Study for Darcy-Brinkman model connected Oldroyd–B Constitutive Model related with Solutions of Velocity of Viscoelastic Fluid Flow in a circular Pipe filled with Porous Media

Purpose – The paper aims to clarify the relationship between the micro-structures of porous media and the coefficient of permeability. Most materials involve different types of defects like caves, pores and cracks, which are important characters of porous media and have a great influence on the physical properties of materials. To study the seepage mechanical characteristics of damaged porous media, the constitutive model of porous media dealing with coupled modeling of pores damage and its impact on permeability property of a deforming media was studied in this paper. Design/methodology/approach – The paper opted for an exploratory study using the approach of continuum damage mechanics (CDM). Findings – The paper provides some new insights on the fluid dynamics of porous media. The dynamic evolution model of permeability coefficient established in this paper can be used to model the fluid flow problems in damaged porous media. Moreover, the modified Darcy's law developed in this paper is considered to be an extension of the Darcy's law for fluid flow and seepage in a porous medium. Research limitations/implications – Owing to the limitations of time, conditions, funds, etc., the research results should be subject to multifaceted experiments before their innovative significance can be fully verified. Practical implications – The paper includes implications for the development of fluid dynamics of porous media. Originality/value – This paper fulfils an identified need to study the relationship between the micro-structures of porous media and the coefficient of permeability.

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Effect of Fluid Friction on Interstitial Fluid Flow Coupled with Blood Flow through Solid Tumor Microvascular Network

10.32920/14637081.v1 ◽

2021 ◽

Author(s):

Mostafa Sefidgar ◽

M. Soltani ◽

Kaamran Raahemifar ◽

Hossein Bazmara

Keyword(s):

Blood Flow ◽

Porous Media ◽

Fluid Flow ◽

Solid Tumor ◽

Interstitial Fluid ◽

Brinkman Model ◽

Fluid Friction ◽

Darcy Model ◽

Flow Through ◽

Interstitial Velocity

A solid tumor is investigated as porous media for fluid flow simulation. Most of the studies use Darcy model for porous media. In Darcy model, the fluid friction is neglected and a few simplified assumptions are implemented. In this study, the effect of these assumptions is studied by considering Brinkman model. A multiscale mathematical method which calculates fluid flow to a solid tumor is used in this study to investigate how neglecting fluid friction affects the solid tumor simulation. The mathematical method involves processes such as blood flow through vessels and solute and fluid diffusion, convective transport in extracellular matrix, and extravasation from blood vessels. The sprouting angiogenesis model is used for generating capillary network and then fluid flow governing equations are implemented to calculate blood flow through the tumor-induced capillary network. Finally, the two models of porous media are used for modeling fluid flow in normal and tumor tissues in three different shapes of tumors. Simulations of interstitial fluid transport in a solid tumor demonstrate that the simplifications used in Darcy model affect the interstitial velocity and Brinkman model predicts a lower value for interstitial velocity than the values that Darcy model predicts.

Download Full-text

Effect of Fluid Friction on Interstitial Fluid Flow Coupled with Blood Flow through Solid Tumor Microvascular Network

10.32920/14637081 ◽

2021 ◽

Author(s):

Mostafa Sefidgar ◽

M. Soltani ◽

Kaamran Raahemifar ◽

Hossein Bazmara

Keyword(s):

Blood Flow ◽

Porous Media ◽

Fluid Flow ◽

Solid Tumor ◽

Interstitial Fluid ◽

Brinkman Model ◽

Fluid Friction ◽

Darcy Model ◽

Flow Through ◽

Interstitial Velocity

A solid tumor is investigated as porous media for fluid flow simulation. Most of the studies use Darcy model for porous media. In Darcy model, the fluid friction is neglected and a few simplified assumptions are implemented. In this study, the effect of these assumptions is studied by considering Brinkman model. A multiscale mathematical method which calculates fluid flow to a solid tumor is used in this study to investigate how neglecting fluid friction affects the solid tumor simulation. The mathematical method involves processes such as blood flow through vessels and solute and fluid diffusion, convective transport in extracellular matrix, and extravasation from blood vessels. The sprouting angiogenesis model is used for generating capillary network and then fluid flow governing equations are implemented to calculate blood flow through the tumor-induced capillary network. Finally, the two models of porous media are used for modeling fluid flow in normal and tumor tissues in three different shapes of tumors. Simulations of interstitial fluid transport in a solid tumor demonstrate that the simplifications used in Darcy model affect the interstitial velocity and Brinkman model predicts a lower value for interstitial velocity than the values that Darcy model predicts.

Download Full-text