Browsing by Author "Tiwari, Ashish"

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Analytical study of micropolar fluid flow through porous layered microvessels with heat transfer approach
(Springer, 2020-02) Tiwari, Ashish
The transport theory of three-layered fluid flow and heat transfer aspects in porous layered tubes is considered in the present work to study the flow of microlevel fluids through porous layered microvessels. The transportation of energy through porous media and the applications associated with heat transfer in physiological aspects are analyzed. Blood is considered as three-layered liquid model in which the core and peripheral regions of the tube are occupied by micropolar and Newtonian fluids, respectively. A thin glycocalyx layer near the wall is considered that represents the porous region due to the deposition of carbohydrates, fibrous tissues or macromolecules inside the interior surface of the tube wall. Analytical expressions for the various flow quantities like velocity, temperature profile, flow rate, flow impedance and additional quantities like hematocrit and Fahraeus effect are obtained and the impacts of various parameters like heat transfer and porous layer parameters are analyzed pictorially for two different formulations (no-spin and no-couple stress conditions). A noteworthy observation is that the impact of no-couple stress condition is relatively more significant in flow quantities, hematocrit and Fahraeus effect than the no-spin condition at the interface. The motivational work of the blood flow through porous blood vessels by selecting the micropolar fluid for the microlevel effects of the molecules may leave a significant impact in the treatment of the various diseases in medical sciences.
Analytical study of the effect of complex fluid rheology and membrane parameters on heat transfer in fluid flow through a swarm of cylindrical particles
(Elsevier, 2024-11) Tiwari, Ashish
The present research investigates the flow characteristics of a Carreau-Yasuda fluid, which is non-Newtonian in nature, passing through a membrane composed of biporous layered cylindrical particles, utilizing a variable permeability approach. The process of formulating the governing equations entails utilizing both the empirical particle-in-cell model and a heat transfer approach. The structure of the proposed research is configured so that fluid flow near the solid core of the cylindrical particle is governed by the Brinkman-Forchheimer equation with variable permeability. In the intermediate region enveloping the Brinkman-Forchheimer region, the fluid flow is regulated by the Brinkman equation with variable permeability. Meanwhile, the peripheral region, adjacent to the hypothetical cell surface, is governed by the Stokes equation due to its non-porous nature. The thermal equations in a steady-state condition are simplified under viscous dissipation. The nonlinearity and coupling of equations arise in the study of Carreau-Yasuda fluid flow through a biporous layered cylindrical particle. This is attributed to the inclusion of a nonlinear inertia term in the Brinkman-Forchheimer equation, variable permeability, and a nonlinear correlation between shear stress and strain in the Carreau-Yasuda fluid. In addressing this issue, the empirical regular perturbation method is employed to derive asymptotic solutions for the governing equations under conditions of high permeability and low Weissenberg number. Additionally, a numerical approach utilizing the NDSolve command in Mathematica software is applied to illustrate graphical analyses under conditions of low permeability and Weissenberg number. The flow profiles' expressions are employed for analyzing the membrane permeability, Kozeny constant, and temperature variation. The graphical discussion delves into the influence of various control parameters, such as Carreau-Yasuda fluid parameters, variable permeability parameters, and Forchheimer number, on hydrodynamic and thermal quantities like fluid velocity, membrane permeability, Kozeny constant, temperature variations, and Nusselt number. The notable finding of the present study is that increasing variable permeability parameters in both the Forchheimer and Brinkmann regions, along with the Forchheimer number, lead to a decrease in fluid velocity and temperature profiles across the flow domain, ultimately resulting in a reduced Nusselt number profile. The present study includes a comparative analysis with existing works, focusing on reduced cases, and reveals that the findings closely match with the previously published studies on membrane filtration processes. The findings of the current study show potential for enhancing our comprehension of crucial physical and biological applications, such as filtration processes in wastewater treatment, characteristics of petroleum reservoir rocks, and the dynamics of blood flow through smooth muscle cells.
Analytical Study of the Effect of Variable Viscosity and Heat Transfer on Two-Fluid Flowing through Porous Layered Tubes
(Springer, 2022-04) Tiwari, Ashish
The proposed study is an attempt to perceive theoretically the heat transfer phenomenon in the flow of temperature-dependent viscous blood through microvessels internally surrounded by a thin layer of endothelial glycocalyx at the wall. While flowing through microvessels, the blood separates into erythrocytes suspended fluid and cell-depleted fluid into core and peripheral regions respectively. Therefore, to best represent the flow of human blood in microvessels, it has been modeled as a two-fluid. Erythrocytes appearing in the core stimulates the non-Newtonian behavior of the fluid is manifested here by Herschel-Bulkley fluid with temperature-dependent viscosity. The plasma surrounded over the blood cells in the peripheral layer is expressed as a Newtonian fluid with constant viscosity. An added advantage of utilizing the Brinkman-Forchheimer equation to govern the flow through the layer of endothelial glycocalyx (EGL) is that it is credible for both small and large Darcy numbers (permeability). Linear approximation of the Reynolds, viscosity model is exercised to obtain the analytical solutions for the governing equations of Herschel-Bulkley fluid flowing through the core region. In the non-porous peripheral region, the analytical solutions have been obtained for Newtonian fluid with constant viscosity directly and in the porous peripheral region, the Brinkman-Forchheimer equation is solved using regular perturbation for large Darcy number and singular perturbation with a matched asymptotic condition for small Darcy number. Analytical expressions for the velocity, flow rate, flow impedance, and temperature field have been obtained for the different regions. Graphical analysis revealing significant results regarding the variable viscosity, thermal conductivity, Grashof number, Forchheimer number, Richardson number, and permeability on the hemodynamical variables are conducted and results are discussed in detail. The study concludes that an EGL adjacent to the vessel wall increase the resistance to blood flow. The notable discovery of the study is that the temperature parameters influence all the quantities and therefore establish that the temperature-dependent viscosity plays a vital role in medical treatments involving temperature variation such as chemotherapy.
Asymptotic analysis of electrohydrodynamic flow through a swarm of porous cylindrical particles
(AIP, 2024-04) Tiwari, Ashish
The present article reveals the study of an electrohydrodynamic flow through a membrane composed of a swarm of porous layered cylindrical particles adopting a heat transfer approach. The configuration of the proposed theoretical model is segregated into two regions in which the region proximate to the solid core of the cylindrical particle is a porous region. However, a region surrounded by a porous region is a non-porous (clear fluid) region. The thermal equations are employed under steady-state conditions to establish the temperature distribution when heat conduction prevails over heat convection. The Brinkman and Stokes equations regulate fluid flow through a swarm of porous layered cylindrical particles in porous and non-porous regions, respectively. With the purpose of addressing an electric field in the fluid flow process through a swarm of porous layered cylindrical particles to understand the role of a Hartmann electric number, the momentum equation and the charge density are coupled and nonlinear. The nonlinear second-order differential equation governs the momentum equation and regulates fluid flow through a swarm of porous cylindrical particles. The solutions of the energy equations for both regions are analytically obtained. The asymptotic expansions of velocities for porous and non-porous regions have been derived using the perturbation technique for the small and large values of the nonlinearity parameter α. The effects of various parameters like Hartmann electric number, Grashof number, radiation parameter, viscosity ratio parameter, and porosity of the porous material on the hydrodynamical permeability, Kozeny constant of the membrane, and temperature are analyzed graphically. A noteworthy observation is that a rising Hartmann electric number, the ratio of electric force to the viscous force, enhances the velocity, which is relatively more significant for higher permeability and hence enhances the membrane permeability; however, decay in Kozeny constant is reported with a rising Hartmann electric number. Significant velocity and membrane permeability growth are described with a rising Grashof number, a ratio of thermal buoyancy and viscous forces. The observations from the present study hold promise for advancing our understanding of critical physical and biological applications, including wastewater treatment filtration processes, petroleum reservoir rocks, and blood flow through smooth muscle cells.
Asymptotic analysis of Jeffreys–Newtonian fluids flowing through a composite vertical porous layered channel: Brinkman–Forchheimer model
(AIP, 2023-12) Tiwari, Ashish
This study examines the flow of a Newtonian fluid enclosed between two non-Newtonian Jeffreys fluids with viscosity that varies with temperature within a composite vertical channel. Including a corotational Jeffreys liquid allows for considering stress dependence on the present deformation rate and its history. The proposed study's framework comprises three distinct regions, wherein the intermediate region governs Newtonian fluid flow under temperature-dependent viscosity. However, the outer layers oversee the flow of Jeffreys fluids within the porous medium, demonstrating temperature-dependent viscosity. The Brinkman–Forchheimer equation is employed to establish the governing equations applicable to both low and high permeabilities of the porous medium. This equation is nonlinear, making it challenging to find an analytical solution. Therefore, the regular and singular perturbation methods with matched asymptotic expansions are applied to derive asymptotic expressions for velocity profiles in various regions. The hydrodynamic quantities, such as flow rate, flow resistance, and wall shear stresses, are determined by deriving their expressions using velocities from three distinct regions. The graphical analysis explores the relationships between these hydrodynamic quantities and various parameters, including the Grashof number, Forchheimer number, viscosity parameter, Jeffreys parameter, conductivity ratio, effective viscosity ratio, absorption ratio, and the presence of varying thicknesses of different layers. An interesting finding is that a more pronounced velocity profile is noticed when the permeability is high and the viscosity parameter of the Newtonian region, denoted as α2, is lower than that of the surrounding area. This heightened effect can be linked to a relatively more significant decrease in the viscosity of the Jeffreys fluid, represented by μ1, as compared to the viscosity of the Newtonian fluid, μ2, as the temperature increases. The outcomes of this research hold special significance in situations like the extraction of oil from petroleum reserves, where the oil moves through porous layers with varying viscosities, including sand, rock, shale, and limestone.
Creeping flow of Jeffrey fluid through a swarm of porous cylindrical particles: Brinkman–Forchheimer model
(Elsevier, 2021-12) Tiwari, Ashish
The majority of the previous studies analyzed the flow of fluids with constant viscosity through membranes composed of porous cylindrical particles using the particle-in-cell approach with the Brinkman equation governing the flow through porous media. However, a slight variation in temperature affects the viscosity of the fluids and hence affects the filtration process of fluids through membranes. The motivation of this problem came from the fact that viscosity is concentration dependent due to presence of impurities and contaminants in the fluids and hence can be taken as function of position or temperature. The present work is a theoretical attempt to investigate the impact of temperature-dependent viscosity on the creeping flow of Jeffrey fluid through membrane consisting of the aggregates of the porous cylindrical particles. The flow pattern of the Jeffrey fluid is taken along the axial direction of the cylindrical particles, and the cell model approach is utilized to formulate the governing equations driven by a constant pressure gradient. The flow regime is divided into two-layer form, one is inside the porous cylindrical particle enclosing a solid core, which is governed by the Brinkman–Forchheimer equation, and another one is outside of the porous cylindrical particle, which is governed by the Stokes equation. Being a nonlinear equation, an analytical solution of the Brinkman–Forchheimer equation is intractable. To overcome this difficulty, the regular and singular perturbation methods have been employed to solve the Brinkman–Forchheimer equation under the assumption of temperature-dependent viscosity for small and large permeability of the porous medium, respectively; however, an analytical approach is utilized to solve the Stokes equation.
Creeping flow of micropolar fluid parallel to the axis of cylindrical cells with porous layer
(Elsevier, 2019-08) Tiwari, Ashish
The present paper considers the flow of micropolar fluid through a membrane modeled as a swarm of solid cylindrical particles with porous layer using the cell model technique. Traditional boundary conditions on hypothetical cell surface were added with an additional condition: the no spin condition / no couple stress condition. Expressions for velocity and microrotation vector components have been obtained analytically. Effect of various parameters such as particle volume fraction, permeability parameter, micropolarity number etc. on hydrodynamic permeability of membrane has been discussed
Creeping flow of micropolar fluid through a swarm of cylindrical cells with porous layer (membrane)
(Elsevier, 2019-11) Tiwari, Ashish
The flow of micropolar fluid through a membrane modeled as a swarm of solid cylindrical particles with porous layer using the cell model technique is considered. The flow is directed perpendicular to the axis of the cylinders. Boundary value problem involves traditional conditions of velocities and stresses continuity, no-stress and no-couple stress/no-spin condition on hypothetical cell surface. The problem is solved analytically and the influence of micropolar and porous medium parameters on hydrodynamic permeability of a membrane is investigated.
Creeping flow of non-Newtonian fluid through membrane of porous cylindrical particles: A particle-in-cell approach
(AIP, 2023-04) Tiwari, Ashish
The present study is an attempt to deal with hydrodynamic and thermal aspects of the incompressible Carreau fluid flow past a membrane consisting of uniformly distributed aggregates of porous cylindrical particles enclosing a solid core which aims to provide a comprehensive study of the impact of non-Newtonian nature of Carreau fluid in the filtration process through membranes. The non-Newtonian characteristic of Carreau fluid is adopted to describe the mechanism of the pseudoplastic flow through membranes. The layout of the fluid flow pattern is separated into two distinct areas in which the area adjacent to the solid core of the cylindrical particle is considered as porous. However, the region surrounding the porous cylindrical particle is taken as non-porous (clear fluid region). The Brinkman equation governs the porous region, whereas the non-porous region is regulated by the Stokes equation. The nonlinear governing equations of the Carreau fluid flow in the different regions are solved using an asymptotic series expansion in terms of the small parameters, such as Weissenberg number ( We ≪ 1 ) and a non-dimensional parameter ( S ≪ 1 ), for the higher permeability of the porous material. For large permeability, the expression of velocity is derived, and the same has been used to compute the hydrodynamic permeability, Kozeny constant, and temperature profile. The numerical scheme (NDSolve in Mathematica) is used to solve the singularly perturbed boundary value problems in the case of small permeability of the porous medium [i.e., ( S ≫ 1 )]. The graphical analysis illustrating the outcomes of the effects of varying control parameters such as the power-law index, viscosity ratio parameter, permeability of the porous medium, Weissenberg number, and Nusselt number on the membrane permeability, Kozeny constant and temperature profile are discussed comprehensively and validated with previously published works on the Newtonian fluid in the limiting cases. The notable determination of the present study is that the Carreau fluid parameters, such as the Weissenberg number, power-law index, and viscosity ratio parameter, have a significant impact on the velocity, and hence, the membrane permeability, Kozeny constant, and temperature profile. The results showed a significant increase in the flow velocity and hydrodynamic permeability as the dominance of elastic forces over viscous forces increased in the case of high permeability ( S ≪ 1 ). The velocity gets a slight reduction for lower permeability of the porous material ( S ≫ 1 ); however, the hydrodynamic permeability behaves similar to the higher permeability of the porous material. The findings of the proposed work may be instrumented in analyzing various processes, including wastewater treatment filtration processes, and blood flow through smooth muscle cells. The proposed work, however, requires experimental verification.
Effect of the magnetic field on the hydrodynamic permeability of a membrane
(Springer, 2012-07) Tiwari, Ashish
The present paper concerns the influence of the magnetic field on the permeability of a membrane of solid cylindrical particles covered with porous layer. Here, we have considered the flow along the axis of cylinder and the alignment of uniform magnetic field is assumed to be perpendicular to the axis. The Brinkman equation is used for flow through porous region and Stokes equation is used for flow through clear fluid region. To model flow through assemblage of particles, cell model technique has been used i.e. the porous cylindrical shell is assumed to be confined within a hypothetical cell of same geometry. The stress jump condition has been employed at the fluid-porous interface and all four alternative conditions Happel, Kuwabara, Kvashnin and Mehta-Morse/Cunningham are used at the hypothetical cell. Effect of the Hartmann number on the hydrodynamic permeability of the membrane is discussed
Effect of varying viscosity on a two-layer model of the blood flow through porous blood vessels
(Springer, 2019-01) Tiwari, Ashish
The present work concerns the effect of radially varying viscosity on blood flow through blood vessels with porous walls. Blood is assumed as a two-fluid model consisting of a core region of suspension of all red cells constituted by the Herschel-Bulkley fluid and a peripheral layer of plasma free from the cells modeled as a Newtonian fluid. No slip condition has been used on the wall and the pressure gradient has been taken as constant. The wall of the blood vessel is composed of a thin porous (Brinkman) layer representing the glycocalyx layer. On the fluid interface the stress jump boundary condition as suggested by Ochoa-Tapia and Whitaker has been used. Analytical expressions for velocity profile, wall shear stress, rate of flow and resistance to flow have been obtained for different regions and the effects of plasma layer thickness, varying viscosity, yield stress, permeability and viscosity ratio parameter on the hemodynamical quantities are discussed and depicted graphically. A comparative analysis for a relative change in flow resistance between our model and the previously studied single and two-fluid models without porous walls has been done. The effects of various parameters on hematocrit and Fahraeus effect have also been analyzed and results of earlier works have been established as special limiting cases of the present study. A novel observation is that a decreasing viscosity ratio parameter (λ1) leads to decay in average concentration of RBCs leading to decay in hematocrit (Ht). It is concluded that a thick porous layer with high porosity at wall due to either a glycocalyx layer or the deposition of fatty plaques of cholesterol may lead to significant decay in hematocrit Ht and may lead to anemia.
Effect of varying viscosity on two-fluid model of pulsatile blood flow through porous blood vessels: A comparative study
(Elsevier, 2019-05) Tiwari, Ashish
Present work concerns the pulsatile blood flow of two-fluid model through porous blood vessels under the effect of radially varying viscosity. Blood is modeled as two-phase fluid model consisting a core region by non-Newtonian (Herschel-Bulkley) fluid and a plasma region modeled as Newtonian fluid. No slip condition has been used on wall and pressure gradient is taken as periodic function of time. Up to first order approximate solutions of governing equations are obtained using perturbation approach. A comparative analysis for relative change in flow resistance between our model and previously studied single and two-fluid models without porous layer near wall has also been done. The wall of the blood vessel is composed by a thin Brinkman (porous) layer. The stress jump condition has been imposed on fluid-porous interface. Analytical expressions for the velocity profile, flow rate, wall shear stress and flow resistance have been obtained for different regions and the effect of plasma layer thickness, varying viscosity, yield stress, permeability and viscosity ratio parameter on the flow variables are pictorially discussed. It is perceived that values of flow rate for two-fluid model with porous region near wall is higher in comparison to two-fluid model without porous region near wall. Present study reveals a significant impact of glycocalyx layer on blood flow through blood vessels with a porous layer near wall.
Effect of Varying Viscosity on Two-Layer Model of Pulsatile Flow through Blood Vessels with Porous Region near Walls
(Springer, 2019-06) Tiwari, Ashish
The present work concerns the effect of hematocrit-dependent viscosity on pulsatile flow of blood through narrow tube with porous walls. Two-fluid model of blood is assumed to be consisting of a core region (Casson fluid) and a plasma region (Newtonian fluid). No slip condition is assumed on wall and pressure gradient has been considered as periodic function of time. The wall of the blood vessel composed of a thin porous (Brinkman) layer. The stress jump condition has been employed at the fluid–porous interface in the plasma region. Up to first order, approximate solutions of governing equations are obtained using perturbation approach. A comparative analysis for relative change in resistance offered against the flow between our model and previously studied single and two-fluid models without porous walls has also been done. Mathematical expressions for velocity, rate of flow and resistance offered against the flow have been obtained analytically for different regions and influence of plasma layer thickness, varying viscosity, stress jump parameter, permeability and viscosity ratio parameter on above quantities are pictorially discussed. It is perceived that the values of flow rate for two-fluid model with porous region near walls are higher in comparison with two-fluid model without porous region near walls. Dependency of hematocrit (Ht) on the porosity parameters is graphically discussed. The study reveals a significant impact of various parameters on hematocrit (Ht). A novel observation is that a slight increase in pressure wave amplitude leads to significant fluctuation in hematocrit (Ht) which also indicates how systole and diastole (which controls the pressure gradient amplitudes) leads to changes on blood hematocrit (Ht).
Electro-diffusio-osmosis in an anisotropic channel
(Elsevier, 2025-09) Tiwari, Ashish
Solute dispersion i.e., the combined result of convection and diffusion, within the electroosmotic flow, holds immense promise for diverse applications spanning lab-on-a-chip devices, biomedical engineering, and hydrocarbon production. Beyond mere diffusion, the concentration gradient of an external solute can significantly influence fluid flow. In the present study, the fluid flow driven by the osmotic pressure gradient induced simultaneously by the concentration gradient (diffusioosmosis) and the externally applied electric potential (electroosmosis) in an anisotropic porous microchannel is theoretically analyzed. The classic Taylor’s dispersion model governs the solute dynamics where the initial Gaussian distribution of the solute induces the diffusioosmotic pressure gradient. The momentum balance and advection–diffusion equations are coupled with the diffusioosmotic slip boundary conditions. The multi-time scale approach is used to obtain the closed-form solution of the flow dynamics, which further are utilized to study the behavior of the first-order corrections of the flow dynamics with various vital parameters. Initially, the flow is driven by the electric potential gradient, which contributes to the solute’s transport via convection. The mechanism at any non-zero time is similar, but the additional convection the solute experiences is due to the flow of solvent owing to the solute concentration gradient. This recurring complex phenomenon is thoroughly examined and illustrated graphically. The competing nature of electroosmotic convection against diffusioosmosis is observed, resulting in particle trapping, which can be helpful for applications including particle mixing and separation. The first-order solute concentration for the combined electro-diffusio-osmotic flow surpasses that observed in either pure electroosmotic or pure diffusioosmotic scenarios. The electroosmotic and diffusioosmotic driving forces can be precisely modulated through system parameters, offering a controllable platform for particle transport, which could be a promising avenue for advanced drug delivery systems and optimized microfluidic environments where precise control over particle trajectories is critical.
Electroosmotic flow in a concentrated suspension of polyelectrolyte-grafted solid cylindrical particles: a particle-in-cell approach
(AIP, 2024-12) Tiwari, Ashish
The present study attempts to deal with electrokinetic and hydrodynamic characteristics of mixed electroosmotic and pressure-driven flow through a membrane composed of a swarm of poly-electrolyte-coated solid cylindrical particles. The unit cell model approach is utilized to analyze the hydrodynamic interactions between particles of the multiparticle system. The electroosmotic flow is generated under the influence of an externally applied electric field, and a pressure gradient is assumed in the axial direction of the cylinder. The poly-electrolyte coating over the solid cylindrical particle is considered as a heterogeneous porous medium having variable permeability characteristics. The electrolyte fluid contains charged ions, which can be present and migrate in both inside and outside of the poly-electrolyte layer (PEL). Hence, PEL acts as a semi-permeable porous layer. The PEL is referred to as a fixed charged layer (FCL) owing to an extra number density of immobilized charged ions, fixed on the poly-electrolyte fibers. In order to derive the electric potential distribution in the membrane, the Debye–Hückel approximation is used to linearize the Poisson–Boltzmann equation, which is further used in hydrodynamic governing equations to investigate the electrokinetic effects in the membrane. The flow domain is divided into two subdomains: the FCL region, governed by the Brinkmann–Forchheimer equation, and the clear fluid region, governed by the Stokes equation. The effect of electroosmotic parameters such as electric double layer (EDL) thickness, thickness ratio parameter, and zeta potential, and the membrane parameters such as viscosity ratio, particle volume fraction, stress-jump parameter, Forchheimer number, and variable permeability parameter are analyzed on the flow profile as well as hydrodynamic quantities of the membrane such as hydrodynamic permeability and the Kozeny constant. It is observed that the increasing thickness of the EDL and equivalent EDL reduce the hydrodynamic permeability of the membrane; however, the membrane becomes more hydrodynamic permeable with the enhancement of the zeta potential.
Homogeneous reactive mass transport in a four layer model of KL-Newtonian fluids flowing through biporous layered microvessels
(Elsevier, 2024-05) Tiwari, Ashish
The present work is an effort to investigate the dispersion process of reactive mass transport in human blood vessels for varying viscosity and permeability. Considering a four-layer model of Luo and Kuang (KL)-Newtonian fluids flowing through a biporous layered microvessel, the current research focuses on unsteady mass transport under the first-order chemical reaction. A two-fluid model is adopted where the core region contains the KL fluid, depicting the flow of blood cells, and the coaxial peripheral region represents the plasma region. The outer plasma layer containing Newtonian fluid is segregated into three sublayers, where adjacent to the KL fluid is the non-porous plasma region. The outer two regions, the Brinkman and the Brinkman-Forchheimer regions exhibit radially varying permeability and viscosity characteristics. Analyzing the impact of the Froude number on the solute dispersion process necessitates incorporating an additional body force into the analysis. The porous medium equations are solved using regular and singular perturbation techniques to obtain closed-form solutions. Nevertheless, analytical solutions for the KL fluid and non-porous plasma layer have been derived. The analytical solution of mass distribution due to advection and diffusion is obtained through the Gill and Sankarasubramanian (1970) approach with the aid of Hankel transformation. The effect of various parameters such as Darcy's number, Forchheimer number, Reynolds number, Froude number, permeability parameters , and viscosity parameters on the transport coefficients and mean concentration are discussed graphically. Higher Froude numbers caused weaker dispersion, while the parameters of the Brinkman-Forchheimer region have a significant effect on mass transport compared to the parameters of the Brinkman region. The findings of the current study may assist physiologists in developing a more nuanced understanding of these complex processes, ultimately leading to improved clinical outcomes.
Hydrodynamic permeability of a membrane built up by spheroidal particles covered by porous layer
(Springer, 2017-12) Tiwari, Ashish
This paper concerns the motion of a viscous steady incompressible fluid through a membrane, where the membrane is built up by impermeable spheroidal particles covered by a porous layer. In this work, we discuss the hydrodynamic permeability of a membrane built up by spheroidal particles. Cell model technique has been used to find the hydrodynamic permeability of the membrane. The emphasis is placed on the hydrodynamic permeability of the membrane and its controlling parameters like the permeability of the porous medium, particle volume fraction, deformation parameters, stress jump coefficient. The dependency of the hydrodynamic permeability of the membrane on the above controlling parameters is discussed graphically. Some previous results for hydrodynamic permeability and drag force are verified.
Hydrodynamic permeability of aggregates of porous particles with an impermeable core
(Elsevier, 2011-05) Tiwari, Ashish
A hydrodynamic permeability of membranes built up by porous cylindrical or spherical particles with impermeable core is investigated. Different versions of a cell method are used to calculate the hydrodynamic permeability of the membranes. Four known boundary conditions, namely, Happel's, Kuwabara's, Kvashnin's and Cunningham/Mehta-Morse's, are considered on the outer surface of the cell. Comparison of the resulting hydrodynamic permeability is undertaken. A possible jump of a shear stress at the fluid-membrane interface, its impact on the hydrodynamic permeability is also investigated. New results related to the calculated hydrodynamic permeability and the theoretical values of Kozeny constant are reported. Both transversal and normal flows of liquid with respect to the cylindrical fibers that compose the membrane are studied. The deduced theoretical results can be applied for the investigation of the hydrodynamic permeability of colloidal cake layers on the membrane surface, the hydrodynamic permeability of woven materials.
Hydrodynamic permeability of biporous membrane
(Springer, 2013-07) Tiwari, Ashish
This paper concerns the hydrodynamic permeability of biporous medium built up by porous cylindrical particles located in another porous medium by using cell model technique. It is continuation of the previous work of authors where biporous membrane was built up by porous spherical particles embedded in accompanying porous medium. Four known boundary conditions, namely, Happel’s, Kuwabara’s, Kvashnin’s and Cunningham/Mehta-Morse’s, are considered on the outer surface of the cell. The variation of hydrodynamic permeability of biporous medium (membrane) with viscosity ratio, Brinkman constants, and solid fraction are presented and discussed graphically. Comparison of the resulting hydrodynamic permeability is undertaken. Some previous results for dimensionless hydrodynamic permeability have been verified.
Hydrodynamic permeability of membranes built up by spherical particles covered by porous shells: effect of stress jump condition
(Springer, 2010) Tiwari, Ashish
This paper concerns the flow of an incompressible, viscous fluid past a porous spherical particle enclosing a solid core, using particle-in-cell method. The Brinkman’s equation in the porous region and the Stokes equation for clear fluid are used. At the fluid–porous interface, the stress jump boundary condition for the tangential stresses along with continuity of normal stress and velocity components are employed. No-slip and impenetrability boundary conditions on the solid spherical core have been used. The hydrodynamic drag force experienced by a porous spherical particle enclosing a solid core and permeability of membrane built up by solid particles with a porous shell are evaluated. It is found that the hydrodynamic drag force and dimensionless hydrodynamic permeability depends not only on the porous shell thickness, particle volume fraction γ and viscosities of porous and fluid medium, but also on the stress jump coefficient. Four known boundary conditions on the hypothetical surface are considered and compared: Happel’s, Kuwabara’s, Kvashnin’s and Cunningham’s (Mehta–Morse’s condition). Some previous results for the hydrodynamic drag force and dimensionless hydrodynamic permeability have been verified.