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Item Electroosmotic flow in a concentrated suspension of polyelectrolyte-grafted solid cylindrical particles: a particle-in-cell approach(AIP, 2024-12) Tiwari, AshishThe 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.Item Solute dispersion in an electroosmotic flow of Carreau and Newtonian fluids through a tube: analytical study(Springer, 2025-03) Tiwari, AshishThe study presents a comprehensive theoretical analysis of solute transport under the electroosmotic flow of a two-fluid model consisting of Carreau–Newtonian fluids in a cylindrical tube, to predict more accurate dispersion dynamics. To accommodate the broader physical situation, the induced streaming potential resulting from a gradient in ion accumulation along the flow direction owing to the convective transport is considered. The analysis specifically accounts for the effect of slip and no-slip boundary conditions at the tube wall, addressing hydrophobic and hydrophilic properties of the Newtonian fluid, respectively. For the hydrophobic case, the influence of slip flow on the solid–liquid interface is considered, leading to the slip-dependent zeta potential. The closed-form solution of the velocity profile is obtained using the perturbation technique, assuming the Weissenberg number as the small perturbation parameter for both slip and no-slip formulations. The combined advection–diffusion equation for solute transport is addressed using a hybrid method incorporating Gill’s approach and the Hankel transformation to obtain the analytical expressions for the dispersion coefficient, mean concentration, and concentration distributions. The apparent slip-dependent zeta potential within the electric double layer due to the slip flow at the wall is shown to have a significant impact on the dispersion dynamics. The study examines the impact of various dynamic parameters, namely the Carreau fluid parameters (Weissenberg number and power law index), zeta potential at the wall, inverse Debye length, viscosity ratio parameter, and slip length, on the concentration distribution through convection, ultimately affecting the dispersion coefficient. The effect of wall slip condition on the solute plume distribution is more pronounced at the higher time level. It is noted that the effect of all the dynamical parameters on solute dispersion is observed to be more significant for the slip-dependent zeta potential at the wall compared to the no-slip condition at the wall. The findings of this work have broad implications in biomedical engineering, drug delivery systems, chemical mixing, and separation processes.Item Electro-diffusio-osmosis in an anisotropic channel(Elsevier, 2025-09) Tiwari, AshishSolute 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.Item Multiscale analysis of diffusioosmotic transport of micropolar fluids in microchannels(AIP, 2025-09) Tiwari, AshishThe ability of the applied chemical concentration gradients to move the fluid, i.e., diffusioosmosis, requires a more robust mathematical model to predict the interdependency of the solute dispersion and the fluid movement. The present work illustrates the influence of applied concentration gradient on the movement of micropolar fluid within the microchannel using the mathematical model of diffusioosmosis. The model consists of a rectangular channel filled with micropolar fluid in which the solute concentration gradient is imposed, having a standard Gaussian distribution. The model for combined advection-diffusion, i.e., Taylor's dispersion model, is employed to regulate the solute distribution. The diffusioosmotic pressure gradient purely drives the micropolar fluid through the diffusioosmotic slip flow at the wall. A multi-timescale approach is utilized to obtain the closed-form solution of the flow and concentration profiles. The combined approach of homogenization and the Laplace transformation is used to find the analytical expressions of the concentration profile. The pure diffusion and the solute wall interaction induce the slip flow at the wall, which further contributes to solute dispersion by advection, leading to the combined advection-diffusion process. The two different boundary constraints for microrotation at the wall, including no-spin (NS) and no-couple stress (NCS), have been thoroughly studied. The graphical illustrations of the various dynamic quantities provide a comprehensive analysis of their physical behavior under the influence of relevant flow parameters. It is noted that for stronger diffusioosmosis, all the dynamic quantities, including the velocity profile, rotational velocity, effective diffusivity, wall shear stress (WSS), and mean concentration, are sensitive to micropolar fluid parameters like micro-scale parameter and coupling number. It is observed that the velocity profile and mean concentration show less variation concerning different parameters for no-couple stress at the wall, compared to the no spin of the microparticles at the wall. Further, the outcomes from the mathematical model advance the understanding of fluid flow induced by concentration gradients, which can assist the researchers in analyzing drug delivery, the separation process, and various species transport applications in the novel framework of diffusioosmosis.Item Impact of anisotropic porosity on electroosmotic flow of micropolar fluid in wavy channel(Elsevier, 2025-09) Tiwari, AshishThe influence of weak anisotropy on electroosmotic flow of micropolar fluids in geometrically non-uniform microchannels is explored through a comprehensive theoretical framework. Using a rigorous mathematical framework, a comprehensive model is developed that couples the Poisson–Boltzmann equation governing the electric double layer dynamics and the Brinkman equation with the micro rotational term. To tackle this difficulty, the perturbation technique is employed to resolve the coupled equations with appropriate boundary conditions, where the channel’s aspect ratio () is taken as the perturbation parameter. A comprehensive analysis is conducted to examine the effects of critical parameters such as the ü parameter, anisotropic ratio, fluctuation parameter, micro-scale parameter (), and coupling parameter () on various flow characteristics. The findings indicate that a stronger micropolar effect leads to a decrease in linear velocity near the wavy wall, while a contrasting increase in linear velocity is observed at greater distances from the wall. The velocity profiles computed numerically using the finite difference method show negligible difference between solutions from linearized Poisson–Boltzmann equations (Debye–Hückel approximation) and non-linear Poisson–Boltzmann equations for weak anisotropy. These findings have significant implications for optimizing microfluidic devices in biomedical applications, chemical separation processes, and micro-scale heat exchangers where precise flow control is paramount.Item Analytical Study of the Effect of Variable Viscosity and Heat Transfer on Two-Fluid Flowing through Porous Layered Tubes(Springer, 2022-04) Tiwari, AshishThe 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.Item Solute dispersion in non-Newtonian fluids flow through small blood vessels: A varying viscosity approach(Elsevier, 2022) Tiwari, AshishPresent work concerns the combined effect of Jeffrey fluid parameter and varying nature of viscosity on the solute dispersion in non-Newtonian fluids flow through small blood vessels. The generalized dispersion model of Sankarasubramanian and Gill (1973) has been considered. The objective of the present work is to understand the solute dispersion in non-Newtonian fluids flow through microvessels with absorbing walls under varying viscosity assumption. For more realistic modeling of blood flow in microvessels, Jeffrey and Herschel–Bulkley fluids model have been considered for a comparative study due to its low shear rate flow in small blood vessels such as arterioles, venules and capillaries. The whole solute dispersion analysis has been done for two alternative non-Newtonian fluids (Herschel–Bulkley and Jeffrey fluids) owing to their physiological importance. The present model has been validated by reducing it to previously studied specific cases of Newtonian, Bingham-plastic and Power-law fluids with constant/varying viscosities. It is perceived that the mean concentration, convection and axial dispersion coefficients are significantly affected by varying viscosity and Jeffrey fluid parameters. A noteworthy observation is that an increase in ratio of relaxation to retardation times (Jeffrey fluid parameter) enhanced the values of the transport coefficients. The outcome of the present study shows the diffusion of drugs to the physiological system through small blood vessels is significantly affected by the varying nature of viscosity and Jeffrey fluid parameters.Item Creeping flow of non-Newtonian fluid through membrane of porous cylindrical particles: A particle-in-cell approach(AIP, 2023-04) Tiwari, AshishThe 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.Item Asymptotic analysis of Jeffreys–Newtonian fluids flowing through a composite vertical porous layered channel: Brinkman–Forchheimer model(AIP, 2023-12) Tiwari, AshishThis 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.Item Asymptotic analysis of electrohydrodynamic flow through a swarm of porous cylindrical particles(AIP, 2024-04) Tiwari, AshishThe 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.