A mathematical model of fluid flow in tight porous media based on fractal assumptions

Jin, Yi; Li, Xiang; Zhao, Meiqi; Liu, Xianhe; Lĭ, Hui

doi:10.1016/j.ijheatmasstransfer.2016.12.096

Cited by 90 publications

(31 citation statements)

References 38 publications

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“…This classical result has been found to be valid for both unidirectional and radial capillary penetration in porous media [22][23][24][25], and is further extended to the hemispherical penetration in a semi-infinite porous medium [26] and imbibition in structured porous media with axially variable geometries [27]. However, recent studies have also indicated that this simple model is not applicable for some complex cases, such as flow processes in heterogeneous and random porous media, and some other effects, e.g., fractal and disorder, should be incorporated into the analysis [28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Tuning capillary penetration in porous media: Combining geometrical and evaporation effects

Liu

Gan

et al. 2018

International Journal of Heat and Mass Transfer

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Capillary penetration of liquids in porous media is of great importance in many applications and the ability to tune such penetration processes is increasingly sought after. In general, liquid penetration can be retarded or restricted by the evaporation of volatile liquid at the surface of the porous media. Moreover, when capillary penetration occurs in a porous layer with non-uniform cross section, the penetration process can be accelerated or impeded by adjusting the section geometry. In this work, on the basis of Darcy's Law and mass conservation, a theoretical model of capillary penetration combining evaporation effects in two-dimensional homogeneous porous media of varying cross-section is developed and further examined by numerical simulations. The effects of sample geometry and liquid evaporation on capillary penetration are quantitatively analyzed. Results show that the penetration velocity is sensitive to the geometry of the porous layer, and can be tuned by varying the evaporation rate for a given geometry. Under given evaporation conditions, penetration is restricted to a limited region with a predictable boundary. Furthermore, we find that the inhibition of liquid penetration by evaporation can be offset by varying the geometry of the porous layer. In addition, the theoretical model is further extended to model the capillary flow in three-dimensional porous media, and the interplay of geometry and evaporation during the capillary flow process in 3D conditions is also investigated. The results obtained can be used for facilitating the design of porous structures, achieving tunable capillary penetration for practical applications in various fields.

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Section: Introductionmentioning

confidence: 99%

Tuning capillary penetration in porous media: Combining geometrical and evaporation effects

Liu

Gan

et al. 2018

International Journal of Heat and Mass Transfer

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“…Actually, problems dealing with transport phenomena are very important in science and engineering, particularly, in the study of porous media there is a great research activity both theoretical and experimental [27,33,34,[40][41][42][43][45][46][47][48][49][50][51][52][53][54].…”

Section: Discussionmentioning

confidence: 99%

Generalities on finite element discretization for fractional pressure diffusion equation in the fractal continuum

2019

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In this study we explore the application of the novel fractional calculus in fractal continuum (FCFC), together with the finite element method (FEM), in order to analize explicitly how these differential operators act in the process of discretizing the generalized fractional pressure diffusion equation for a three-dimensional anisotropic continuous fractal flow. The master finite element equation (MFEE) for arbitrary interpolation functions is obtained. As an example, MFEE for the case of a generic linear tetrahedron in $\mathbb{R}^3$ is shown. Analytic solution for the spatial variables is determined over a canonical tetrahedral finite element in global coordinates.

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“…Extended studies of hydromechanical processes occurring in the working channel of a magnetic peristaltic pump can be performed by conducting a computational experiment or with the help of a carefully designed physical experiment [6][7][8][9][10][11][12]. However, phenomena of practical interest accompanying the process of moving a heterogeneous flow through a channel of variable cross section are characterized by multidimensionality, nonstationarity, and the presence of boundary layers, which makes the implementation of comprehensive physical modeling very difficult.…”

Section: Methodsmentioning

confidence: 99%

Modeling of wave processes when the heterogeneous flow is moving in a low-frequency magnetic peristaltic pump of pulsating type

Vasilyeva¹

2019

Vib. proced.

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The paper presents the results of a multiphysical simulation of the movement of a heterogeneous flow in the working channel of a magnetic peristaltic pump, which describes in detail the state of the flow particles at all points of the considered area at different points in time, taking into account the design parameters of the channel. The developed model made it possible to reveal a rational range of parameters in the conditions of the wave variation of the internal cross section of the working channel of a magnetic peristaltic pump in a running magnetic field.

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A mathematical model of fluid flow in tight porous media based on fractal assumptions

Cited by 90 publications

References 38 publications

Tuning capillary penetration in porous media: Combining geometrical and evaporation effects

Tuning capillary penetration in porous media: Combining geometrical and evaporation effects

Generalities on finite element discretization for fractional pressure diffusion equation in the fractal continuum

Modeling of wave processes when the heterogeneous flow is moving in a low-frequency magnetic peristaltic pump of pulsating type

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