Effect Of Axial Diffusion Research Articles

Solute dispersion of Hershel-Bulkley fluid through an inclined artery

Different types of arteries in the human body possess inclinations that impact blood flow behavior and affect the effectiveness of medical treatments, such as intra-arterial injections that rely on accessing the bloodstream through these arteries. Hence, this present study analyses the behavior of blood flow and solute dispersion in an inclined artery while considering the Herschel-Bulkley model representing the blood rheology to investigate the influence of arterial inclination. The solutions for flow velocity and solute concentration are solved using the integration method. The Taylor-Aris method has been implemented to obtain effective axial and relative axial diffusion. This research investigates the impact of artery inclination on blood flow, solute dispersion characteristics (flow velocity, solute concentration, and axial diffusions), as well as explores the influence of gravitational acceleration on blood flow and solute dispersion behaviors. Results show that the angle of artery inclination directly influences the gravitational acceleration effect which correlates to the resulting flow velocity and solute dispersion. 90o and 270o inclination angle has the highest effect in increasing and decreasing the flow velocity, solute concentration and diffusions respectively. Meanwhile, 0o, 180o and 360o eliminate the gravitational acceleration effect on the flow behavior and dispersion process.

A study on the multi-objective optimization method and characteristic analysis of installation locations of submersible mixer for sewage

In this study, the performance of submersible mixers in sewage treatment was improved by optimizing the installation position parameters of the mixer. The aim was to enhance the average flow velocity and mixing efficiency in the pool. The study employed ISIGHT software, integrated with Creo Parametric 6.0 software and ANSYS Workbench 2020 software, to analyze the factors affecting mean flow velocity and completed a multi-objective optimized design using Non-dominated Sorting Genetic Algorithm (NSGA-II). The study used the ISIGHT software to analyze the factors affecting mean flow velocity in the pool. The installation position parameters of the submersible mixer were selected as design variables. The study employed Creo Parametric 6.0 software to create a three-dimensional model of the pool and the submersible mixer. ANSYS Workbench 2020 software was used to simulate fluid flow in the pool. The Non-dominated Sorting Genetic Algorithm (NSGA-II) was used for multi-objective optimization. The results of the study indicated an increase of approximately 0.021 m/s in average flow velocity and an improvement of approximately 0.47% in mixing efficiency compared to pre-optimization values. The effective axial propulsion distance and effective radial diffusion radius were significantly increased by 6.71% and 8.33%, respectively, after optimization. The fluid distribution in the pool became more uniform, and the low-speed zone was greatly reduced, resulting in an enhanced flow state of the fluid in the pool and a strengthened mixing effect. The study provides insights into the control of the submersible mixer’s installation position to improve the average flow velocity inside the pool. Automatic optimization of submersible mixer installation locations using the ISIGHT software can effectively improve mixing efficiency, overall plant operating efficiency, and economic benefits in sewage treatment plants. The multi-objective optimization platform based on the ISIGHT platform for wastewater treatment mixer installation location can be successfully applied in engineering practice.

Multiparametric Quantitative MRI of Peripheral Nerves to Differentiate Axonal from Demyelinating Neuropathies (P11-8.002)

<h3>Objective:</h3> To develop a multiparametric quantitative MRI (qMRI) method to track pathological changes of peripheral nerves in patients with peripheral neuropathies. <h3>Background:</h3> Irrespective of the causes or types of polyneuropathies, peripheral nerves are mainly afflicted by two kinds of pathologies – axonal loss and demyelination. It is critical to differentiate the two as treatments are different for the two conditions. While nerve conduction studies (NCS) have been used to differentiate the two pathologies in the distal nerves, there are no tools to probe the pathologies in the proximal peripheral nerves. This is particularly needed when distal nerves become non-responsive in NCS. <h3>Design/Methods:</h3> We have developed a multiparametric qMRI method that quantifies the sciatic and tibial nerves with 10 parameters that are sensitive to different aspects of myelin and axonal pathologies: magnetization transfer ratio (MTR), magnetization transfer saturation index (MTsat), longitudinal relaxation time (T1), proton density (PD), effective transverse relaxation time (T2*), fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD), radial diffusivity (RD), and nerve fascicular volume (fVol). In this pilot study, we studied 4 patients with Charcot-Marie-Tooth type-1A (CMT1A), 2 patients with CMT type-2S (CMT2S), and 17 healthy controls. <h3>Results:</h3> Compared with healthy controls, patients with CMT2S (reportedly as axonal type) had comparable MTR, MTsat, T1, PD and fVol, but reduced T2*. While patients with CMT1A (dysmyelinating type) had reduced MTR and MTsat, increased fVol, T1 and PD, and comparable T2*. All the 6 patients shared changes of reduced FA which was driven by a reduced AD and an increased RD. <h3>Conclusions:</h3> The data show different qMRI patterns between axonal and demyelinating neuropathies. The differential changes will be further verified in a larger cohort of patients with peripheral neuropathies. <b>Disclosure:</b> Dr. Chen has nothing to disclose. Mr. Baraz has nothing to disclose. Ms. Xuan has nothing to disclose. Sadaf Saba has nothing to disclose. Dr. Yang has nothing to disclose. Dr. Castoro has nothing to disclose. Yang Xuan has nothing to disclose. Dr. Roth has nothing to disclose. The institution of Dr. Dortch has received research support from NIH. The institution of Dr. Dortch has received research support from DOD. Dr. Li has received personal compensation in the range of $500-$4,999 for serving on a Scientific Advisory or Data Safety Monitoring board for Guidepoint. The institution of Dr. Li has received research support from NIH. Dr. Li has a non-compensated relationship as a Board of Directors with ANA that is relevant to AAN interests or activities.

Herschel-Bulkley Model of Blood Flow through an Asymmetric Stenosed Artery on Unsteady Reactive Solute Dispersion

This study examined the effects of chemical reaction, stenosis shape parameter and non-Newtonian behaviour on solute dispersion in blood flow via an asymmetric stenosed artery using the generalised dispersion model (GDM). The Herschel–Bulkley (H-B) fluid model, which consists of a yield stress and power-law index, is used to represent the non-Newtonian characteristics of blood in a narrow artery at a low shear rate. The impact of stenosis shape parameter, chemical reaction, power-law index and plug flow radius on the dispersion coefficient and effective axial diffusion of solute is shown. The findings showed that the aforementioned parameters significantly impact the overall process of the chemically reactive solute in a bulk flow. The dispersion coefficient and effective axial diffusion decreases with an increase in the chemical reaction rate, stenosis shape parameter and power-law index. As time passes, the dispersion process slows and becomes almost constant implying a steady state of diffusion. In short, this study provides further insights into the physiological processes involved in the dispersion of drugs and nutrients in the circulatory system.

Analytical solution for thermally developing laminar core-annular flow with two immiscible liquids considering axial diffusion in semi-infinite ducts

Flows involving core-annular immiscible liquids provide a wide range of useful engineering applications, such as transportation of heavy oils and cooling processes. The present article considers an analytical solution for the internal convection heat transfer in hydrodynamically developed and thermally developing laminar core-annular liquid–liquid immiscible flows in circular ducts. The axial diffusion is considered in the model and the problem is investigated for semi-infinite domain under convective boundary condition on duct walls and prescribed inlet flow temperature. The steady-state problem is solved through the generalized integral transform technique (GITT) with a single domain approach, in which, the coupled ODE system arising from the GITT is analytically solved using the matrix exponential method. Moreover, integral balance is used to compute the Nusselt number. The convergence process of the local Nusselt number is shown in different flow regions and the results are presented for multiple flow parameters. The effects of the boundary conditions, flow properties, and other parameters are discussed. An analysis of axial diffusion effects is performed, which confirms that it can interfere with the local Nusselt number, especially for lower Péclet numbers.

Herschel-Bulkley Model of Blood Flow through a Stenosed Artery with the Effect of Chemical Reaction on Solute Dispersion

A non-Newtonian mathematical model of blood described as a Hershel-Bulkley fluid model flowing in a stenosed artery with the effect of a chemical reaction is mathematically studied. The expressions of the shear stress, mean velocity and absolute velocity in the plug and non-plug flow field are evaluated analytically. The convective-diffusion equation is solved using the Taylor-Aris technique subject to the relevant boundary constraint in determining the concentration, relative and effective axial diffusivity. The efficiency of the dispersion process is affected by the presence of chemical reaction and stenosis in blood flow. The normalized velocity decreases as stenosis height and stenosis length increase. The relative axial diffusivity is significantly lower while the effective axial diffusivity decreases considerably as the chemical reaction rate, the height of the stenosis and the length of the stenosis increase. Besides, it is observed that as the solute disperses in the presence of stenosis, the flow quantities are lesser than in the absence of stenosis. Further, this study helps in understanding many physiological processes for instance dispersion of drugs or nutrients in the circulatory system. Also, to enhance the dispersion of a solute in blood flow through narrow arteries in the presence of chemical reaction and stenosis.

A new method for analytical modeling of microfluidic extraction

Despite single-phase parallel flows for which analytical solutions are available for species conservation equation in its most general form, little progress has been made in analytical modeling of cross-stream diffusion in stratified multiphase flows. The main reason is that solute concentration and fluid properties are discontinuous at the interface of phases. In the present study, a new method of solution is presented for the analytical treatment of solute transport in stratified multiphase flows. The solution methodology starts with developing separate species conservation equations for the phases, which, upon non-dimensionalization, are replaced with a single equation for which series solutions are obtained utilizing the variational calculus. Using the method proposed, analytical solutions are obtained for mass transport in microfluidic two-phase extraction by taking the influences of the non-uniform velocity and the axial diffusion effects into account. The inclusion of the non-uniform velocity effects, which leads to 3D solutions, enables us to capture the heterogeneous transport of solutes, a phenomenon that is ignored by the available simple 2D solutions. The results indicate that axial diffusion in stratified multiphase flows is significantly more important than in single-phase flow and is not characterized solely by the Peclet number. It is also found that the only parameter controlling the length required for a complete extraction is the solvent-to-solution viscosity ratio.

Combustion characteristics of syngas laminar microjet diffusion flames

Two-dimensional numerical investigations of laminar microjet syngas (H2 - CO) diffusion flames are carried out in the present study. A detailed parametric study on the effects of fuel jet velocity and fuel composition on global flame characteristics is analyzed. Results show that the flame height increases with an increase in fuel jet velocity, and it decreases with an increase in hydrogen content in the fuel mixture. The dependence of fuel composition and jet velocity on the rate of tube wall heat recirculation is explored. The radial extent of flame increases with increase in hydrogen content in the fuel mixture. The analysis of key reactions in the standoff region revealed the significant contribution of HO2 radical in the formation of high-temperature reaction zone. Flame extinction is observed at lower fuel jet velocities, as the composition of hydrogen in fuel mixture increases from 10 to 90%. Near extinction, the combined effect of axial and radial diffusion results in the formation of spherically shaped flames.

Theoretical analysis of thermal entrance problem for blood flow: An extension of classical Graetz problem for Casson fluid model using generalized orthogonality relations

An analysis of classical Graetz problem is carried out for the case of fluid obeying the Casson constitutive equation. The considered model physically corresponds to the thermal entry flow of blood in a duct. The governing equation for the premeditated problem is investigated by employing the separation of variables approach in conjunction with the MATLAB built in package bvp4c for the calculation of the eigenvalues and related numerical solution of the eigenvalue problem. The solution is computed for the case of uniform surface temperature boundary condition for both flat and circular geometries. The axial diffusion and viscous dissipation effects on temperature field are also taken into account. The expressions of bulk mean temperature and Nusselt number are presented and discussed in terms of the main effect brought by the yield stress parameter, Peclet number and Brinkman number. It is found that both local and mean Nusselt numbers for blood enhance considerably with the increase of dimensionless plug radius and Brinkman number. In contrast, the thermal entrance length reduces with the rise of Peclet number. The results of present analysis have potential applications in development of nano fluidic, microfluidic and bio-medical devices used in haemodialysis and oxygenation.

Effect of axial diffusion on impurity adsorption in a circular tube

Circular tubes can be used to irreversibly adsorb impurities from a dilute solution of the impurity and a non-adsorbing fluid. An analysis of the unsteady adsorption process over the region $$z = - \infty $$ to $$z = \infty $$ can be carried out with or without axial diffusion. The transport equation in the presence of axial diffusion can be solved using the complex Fourier transform and the Green’s function method. In the absence of axial diffusion, the transport equation can be solved using the Laplace transform method. Previously reported studies over the region $$0\le z\le L$$ limited the contribution of axial diffusion. Analytical solutions of the pertinent differential equations are used to determine the impurity concentration everywhere in the circular tube.

Conjugated heat transfer in circular microchannels with slip flow and axial diffusion effects

An integral transforms analysis is undertaken for conjugated heat transfer in circular microchannels with laminar gaseous flow in the slip flow regime. The solution methodology is based on the Generalized Integral Transform Technique applied to a single domain formulation that models the coupled heat transfer phenomena at the fluid stream and at the channel wall. The single domain formulation results in just one partial differential equation for the energy balance, making use of spatially variable coefficients with abrupt transitions, and accounting for the temperature jump at the interface due to the Knudsen numbers within the slip flow regime. This work extends the single domain formulation strategy, not a priori applicable to problems with discontinuities, by considering a very thin fictitious layer at the fluid-wall interface region, so as to mathematically represent an equivalence to the temperature jump. An integral balance technique for enhancing the convergence of the eigenfunctions is employed, so as to achieve more accurate results and improve convergence for the so derived multiscale problem. The results obtained are critically compared against a dedicated finite difference numerical solution for the original multi-region problem. Results for the Nusselt number are presented in order to investigate its behavior with respect to different Péclet and Knudsen numbers, and different wall thicknesses values, confirming the importance of the combined effects of slip flow, axial conduction and heat transfer conjugation in the analysis.

Effects of pressure work, viscous dissipation, shear work and axial conduction on convective heat transfer in a microtube

This paper investigates the effects of viscous dissipation, pressure work, shear work, rarefaction and axial heat diffusion on convective heat transfer in a microtube gaseous flow. The problem is investigated numerically for the whole flow region using a finite difference scheme and the line Gauss-Seidel iterative technique. Exact solutions of the problem in terms of temperature distribution and Nusselt number variations are also derived under fully developed flow conditions. The microtube is assumed to be sufficiently long, so that fully developed conditions are established. The analysis presented demonstrate that the effect of the boundary shear work is significant and its contribution to heat transfer can be as high as that due to heat conduction close to the upper limit of the slip flow regime. As the shear work is a result of the combined effects of viscous dissipation and pressure work at the boundary, including these effects in the analysis leads to better predictions of heat transfer phenomena. Axial heat diffusion effect on Nusselt number and the thermal entrance length are also quantified.

Determination of dynamic dispersion coefficients for passive and reactive particles flowing in a circular tube

Using the moment analysis method and the Green’s function, mathematical formulations valid across the full-time scale have been derived to determine dynamic dispersion coefficients for passive and reactive particles flowing in a circular tube with fully-developed laminar flow under different source conditions. The newly proposed formulations were verified through agreements with both analytical solutions and random walk particle tracking (RWPT) simulations. The relationship between particle size and dispersion coefficient for passive particles varies with time and they are positively correlated if Peclet number is larger than its critical value; otherwise, they are negatively correlated. Furthermore, the critical Peclet number decreases as time increases. Compared to an instantaneous point source, the critical Peclet number for a volumetric planar source is much smaller. At a small size ratio, size-exclusion effects on passive particle dispersion can be neglected across the full-time scale for both instantaneous point and volumetric planar sources; whereas, at a large size ratio, its significance needs to be considered, depending upon time and source condition. Using Dre_diff=0.02 (Dre_diff=(D−Dnon_ad)/D, where D and Dnon_ad are dispersion coefficients with and without axial diffusion, respectively) as the critical value, axial-diffusion effects on dispersion are negligible for passive solutes at long times if Peclet number is not smaller than 50; however, due to size exclusion this is not applicable for passive particles. At early times, reaction rate, center-of-mass velocity, and dispersion coefficient are not sensitive to Damköhler number for reactive particles. At long times, reaction rate and enter-of-mass velocity increases in magnitude as the Damköhler number increases, while the dispersion coefficient decreases with increasing Damköhler number. Consequently, reaction at the tube walls greatly affects concentration distributions.

Analytical solutions for species transport in a T‐sensor at low peclet numbers

A 3D analytical solution is presented for the problem of mass transport in a T‐sensor by taking the axial diffusion effects into account. The solution methodology is based on an eigenfunction expansion of the solute concentration and enjoys the variational calculus for the solution of the associated eigenvalue problem. The method is capable of handling a mixed electroosmotic and pressure‐driven velocity profile and is executed assuming a rectangular channel cross‐section although it can be easily extended to more complex geometries. Two simplified models, one based on a uniform velocity profile, valid for the channel half height to Debye length ratios of above 100, and the other based on a depthwise averaging of the species concentration to be used for cases in which the channel width to height ratio is above 5 are also presented. As a part of the latter, expressions are derived for the Taylor dispersion coefficient of the mixed flow in a slit microconduit. The most interesting finding of this study is that, when the diffusion mechanism significantly contributes to the axial movement of the species, the well‐known heterogeneous mass transport evolves into a nearly uniform pattern in the depthwise direction and the mixing length noticeably increases. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4119–4130, 2016

Effect of axial diffusion on the response of diffusion flames to axial flow perturbations

This paper elucidates the behavior and dynamics of non-premixed flames responding to bulk fluctuations in flow velocity. It expands previous work on this problem by consistently incorporating finite Peclet number (▪) effects, and differentiating inflow boundary and dynamical effects on the flame dynamics. For analytical tractability, prior treatments of this problem generally prescribe the inflow boundary conditions into the domain. This paper shows, however, that prescribed inflow conditions, such as a step or constant local diffusive flux boundary condition, neglect axial diffusion effects in the region where their effects are most important; i.e., in the near-burner exit region where high transverse gradients and mass burning rates control the heat release dynamics. As the burning rate of non-premixed flames are controlled by mixture fraction gradients, the influence of axial diffusion substantively influences several burning rate characteristics of the flame. In addition, these effects cause the leading edge position of the flame front to oscillate, even for infinitely fast chemistry. Even in Pe≫1 flames, axial diffusion introduces several fundamentally new features to the problem, resulting in exponentially decaying, dispersive flame wrinkle propagation with downstream distance. Also investigated here are asymptotic results for the heat release dynamics. It is shown that axial diffusion introduces a triple-zone asymptotic structure into the unsteady heat release characteristics, resulting in O(1) flame transfer function trends for St≪1 (to which an n–τ model is developed), O(1/St1/2) for intermediate Strouhal numbers, and O(1/St) for high Strouhal numbers. Finally, it is shown that the phase of the heat release response is approximately half that of a premixed flame with the same length, due to the concentration of unsteady heat release near the burner outlet, where transverse gradients are largest.

Axial diffusion effect on concentration dispersion

This work presents an analytical attempt to illustrate the effect of axial diffusion on concentration dispersion in packed tube flows. The concentration moment method is applied to derive the analytical solution for time-dependent Taylor dispersion coefficient. With the increase in the packing parameter α as a damping factor, the concentration dispersion is characterized by three modes: (I) the shear-induced dispersion dominated mode, with dispersion coefficient determined by α; (II) the transition mode; and (III) the diffusion dominated mode, with dispersion coefficient determined by Péclet number Pe. In contrast to the usually negligible effects of axial diffusion for dispersion in pure fluid flows even at a relatively small Pe, axial diffusion with typical α plays an important role for packed media flows even with large Pe.

Transient conjugated heat transfer in microchannels: Integral transforms with single domain formulation

The transient behaviour of conjugated heat transfer in laminar microchannel flow is investigated, taking into account the axial diffusion effects, which are often of relevance in microchannels, and including pre-heating or pre-cooling of the region upstream of the heat exchange section. The solution methodology is based on the Generalized Integral Transform Technique (GITT), as applied to a single domain formulation proposed for modelling the heat transfer phenomena at both the fluid stream and the channel wall regions. By making use of coefficients represented as space dependent functions with abrupt transitions occurring at the fluid–wall interfaces, the mathematical model carries the information concerning the transition of the two domains, unifying the model into a single domain formulation with variable coefficients. The proposed approach is illustrated for microchannels with polymeric walls of different thicknesses. The accuracy of approximate internal wall temperature estimates deduced from measurements of the external wall temperatures, accounting only for the thermal resistance across the wall thickness, is also analyzed.

Analysis of the advection–diffusion mixing by the mapping method formalism in 3D open‐flow devices

This article extends the analysis of laminar mixing driven by a chaotic flow in the presence of diffusion to three‐dimensional open‐flow devices by means of the mapping‐matrix method. The extended formulation of the mapping matrix recently proposed by Gorodetskyi et al. (2012) allows inclusion of the molecular diffusion in the mixing process. This provides an efficient numerical tool for understanding the interplay between a chaotic advective field and diffusion, especially for high Péclet numbers. As a prototypical open‐flow device we consider the partitioned‐pipe mixer. Results deriving from the application of the extended mapping method are compared with Galerkin simulations, and a close agreement is found. Short‐term properties in the evolution of the concentration and the effect of axial diffusion are also addressed. © 2013 American Institute of Chemical Engineers AIChE J, 60: 387–407, 2014

Heat Transfer in Microchannels with Upstream–Downstream Regions Coupling and Wall Conjugation Effects

Heat transfer in microchannels is analyzed, including the coupling between the regions upstream and downstream of the heat transfer section and taking into account the wall conjugation and axial diffusion effects which are often of relevance in microchannels. The methodology is based on a recently proposed single-domain formulation for modeling the heat transfer phenomena simultaneously at the fluid stream and the channel walls, and applying the generalized integral transform technique (GITT) to find a hybrid numerical–analytical solution to the unified partial differential energy equation. The proposed mathematical model involves coefficients represented as space-dependent functions, with abrupt transitions at the fluid–wall interfaces, which carry the information concerning the transition of the two domains, unifying the model into a single-domain formulation with variable coefficients. Convergence of the proposed eigenfunction expansions is thoroughly investigated and the physical analysis is focused on the effects of the coupling between the downstream and the upstream flow regions.

Conjugated Convection-Conduction Analysis in Microchannels With Axial Diffusion Effects and a Single Domain Formulation

An extension of a recently proposed single domain formulation of conjugated conduction–convection heat transfer problems is presented, taking into account the axial diffusion effects at both the walls and fluid regions, which are often of relevance in microchannels flows. The single domain formulation simultaneously models the heat transfer phenomena at both the fluid stream and the channel walls, by making use of coefficients represented as space variable functions, with abrupt transitions occurring at the fluid-wall interface. The generalized integral transform technique (GITT) is then employed in the hybrid numerical–analytical solution of the resulting convection–diffusion problem with variable coefficients. With axial diffusion included in the formulation, a nonclassical eigenvalue problem may be preferred in the solution procedure, which is itself handled with the GITT. To allow for critical comparisons against the results obtained by means of this alternative solution path, we have also proposed a more direct solution involving a pseudotransient term, but with the aid of a classical Sturm-Liouville eigenvalue problem. The fully converged results confirm the adequacy of this single domain approach in handling conjugated heat transfer problems in microchannels, when axial diffusion effects must be accounted for.