Diffusive Flux Model Research Articles

Computational analysis of magnetized Casson liquid stretching flow adjacent to a porous medium with Joule heating, stratification, multiple slip and chemical reaction aspects

This article aims to investigate the characteristics of thermo-solutal magnetohydrodynamic (MHD) non-Newtonian smart coating boundary layer flow of a stretching substrate adjacent to a porous medium, considering the influence of chemical reactions and thermal radiation subject to a transverse static magnetic field. A non-Darcy drag force model is deployed to capture both Darcy bulk drag and inertial Forchheimer (quadratic) drag effects. A diffusion flux model is deployed for radiative heat transfer. The Casson viscoplastic model has been utilized to simulate rheological characteristics. Due to polymeric slip effects, three slip phenomena are included at the wall (hydrodynamic, thermal and concentration) in the formulation. Furthermore, viscous dissipation and Ohmic heating (Joule dissipation) are also included. Robust scaling similarity variables are deployed to transform the governing partial differential equations into ordinary differential equations. Subsequently, the emerging dimensionless coupled nonlinear boundary value problem is solved utilizing the Bvp4c method in MATLAB version 2022. This numerical approach allows for a logical parametric examination of all key control parameters on the transport phenomena, enabling a comprehensive understanding of the system behavior. Validation with previous studies is included. Detailed graphical and tabular computations are included for velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number, for the influence of Darcian parameter, Forchheimer inertial parameter, mixed convection, velocity (momentum) slip, magnetic number, Casson parameter, nonlinear thermal convection parameter, nonlinear concentration convection parameter, radiation parameter, thermal stratification parameter, Prandtl number, heat source/sink parameter, Eckert number, thermal slip parameter, Schmidt number, chemical reaction, solutal stratification parameter and solutal slip parameter. Detailed interpretation of the physics associated with these multiple effects is included. The simulations provide further insight into the transport characteristics of electromagnetic viscoplastic coating material manufacturing.

A homogenized two-phase computational framework for meso- and macroscale blood flow simulations

Background and ObjectiveOwing to the complexity of physics linked with blood flow and its associated phenomena, appropriate modeling of the multi-constituent rheology of blood is of primary importance. To this effect, various kinds of computational fluid dynamic models have been developed, each with merits and limitations. However, when additional physics like thrombosis and embolization is included within the framework of these models, computationally efficient scalable translation becomes very difficult. Therefore, this paper presents a homogenized two-phase blood flow framework with similar characteristics to a single fluid model but retains the flow resolution of a classical two-fluid model. The presented framework is validated against four different sets of experiments. MethodsThe two-phase model of blood presented here is based on the classical diffusion-flux framework. Diffusion flux models are known to be less computationally expensive than two-fluid multiphase models since the numerical implementation resembles single-phase flow models. Diffusion flux models typically use empirical slip velocity correlations to resolve the motion between phases. However, such correlations do not exist for blood. Therefore, a modified slip velocity equation is proposed, derived rigorously from the two-fluid governing equations. An additional drag law for red blood cells (RBCs) as a function of volume fraction is evaluated using a previously published cell-resolved solver. A new hematocrit-dependent expression for lift force on RBCs is proposed. The final governing equations are discretized and solved using the open-source software OpenFOAM. ResultsThe framework is validated against four sets of experiments: (i) flow through a rectangular microchannel to validate RBC velocity profiles against experimental measurements and compare computed hematocrit distributions against previously reported simulation results (ii) flow through a sudden expansion microchannel for comparing experimentally obtained contours of hematocrit distributions and normalized cell-free region length obtained at different flowrates and inlet hematocrits, (iii) flow through two hyperbolic channels to evaluate model predictions of cell-free layer thickness, and (iv) flow through a microchannel that mimics crevices of a left ventricular assist device to predict hematocrit distributions observed experimentally. The simulation results exhibit good agreement with the results of all four experiments. ConclusionThe computational framework presented in this paper has the advantage of resolving the multiscale physics of blood flow while still leveraging numerical techniques used for solving single-phase flows. Therefore, it becomes an excellent candidate for addressing more complicated problems related to blood flow, such as modeling mechanical entrapment of RBCs within blood clots, predicting thrombus composition, and visualizing clot embolization.

Computation of stagnation coating flow of electro-conductive ternary Williamson hybrid mathrm{GO}-mathrm{AU}-{mathrm{Co}}_{3}{mathrm{O}}_{4}/mathrm{EO} nanofluid with a Cattaneo–Christov heat flux model and magnetic induction

Modern smart coating systems are increasingly exploiting functional materials which combine multiple features including rheology, electromagnetic properties and nanotechnological capabilities and provide a range of advantages in diverse operations including medical, energy and transport designs (aerospace, marine, automotive). The simulation of the industrial synthesis of these multi-faceted coatings (including stagnation flow deposition processes) requires advanced mathematical models which can address multiple effects simultaneously. Inspired by these requests, this study investigates the interconnected magnetohydrodynamic non-Newtonian movement and thermal transfer in the Hiemenz plane's stagnation flow. Additionally, it explores the application of a transverse static magnetic field to a ternary hybrid nanofluid coating through theoretical and numerical analysis. The base fluid (polymeric) considered is engine-oil (EO) doped with graphene left(GOright), gold left(Auright) and Cobalt oxide left(C{o}_{3}{O}_{4}right) nanoparticles. The model includes the integration of non-linear radiation, heat source, convective wall heating, and magnetic induction effects. For non-Newtonian characteristics, the Williamson model is utilized, while the Rosseland diffusion flux model is used for radiative transfer. Additionally, a non-Fourier Cattaneo–Christov heat flux model is utilized to include thermal relaxation effects. The governing partial differential conservation equations for mass, momentum, energy and magnetic induction are rendered into a system of coupled self-similar and non-linear ordinary differential equations (ODEs) with boundary restrictions using appropriate scaling transformations. The dimensionless boundary value problem that arises is solved using the bvp4c built-in function in MATLAB software, which employs the fourth-order Runge–Kutta (RK-4) method. An extensive examination is conducted to evaluate the impact of essential control parameters on the velocity f{^{prime}}left(zeta right), induced magnetic field stream function gradient g{^{prime}}left(zeta right) and temperature theta left(zeta right) is conducted. The relative performance of ternary, hybrid binary and unitary nanofluids for all transport characteristics is evaluated. The inclusion of verification of the MATLAB solutions with prior studies is incorporated. Fluid velocity is observed to be minimized for the ternary mathrm{GO}–mathrm{Au}–{mathrm{Co}}_{3}{mathrm{O}}_{4} nanofluid whereas the velocity is maximized for the unitary cobalt oxide left({mathrm{Co}}_{3}{mathrm{O}}_{4}right) nanofluid with increasing magnetic parameter (beta ). Temperatures are elevated with increment in thermal radiation parameter (Rd). Streamlines are strongly modified in local regions with greater viscoelasticity i.e. higher Weissenberg number (We). Dimensionless skin friction is significantly greater for the ternary hybrid GO–Au–C{o}_{3}{O}_{4}/EO nanofluid compared with binary hybrid or unitary nanofluid cases.

Accurate modeling of blood flow in a micro-channel as a non-homogeneous mixture using continuum approach-based diffusive flux model

This paper presents a continuum approach for the blood flow simulation, inside the micro-channel of the few micrometers characteristics dimension, within the context of the finite volume method on unstructured grids. The velocity and pressure fields, for the blood flow, are obtained here by solving the Navier–Stokes equations. A particle transport equation, based on the diffusive flux model, provides the hematocrit distribution (i.e., the red blood cells volume-fraction). The momentum conservation equation for a non-Newtonian fluid model is coupled with the particle transport equation through the constitutive blood viscosity model, and this blood viscosity is dependent on hematocrit and shear rate. The continuum approach for blood flow inside the micro-channel of the length scale of a few micrometers to a few hundred micrometers is expected to break down. Interestingly, the present approach provides meaningful insights into biophysics with less computational cost and shows a good match with the experiments and mesoscale simulation with a maximum average deviation of 11% even at the characteristic dimensions of 10–300 μm. A correlation is proposed for additional-local shear rate in terms of the hematocrit and the ratio of red blood cells diameter to the channel diameter, which helps us to demonstrate an increase in the accuracy and also eliminates the issues of unphysical hematocrit reported in the earlier studies available in the literature. The study is extended to provide new results inside a square and rectangular cross section micro-channels, under a range of inlet parameters.

Assessing Thermal Response of Redox Conduction for Anti-Arrhenius Kinetics in a Microbial Cytochrome Nanowire.

A micrometers-long helical homopolymer of the outer-membrane cytochrome type S (OmcS) from Geobacter sulfurreducens is proposed to transport electrons to extracellular acceptors in an ancient respiratory strategy of biogeochemical and technological significance. OmcS surprisingly exhibits higher conductivity upon cooling (anti-Arrhenius kinetics), an effect previously attributed to H-bond restructuring and heme redox potential shifts. Herein, the temperature sensitivity of redox conductivity is more thoroughly examined with conventional and constant-redox and -pH molecular dynamics and quantum mechanics/molecular mechanics. A 30 K drop in temperature constituted a weak perturbation to electron transfer energetics, changing electronic couplings (⟨Hmn⟩), reaction free energies (ΔGmn), reorganization energies (λmn), and activation energies (Ea) by at most |0.002|, |0.050|, |0.120|, and |0.045| eV, respectively. Changes in ΔGmn reflected -0.07 ± 0.03 V shifts in redox potentials that were caused in roughly equal measure by altered electrostatic interactions with the solvent and protein. Changes in intraprotein H-bonding reproduced the earlier observations. Single-particle diffusion and multiparticle steady-state flux models, parametrized with Marcus theory rates, showed that biologically relevant incoherent hopping cannot qualitatively or quantitatively describe electrical conductivity measured by atomic force microscopy in filamentous OmcS. The discrepancy is attributed to differences between solution-phase simulations and solid-state measurements and the need to model intra- and intermolecular vibrations explicitly.

Effects of coupling of mass transport and blood viscosity models for microchannel flows

In this study, various aspects of a continuum transport model for blood, which is treated as a suspension of red blood cells, are thoroughly investigated. Earlier, treating blood as a suspension of rigid spherical particles in plasma was reasonably successful in mimicking flow dynamics in microchannels of size 40 μ m , comparable to 4 μ m , the dimension of a red blood cell (RBC). However, it is still not entirely clear whether such success owes to the coupling of mass and momentum transport, or to a sophisticated viscosity model for blood. To understand this in detail, we obtain semi-analytical solutions to the continuum model, in the presence and absence of the coupling of mass transport of RBCs, that connects the hematocrit concentration to the local viscosity, for fully developed blood flow in circular and rectangular microchannels. In this study, the transport of RBCs in flowing fluid is modeled by the diffusive flux model (DFM). Thus, overall, we have a hierarchy of continuum models using various viscosity models for blood, with progressive inclusion of physical complexities. Our results clearly highlight the importance of such a coupled approach, without which the results are quantitatively, and sometimes even qualitatively, different. In addition, our study serves as a thorough comparison of different viscosity models for blood, especially the steady state and transient models, recently proposed by Apostolidis and Beris (2014) and Apostolidis et al. (2015), respectively. We observe that, though the transient model reduces exactly to the description by the steady model over a range of low to moderate shear rates, the transient model shows some differences, especially for the RBC concentration in the low shear rate region. In the semi-analytical framework, the Darcy friction factor and cell free layer thickness have also been computed for circular cross-sections and a range of aspect ratios of a rectangular microchannel. Our results also indicate that the cell free layer attains a constant thickness when the aspect ratio of a rectangular microchannel reaches a critical maximum value for a specified average hematocrit. • Rectangular microchannel flow is investigated by coupling with the transport of RBC. • Even a finely tuned viscosity model without RBC transport is shown to be inadequate. • Frictional characteristics are derived in the form of a semi-analytical solution. • The model is found to predict the cell free layer thickness quite well. • The steady viscosity model overpredicts WSS when compared to the transient model.

Thermo‐electrokinetic rotating non‐Newtonian hybrid nanofluid flow from an accelerating vertical surface

AbstractThis paper explores the combined effects of Coriolis force and electric force on the rotating boundary layer flow and heat transfer in a viscoplastic hybrid nanofluid from a vertical exponentially accelerated plate. The hybrid nanofluid comprises two different types of metallic nanoparticles, namely silver (Ag) and magnesium oxide (MgO) suspended in an aqueous base fluid. The Casson model is deployed for non‐Newtonian effects. An empirical model is implemented to determine the thermal conductivity of the hybrid nanofluid. Rosseland's radiative diffusion flux model is also utilized. An axial electrical field is considered and the Poisson–Boltzmann equation is linearized via the Debye–Hückel approach. The resulting coupled differential equations subject to prescribed boundary conditions are solved with Laplace transforms. Numerical evaluation of solutions is achieved via MATLAB symbolic software. A parametric study of the impact of key parameters on axial velocity, transverse velocity, nanoparticle temperature and Nusselt number is conducted for both the hybrid (Ag–MgO)–water nanofluid and also unitary (Ag)–water nanofluid. With increasing volume fraction of silver nanoparticles, there is a reduction in both axial velocity and temperatures, whereas there is a distinct elevation in transverse velocity for both unitary and hybrid nanofluids. Elevation in the heat absorption parameter strongly decreases axial velocity, whereas it enhances transverse velocity. Increasing the radiation parameter strongly boosts temperatures. Increasing the heat absorption parameter significantly accelerates the transverse flow. Negative values of Helmholtz–Smoluchowski velocity decelerate the axial flow whereas positive values accelerate it; the opposite behavior is observed for transverse velocity. Increasing Taylor number significantly damps both the axial (primary) and transversal (secondary) flow. Increasing thermal Grashof number strongly enhances the axial flow but damps the transverse flow. The unitary nanofluid achieves higher Nusselt numbers than the hybrid nanofluid but these are decreased with greater radiative effect (due to greater heat transport away from the plate surface), Prandtl number and heat absorption. Nusselt number is significantly reduced with greater time progression and values are consistently higher for the unitary nanofluid compared with hybrid nanofluid. The computations provide insight into more complex electrokinetic rheological nanoscale flows of relevance to biomedical rotary electro‐osmotic separation devices.

Numerical simulation of blood flow modeled as a fluid- particulate mixture

ABSTRACT A continuum model for the transport of red blood cells (RBC) inside arteries and capillaries of small diameters is proposed. The pressure and velocity fields are solved using the Navier-Stokes equations while the distribution of the RBC volume fraction, namely, hematocrit is obtained by solving the particle transport equation arising from the diffusive flux model. The momentum and hematocrit transport equations are coupled through a hematocrit-dependent blood viscosity model. The coupled equations are numerically solved using a 3D unstructured finite volume method. The proposed model predicts the shear induced diffusion of RBCs where RBCs migrate from the wall to the center of the blood vessel leading to a cell free layer (CFL) near the wall. Three geometries with sizes of the order of 40 µm have been considered for the present work. For flow inside a tube, results in terms of the concentration distribution and cell-free layer from the present continuum model show a good match with experiments and DPD simulations. For flow inside a tube with a constriction it is found that hematocrit depletion is greater downstream of the neck of the constriction. In addition, the effect of hematocrit loading on its distribution is correctly predicted. Finally, for a flow inside a tube with a bifurcation the average hematocrit concentration is found to be higher for the branch with the higher flow rate, thereby complying with the well-known bifurcation law.

Effect of catalyst shape and multicomponent diffusion flux models on intraparticle transport-kinetic interactions in the gas-phase Fischer-Tropsch synthesis

Intraparticle Fischer-Tropsch (FT) transport-kinetics interactions for various Fe-based catalyst particle shapes (sphere, solid cylinder, hollow cylinder, 4-hole cylinder, modified 4-hole cylinder, and 7-hole cylinder) under typical gas-phase FT process conditions (T = 493–533 K, P = 25–30 bar, and H2/CO = 2) are investigated using different multicomponent diffusion flux models. A Fe-based microkinetic gas-phase FT model is used to describe the intrinsic reaction rates for all reactants and products. The Soave-Redlich-Kwong (SRK) EOS is used to describe the vapor-liquid equilibrium associated with the FT product distribution. The effect of process conditions and catalyst shape on the effectiveness factor, particle volume-averaged key component concentrations, liquid-to-vapor (L/V) ratios and diesel range concentration profiles, along with methane-based diesel selectivities, are presented. It is found that the solid cylinder has the highest volume-average diesel concentration (ca. 4.4 mol/m3 at T = 493 K and P = 25 bar) when compared to the other shapes. The hollow cylinder and 7-hole cylinder shapes have the lowest intraparticle liquid-to-vapor (L/V) ratio (ca. 0.004 at T = 493 K and P = 25 bar) and the highest effectiveness factor (η) of 0.35. Temperature-based diffusivity correlations do not consider the change in effective diffusivities of the species in the FT reaction network. The simulations show that the inclusion of Knudsen diffusion through the Wilke-Bosanquet and Dusty-Gas Models resulted in an intraparticle FT product distribution that closely approximate literature results.

Proppant Transport in a Newtonian Fluid Under Laminar Flow

Summary Model proppant transport experiments are conducted at the laboratory scale using a Newtonian carrier fluid in a long tube of rectangular cross section. Under the particular flow conditions studied, we observe the buildup of a dense but flowing sediment, which rapidly reaches a steady-state height. The existence of this steady-state flowing sediment implies that the proppant flux leaving the channel equals that entering the channel; that is, “efficient” proppant transport occurs. As soon as the suspension flow is stopped, the fluidized sediment ceases flowing and quickly becomes more compact. This collapse implies that the particle sediment is maintained in an expanded state while under flow, with an average volume fraction considerably lower than that under static conditions. The relevant mechanism of sediment transport is identified as viscous resuspension because the flow is at a low Reynolds number (Re at approximately 0.1). We estimate the average volume fraction of the resuspended sediment from experimental measurements of the “expanded” flowing sediment height, with the assumption that the corresponding compact sediment volume fraction is ϕ0=0.61, the volume fraction at which the suspension viscosity diverges. Predictions of the resuspended sediment heights are made with a simple approach based on the diffusive flux model by Leighton and Acrivos (1986) using the average shear stress across the channel width. A good agreement is found between the predicted and experimental values, indicating that 2D effects remain weak. Microscopic observations show that the sediment is fully fluidized while under flow for all the flow rates studied in our channel, and one does not observe the buildup of static sediment banks that are observed in larger-scale tests during the suspension flow (Kern et al. 1959; Babcock et al. 1967; Schols and Visser 1974; Sievert et al. 1981). This apparent difference is explained in the context of the viscous resuspension model.

Numerical study of slip and radiative effects on magnetic Fe3O4-water-based nanofluid flow from a nonlinear stretching sheet in porous media with Soret and Dufour diffusion

Increasingly sophisticated techniques are being developed for the manufacture of functional nanomaterials. A growing interest is also developing in magnetic nanofluid coatings which contain magnetite nanoparticles suspended in a base fluid and are responsive to external magnetic fields. These nanomaterials are “smart” and their synthesis features high-temperature environments in which radiative heat transfer is present. Diffusion processes in the extruded nanomaterial sheet also feature Soret and Dufour (cross) diffusion effects. Filtration media are also utilized to control the heat, mass and momentum characteristics of extruded nanomaterials and porous media impedance effects arise. Magnetite nanofluids have also been shown to exhibit hydrodynamic wall slip which can arise due to non-adherence of the nanofluid to the boundary. Motivated by the multi-physical nature of magnetic nanomaterial manufacturing transport phenomena, in this paper, we develop a mathematical model to analyze the collective influence of hydrodynamic slip, radiative heat flux and cross-diffusion effects on transport phenomena in ferric oxide ([Formula: see text]-water) magnetic nanofluid flow from a nonlinear stretching porous sheet in porous media. Hydrodynamic slip is included. Porous media drag is simulated with the Darcy model. Viscous magnetohydrodynamic theory is used to simulate Lorentzian magnetic drag effects. The Rosseland diffusion flux model is employed for thermal radiative effects. A set of appropriate similarity transformation variables are deployed to convert the original partial differential boundary value problem into an ordinary differential boundary value problem. The numerical solution of the coupled, multi-degree, nonlinear problem is achieved with an efficient shooting technique in MATLAB symbolic software. The physical influences of Hartmann (magnetic) number, Prandtl number, Richardson number, Soret (thermo-diffusive) number, permeability parameter, concentration buoyancy ratio, radiation parameter, Dufour (diffuso-thermal) parameter, momentum slip parameter and Schmidt number on transport characteristics (e.g. velocity, nanoparticle concentration and temperature profiles) are investigated, visualized and presented graphically. Flow deceleration is induced with increasing Hartmann number and wall slip, whereas flow acceleration is generated with greater Richardson number and buoyancy ratio parameter. Temperatures are elevated with increasing Dufour number and radiative parameter. Concentration magnitudes are enhanced with Soret number, whereas they are depleted with greater Schmidt number. Validation of the MATLAB computations with special cases of the general model is included. Further validation with generalized differential quadrature (GDQ) is also included.

EFFECT OF STENOSIS SEVERITY ON SHEAR-INDUCED DIFFUSION OF RED BLOOD CELLS IN CORONARY ARTERIES

In large blood vessels, migration of red blood cells (RBCs) affects the concentration of platelets and the transport of oxygen to the arterial endothelial cells. In this work, we investigate the locations where hydrodynamic diffusion of RBCs occurs and the effects of stenosis severity on shear-induced diffusion (SID) of RBCs, concentration distribution and wall shear stress (WSS). For the first time, multiphase mixture theory approach with Phillips shear-induced diffusive flux model coupled with Quemada non-Newtonian viscosity model has been applied to numerically simulate the RBCs macroscopic behavior in four different degrees of stenosis (DOS) geometries, viz., 30%, 50%, 70% and 85%. Considering SID of RBCs, the calculated average WSS increased by 77.70% which emphasises the importance of SID in predicting hemodynamic parameters. At the stenosis throat, it was observed that 85% DOS model had the lowest concentration of RBCs near the wall and highest concentration at the center. For the stenosis models with 70% and 85% DOS, the RBC lumen wall concentration at the distal section of stenosis becomes inhomogeneous with the maximum fluctuation of 1.568%. Finally, the wall regions with low WSS and low RBC concentrations correlate well with the atherosclerosis sites observed clinically.

A two-fluid model for numerical simulation of shear-dominated suspension flows

Suspension flows are ubiquitous in nature (hemodynamics, subsurface fluid mechanics, etc.) and industrial applications (hydraulic fracturing, CO2 storage, etc.). However, such flows are notoriously difficult to model due to the variety of fluid-particle and particle-particle interactions that can occur. In this work, we focus on non-Brownian shear-dominated suspensions, where kinetic collisions are negligible and frictional effects play a dominant role. Under these circumstances, irreversible phenomena such as particle diffusion and migration arise, requiring anisotropic stress models to describe the suspension rheology. On a continuum level, reduced-order models such as the suspension balance model (SBM) or the diffusive flux model are commonly used to predict particle migration phenomena. We propose a new method based on a two-fluid model (TFM), where both the phases are considered as interpenetrating continua with their own conservation of mass and momentum equations. Without employing the nowadays customary simplifications in applying the SBM, we close the “full” TFM instead. Specifically, we show that when an anisotropic stress analogous to that used in the SBM is added to the equilibrium equations for the particle phase, the TFM is able to accurately predict particle migration. Thus, the TFM does not require the assumptions of a steady suspension velocity and a Stokesian (inertialess) fluid, and the TFM can be easily extended to include buoyancy and even kinetic collisional models. We present several benchmark simulations of our TFM implementation in OpenFOAM®, including in curvilinear coordinates and three-dimensional flow. Good agreement between the TFM solutions and previous experimental and numerical results is found.

Particle migration of concentrated suspension flow in bifurcating channels

Flow of suspension in bifurcating channels has extensive applications in industrial and natural settings. A phenomenon of particular interest during the flow of concentrated suspension is shear-induced particle migration. Previous works on suspension transport in branched channels have been limited to dilute flow conditions. We have carried out experiments using the Particle Image Velocimetry (PIV) technique to study concentrated suspension transport in asymmetric T- and symmetric Y-shape channels. Numerical simulations of fluid flow and particle transport equations were also carried out for the same geometry which was used in the experiments. The migration and transport of particles in the simulations were studied using the Diffusive Flux Model. We have observed in both experiments and numerical simulations that due to the shear-induced migration phenomena the particles move towards the center of the channel, and this gives rise to the blunting of velocity profile before the junction. After the bifurcation, the peak of velocity profile moves in the direction of the outer wall, whereas, the maxima in particle concentration was observed near the inner walls. This causes asymmetry in the velocity and concentration profiles in the daughter branches. As we move towards the downstream positions the maxima in velocity and concentration profiles again shifts toward the center of the channel. The results from the experiments and simulations are observed to be in good agreement.

Shear-induced particle migration and segregation in non-Brownian bidisperse suspensions under planar Poiseuille flow

In our previous work [Chun et al., Phys. Fluids 29, 121605 (2017)], we studied the migration behavior of concentrated monodisperse particles in Couette–Poiseuille flows. Here, we extend this study into an investigation of concentrated ( ϕ0=0.3) bidisperse suspensions undergoing pressure-driven flows at various combinations of volume fraction ratio ( ϕS0/ϕ0=0.13−0.67) and size ratio ( aL/aS=1.4−2.4) between small ( 2aS/H=0.022) and large ( 2aL/H=0.031−0.052) particles in a planar channel of height H. The flow behavior of neutrally buoyant hard spheres suspended in a Newtonian fluid was numerically simulated using the lattice Boltzmann method. The time evolution of the distributions of small and large particles showed segregation under inhomogeneous shear flow, resulting in enrichment of large particles and depletion of small particles near the midplane. Size-dependent particle segregation was more pronounced in these simulations than what was previously observed in the experiment. In bidisperse suspensions, the concentration evolution was markedly slower than in monodisperse situations; the characteristic time to reach a steady state was 5–8 times longer in bidisperse systems. The results of lattice Boltzmann simulation were further analyzed within the framework of a reformulated polydisperse diffusive flux model [Shauly et al., J. Rheol. 42, 1329 (1998)]; four coefficients of the diffusive flux model were adjusted to match steady-state ( KL, KS) and transient ( RL, RS) predictions. The model coefficients showed strong dependence on the particle number density ratio (ϕS0/ϕL0)(aL/aS)3; both KL and RL increased almost linearly with this ratio, whereas KS decreased and RS increased with this ratio.In our previous work [Chun et al., Phys. Fluids 29, 121605 (2017)], we studied the migration behavior of concentrated monodisperse particles in Couette–Poiseuille flows. Here, we extend this study into an investigation of concentrated ( ϕ0=0.3) bidisperse suspensions undergoing pressure-driven flows at various combinations of volume fraction ratio ( ϕS0/ϕ0=0.13−0.67) and size ratio ( aL/aS=1.4−2.4) between small ( 2aS/H=0.022) and large ( 2aL/H=0.031−0.052) particles in a planar channel of height H. The flow behavior of neutrally buoyant hard spheres suspended in a Newtonian fluid was numerically simulated using the lattice Boltzmann method. The time evolution of the distributions of small and large particles showed segregation under inhomogeneous shear flow, resulting in enrichment of large particles and depletion of small particles near the midplane. Size-dependent particle segregation was more pronounced in these simulations than what was previously observed in the experiment. In bidisperse suspension...

Experimental and computational study on flow over stepped spillway

The flow over a stepped spillway has complex nature, and its characteristics are remarkably different from other kinds of spillways. This study conducts experimental investigations and numerical simulations on the flow behavior (velocity, concentration profile) and macroscopic features (interface position and self-aeration) of water and neutrally buoyant suspension of non-colloidal particles in a stepped spillway with uniform steps. The development of nappe, transition, and skimming flow regimes is experimentally investigated by using a flow visualization technique. The inception point related to air entrainments is identified in the experimental study. The inception point usually moves downstream and increases the length of the non-aerated region with the increase of flow rate. Results of numerical and experimental studies indicate that a vortex is formed in the triangular cavity below the pseudo-bottom line (imaginary line joining two adjacent step edges) in the stepped channel. This vortex rotates in a clockwise direction for a short time period and returns to the main flow to move downward in the channel. The velocity vector map from numerical simulation predicts the maximum velocity in the middle portion of the spillway, that is, near the pseudo-bottom line. A volume of fluid model coupled with a standard k-e turbulence model is used in the CFD simulations to predict the location of the air-water air-suspension interface. The results are compared with experimental measurements. The calculated interface position agrees well with the experimental measurements. The migration and transport of particles are evaluated based on a diffusive flux model of shear induced particle migration. The contour map for velocity and particle concentration shows a remarkable increase in particle concentration near the air-suspension interface.

A multimodular pseudoheterogeneous model framework for optimal design of catalytic reactors exemplified by methanol synthesis

Model-based design of chemical reactors via dynamic optimization can be performed using a recently developed approach called Multi-Level Reactor Design (MLRD). As a start, the MLRD method, its extensions and applications over the last ten years are reviewed compactly. In the main part of this contribution, a further extension to the model framework applied within this method allowing for the rigorous consideration of intrapellet transport processes in heterogeneously catalyzed systems is introduced. Accordingly, a system of coupled differential equations describing the mass and energy balance of both, reactor and catalyst pellet is set up. Balance equations are kept strictly distinguished from kinetic approaches, leaving the latter to be easily exchangeable. This leads to a multimodular model structure used to incorporate different models for diffusion flux, heat transport and pressure drop. The type of the extended model structure is “pseudoheterogeneous”, i.e., the domain in which chemical reactions take place is shifted from a commonly applied pseudohomogeneous mixed phase to the catalyst interior while a solid phase on reactor scale is not modelled. Applying the extended and modularized method to methanol synthesis as a case study reveals considerable concentration and temperature gradients inside the catalyst. These are neglected implicitly in pseudohomogeneous approaches which can lead to a violation of the allowed range of operating conditions for a given catalyst. The extended MLRD model framework using a pseudoheterogeneous model overcomes this drawback and allows for apparatus independent reactor design while meeting process specific constraints in both the bulk gas and the catalyst phase. Further, a systematic investigation applying 27 combinations of diffusion flux, heat transport and pressure drop models reveals that a certain performance can be reached with any combination, while the deduced reactor design differs significantly.

A computational study of the effect of particle migration on the low-flow limit in slot coating of particle suspensions

Slot coating of particle suspensions is commonly used in the manufacturing of a wide variety of products. An important limit in this process is known as low-flow limit, which refers to the minimum wet film thickness that can be coated at a given substrate velocity. Recent studies have shown that shear-induced particle migration leads to a highly non-uniform particle distribution in the coating bead, playing an important role in the flow dynamics in slot coating of particulate systems. In this work, we extend the previous analyses to investigate the effects of particle migration on the low-flow limit in slot coating of particle suspensions at both dilute and concentrated conditions. As a first approximation, the suspension is modeled as a Newtonian liquid with a concentration-dependent viscosity, and shear-induced particle migration is described according to the diffusive flux model. The resulting set of governing equations is solved with a stabilized finite element method coupled with the elliptic mesh generation method for the free-boundary problem. The results show that particle migration changes the liquid viscosity near the downstream meniscus and strongly affects the force balance that sets the critical operating conditions at the low-flow limit. Remarkably, it was found that particle migration enlarges the operating window of the process when the suspensions are compared to a Newtonian liquid with the same bulk properties, especially at high concentrations.

On the pressure-driven flow of suspensions: Particle migration in apparent yield-stress fluids

Suspensions of particles with viscoplastic characteristics are often found both in nature and industrial applications. However, in contrast with the case of suspensions in Newtonian fluids, the dynamics of shear-induced particle migration in yield-stress suspending materials is not yet fully understood. In this work, we present a numerical study of particle migration in pressure-driven, tube flows of suspensions of non-colloidal, spherical particles dispersed in apparent yield-stress fluids. The suspension viscosity is modeled using the classical Krieger–Dougherty equation with a novel regularized viscosity function for viscoplastic materials as the suspending medium viscosity, and the dynamics of shear-induced particle migration is described with the Diffusive Flux Model. The resulting fully coupled, non-linear, one-dimensional model is solved with a second-order finite difference scheme coupled with Newton’s method. We present a parametric study that elucidates the role played by the suspension bulk concentration, Plastic number, and power-law index on the velocity profile and particle concentration distribution in the flow. Remarkably, the results show that particle migration in apparent yield-stress fluids leads to a strikingly different pattern of velocity and particle distribution profiles relative to the case of suspensions in Newtonian liquids and true yield-stress materials.

Alterations in peristaltic pumping of Jeffery nanoliquids with electric and magnetic fields

The combined effects of electric and magnetic fields on peristaltic flow of Jeffery nanoliquids are analytically investigated. Double-diffusive convection in the asymmetric microchannel is also carried out. The walls of the microchannel are propagating with a finite phase difference in a sinusoidal manner. Rosseland diffusion flux model is employed to examine the thermal radiation effect. The zeta potential on the walls is considered very low to apply Huckel–Debye approximations. The coupled non-linear governing equations are simplified by using dimensional analysis and lubrication theory. The closed form solutions for potential function, nanoparticle fraction field, solute concentration field, temperature field, stream function, and axial velocity are derived under the appropriate boundary conditions. It is noteworthy that the pumping characteristics strongly depend on the magnetic fields, electric fields, electric double layer thickness, Jeffery parameter, thermal radiation and Grashof number. Furthermore, trapping phenomenon is analyzed under the effects of Hartmann number, Jeffrey parameter, Grashof number and Helmholtz–Smoluchowski velocity. The novelty of the present work is the amalgamation of biomimetics (peristaltic propulsion), electro-magneto-hydrodynamics and nanofluid dynamics to produce a smart pump system model for smart drug delivery systems.