spite of the homogeneous pressure distribution in the liquid, the distribution of its saturation in the medium is inhomogeneous. In this case, the non-standard approach to solution of this problem is to formulate balance equations and constitutive relations for processes taking place in the pore space-pressure continuum, [15]. A flow of such liquid, e.g.…”

Section: Introductionmentioning

confidence: 99%

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Macroscopic description of capillary transport of liquid and gas in unsaturated porous materials

Cieszko

2016

Meccanica

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A new macroscopic description of capillary transport of liquid and gas in porous materials is presented within the framework of multiphase continuum mechanics. It is assumed that unsaturated porous material form a macroscopic continuum composed of three constituents: gas, mobile liquid and capillary liquid, while the skeleton is rigid with an isotropic pore space structure. The capillary liquid forms a thin layer on the internal contact surface with the skeleton, is immoveable and contains the whole capillary energy. The remaining part of the liquid, surrounded by the layer of the capillary liquid and menisci, forms the constituent called mobile liquid. Both liquids exchange mass, momentum and energy in the vicinity of menisci surfaces during their motion, which is described by an additional macroscopic velocity field. A macroscopic scalar quantity is introduced, parametrizing changes of saturations, which for quasi static and stationary processes is equal to the capillary pressure. This quantity extends the dimensionality of the description of mechanical processes taking place in unsaturated porous materials. For the three fluid constituents of the medium, balance equations of mass and linear momentum and evolution equations for saturations are formulated. The constitutive relations for quantities describing mechanical processes in such a medium are proposed based on the dissipation inequality of mechanical energy for the whole system. A new approach is proposed, similar to that used in rational thermodynamics, based on entropy inequality analysis and the Lagrange multipliers method.

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Continuum description of quasi-static intrusion of non-wetting liquid into a porous body

Cited by 3 publications

References 20 publications

OFN-Based Brain Function Modeling

OFN-Based Brain Function Modeling

Limit Models of Pore Space Structure of Porous Materials for Determination of Limit Pore Size Distributions Based on Mercury Intrusion Data

Macroscopic description of capillary transport of liquid and gas in unsaturated porous materials

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