Determination of Brinkman Model Parameters Using Stokes Flow Model

Zaripov, S. K.; Марданов, Р. Ф.; Sharafutdinov, V. F.

doi:10.1007/s11242-019-01324-9

Cited by 25 publications

(9 citation statements)

References 37 publications

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“…2020), the Forchheimer term in can also be neglected (Nield & Bejan 2017). The effects of the macroscopic velocity gradient on can be modelled with a Laplacian term, which was first proposed by Brinkman (1949) and then was extensively studied and improved; see Rao, Kuznetsov & Jin (2020), Zaripov, Mardanov & Sharafutdinov (2019), Zhao et al. (2018), Liu, Patil & Narusawa (2007), Valdes-Parada, Ochoa-Tapia & Alvarez-Ramirez (2007), Vafai (2005), Starov & Zhdanov (2001) and Ochoa-Tapia & Whitaker (1995) as examples.…”

Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

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A macroscopic two-length-scale model for natural convection in porous media driven by a species-concentration gradient

et al. 2021

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The modelling of natural convection in porous media is receiving increased interest due to its significance in environmental and engineering problems. State-of-the-art simulations are based on the classic macroscopic Darcy–Oberbeck–Boussinesq (DOB) equations, which are widely accepted to capture the underlying physics of convection in porous media provided the Darcy number, $Da$ , is small. In this paper we analyse and extend the recent pore-resolved direct numerical simulations (DNS) of Gasow et al. (J. Fluid Mech, vol. 891, 2020, p. A25) and show that the macroscopic diffusion, which is neglected in DOB, is of the same order (with respect to $Da$ ) as the buoyancy force and the Darcy drag. Consequently, the macroscopic diffusion must be modelled even if the value of $Da$ is small. We propose a ‘two-length-scale diffusion’ model, in which the effect of the pore scale on the momentum transport is approximated with a macroscopic diffusion term. This term is determined by both the macroscopic length scale and the pore scale. It includes a transport coefficient that solely depends on the pore-scale geometry. Simulations of our model render a more accurate Sherwood number, root mean square (r.m.s.) of the mass concentration and r.m.s. of the velocity than simulations that employ the DOB equations. In particular, we find that the Sherwood number $Sh$ increases with decreasing porosity and with increasing Schmidt number $(Sc)$ . In addition, for high values of $Ra$ and high porosities, $Sh$ scales nonlinearly. These trends agree with the DNS, but are not captured in the DOB simulations.

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Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

“…,Zaripov, Mardanov & Sharafutdinov (2019), Zhao et al (2018), Liu, Patil & Narusawa (2007), Valdes-Parada, Ochoa-Tapia & Alvarez-Ramirez (2007), Vafai (2005), Starov & Zhdanov (2001) and Ochoa-Tapia & Whitaker (1995) as examples. Here, we…”

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confidence: 99%

A macroscopic two-length-scale model for natural convection in porous media driven by a species-concentration gradient

et al. 2021

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“…Furthermore, Table 1 presents Darcy's law and its modifications to describe a system with n-connected sections of varying geometry, the flow rate through the fluidic circuit modeled using an electrical circuit analogy, Equation (7) [55], the Brickman model for flow through highly porous media, Equation (8) [56], the Richards model for the saturation of the media description, Equation ( 9) [57], and the Elizalde et al equation to describe the flow into a porous media with variable cross-sectional sections, Equation (10) [58].…”

Section: Mechanisms and Modelingmentioning

confidence: 99%

Paper and Other Fibrous Materials—A Complete Platform for Biosensing Applications

et al. 2021

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Paper-based analytical devices (PADs) and Electrospun Fiber-Based Biosensors (EFBs) have aroused the interest of the academy and industry due to their affordability, sensitivity, ease of use, robustness, being equipment-free, and deliverability to end-users. These features make them suitable to face the need for point-of-care (POC) diagnostics, monitoring, environmental, and quality food control applications. Our work introduces new and experienced researchers in the field to a practical guide for fibrous-based biosensors fabrication with insight into the chemical and physical interaction of fibrous materials with a wide variety of materials for functionalization and biofunctionalization purposes. This research also allows readers to compare classical and novel materials, fabrication techniques, immobilization methods, signal transduction, and readout. Moreover, the examined classical and alternative mathematical models provide a powerful tool for bioanalytical device designing for the multiple steps required in biosensing platforms. Finally, we aimed this research to comprise the current state of PADs and EFBs research and their future direction to offer the reader a full insight on this topic.

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“…These equations describe the flow in the porous medium at low volume fraction of solids [27,28] and can serve as the starting point for the derivation of Darcy's law. Here k is the damping coefficient and ν/k is the permeability [27], see [33] for recent discussion of the coefficients and more references. We observe that Eq.…”

Section: General Solution Of Brinkman Equationsmentioning

confidence: 99%

Lamb-type solution and properties of unsteady Stokes equations

Fouxon¹,

Leshansky²,

Rubinstein³

et al. 2021

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In the present paper we derive the general solution of the unsteady Stokes equations in an unbounded fluid in spherical polar coordinates. The solution is an expansion in vector spherical harmonics and given as a sum of a particular solution, proportional to pressure gradient exhibiting power-law dependence, and a solution of vector Helmholtz equation decaying exponentially fast at infinity. The proposed decomposition resembles the classical Lamb's solution for the steady Stokes equations: the series coefficients are projections of radial component, divergence and curl of the boundary flow on scalar spherical harmonics. The proposed solution provides an explicit form of the potential far from an oscillating body ("generalized Darcy's law") and high-and low-frequency expansions. The leading order of the high-frequency expansion yields the well-known ideal (inviscid) flow approximation. Continuation of the proposed solution to imaginary frequency provides general solution of the Brinkman equations describing viscous flow in porous medium.

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Determination of Brinkman Model Parameters Using Stokes Flow Model

Cited by 25 publications

References 37 publications

A macroscopic two-length-scale model for natural convection in porous media driven by a species-concentration gradient

A macroscopic two-length-scale model for natural convection in porous media driven by a species-concentration gradient

Paper and Other Fibrous Materials—A Complete Platform for Biosensing Applications

Lamb-type solution and properties of unsteady Stokes equations

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