Flow In Microtube Research Articles

Analytical Solution for Transient Electroosmotic and Pressure-Driven Flows in Microtubes

This study focuses on deriving and presenting an infinite series as the analytical solution for transient electroosmotic and pressure-driven flows in microtubes. Such a mathematical presentation of fluid dynamics under simultaneous electric field and pressure gradients leverages governing equations derived from the generalized continuity and momentum equations simplified for laminar and axisymmetric flow. Velocity profile developments, apparent slip-induced flow rates, and shear stress distributions were analyzed by varying values of the ratio of microtube radius to Debye length and the electroosmotic slip velocity. Additionally, the “retarded time” in terms of hydraulic diameter, kinematic viscosity, and slip-induced flow rate was derived. A simpler polynomial series approximation for steady electroosmotic flow is also proposed for engineering convenience. The analytical solutions obtained in this study not only enhance the fundamental understanding of the electroosmotic flow characteristics within microtubes, emphasizing the interplay between electroosmotic and pressure-driven mechanisms, but also serve as a benchmark for validating computational fluid dynamics models for electroosmotic flow simulations in more complex flow domains. Moreover, the analytical approach aids in the parametric analysis, providing deeper insights into the impact of physical parameters on electroosmotic and pressure-driven flow behavior, which is critical for optimizing device performance in practical applications. These findings also offer insightful implications for diagnostic and therapeutic strategies in healthcare, particularly enhancing the capabilities of lab-on-a-chip technologies and paving the way for future research in the development and optimization of microfluidic systems.

Investigation of drag reduction by slurry-like drag-reducing agent in microtube flow using response surface methodology (RSM)

In this study, we investigated the drag reduction property of a premixed slurry drag reducer in a millimeter-scale pipe. The aim of this study is to establish the correlation between Darcy friction factor and drag reducer concentration (C) and volume flow (Q). First, the experimental plan was designed by using the response surface method (RSM), and then the experimental data were processed to establish the quadratic correlation between the response variable and the description variable. After that, ANOVA analysis of variance was used to verify the accuracy of the experimental data and the correlation. Finally, the prediction model is extended to a larger concentration and volume flow range, and it is found that the accuracy between the predicted value of friction coefficient and the experimental value is ± 30%, thus verifying that the correlation is suitable for the small-scale fully turbulent region. Compared with traditional experimental design and correlation methods, the implementation of Response Surface Methodology (RSM) in this study not only reduces the experimental time but also yields a more robust correlation for predicting the friction coefficient.

Time-periodic electromagnetohydrodynamic flow in a circular microtube with surface charge dependent slip

The time-periodic electromagnetohydrodynamic (EMHD) flow in circular microtubes is studied by considering slip boundary conditions. An oscillating electric field and a constant magnetic field orthogonal to each other are applied externally to drive the fluid flow. The slip length considered here depends on the surface charge of the channel, which is generally a more realistic situation as demonstrated by recent experimental work. The velocity is obtained by using the characteristics of the Bessel equation. The influences of surface charge density σs and electrical oscillating Reynolds number Re on velocity and flow rate are discussed in detail. Our results demonstrate the EMHD slip flow rate can be reduced by up to 8.5% at low Reynolds number (Re=1) by considering the surface charge effect on slip, but enhanced by up to 8% at high Reynolds number (Re=50). These theoretical results can provide some theoretical basis for experimental studies.

Application of CFD-DSMC coupling method in H2 flow and heat transfer in microtube

In the research of porous media and the interior of microelectronic devices, fluids frequently shuttle among pores and wall cracks, therefore it is of great significance to explore the influence of media wall on fluid flow and heat transfer. In this paper, CFD-DSMC coupled iterative algorithm is first used in the research of the flow and heat transfer of gas near the wall in the porous media, which simplified into the flow and heat transfer in micron-scale tube with smooth and rough wall conditions. It is found that compared with the pure CFD method, the velocity field obtained by the coupled method is quite different in the region close to the wall, and this will affect the flow field in the mainstream region, that is, with the higher roughness of the wall, the velocity in the central region will be smaller. There is no significant difference in the temperature distribution in the microtube before and after coupling, but the temperature in the mainstream decreases with the increase of the roughness of the wall. In addition, the temperature jump was found from some of the coupling results close to the wall. The results will contribute to a deeper understanding of the influence of rough surfaces on gas flow and heat transfer near the wall, and provide guidance for the regulation of flow and heat transfer in porous media.

Effects of Reynolds Number on the Overall Characteristics of Flow and Heat Transfer in the Long Micro-Tube with Dimples

The flow and heat transfer characteristics in micro-tube are very important research fields. In order to study the influence of the Reynolds number on the overall characteristics of flow and heat transfer, a 510 mm long micro-tube with dimples was constructed. Thirty-five different working conditions are considered, and the Reynolds number is between 1500 and 8100. At the same time, the change of physical properties of coolant with temperature is considered. The reliability of numerical simulation results is verified by the grid independence verification and the comparison of experimental data. The results show that the dimple will promote the instability of the flow state and improve the heat transfer efficiency. The flow state evolution formed in the stream-wise direction is basically similar, and its fully developed position remains at 76 mm, which is independent of the Reynolds number. For the fully developed region, the partial derivation of static pressure in the stream-wise component has a quasi-linear relationship with the stream-wise direction. With the development in the stream-wise direction, the partial derivation of static temperature in the steam-wise component decreases. With the increase of Reynolds number, the friction factor f and heat transfer factor j decrease. The ratio of factor heat transfer f to Reynolds number relative collapses for the different cases, especially when the Reynolds number is larger than 3800. The heat transfer factor j is an exponential function of the Reynolds number and decreases with the increased Reynolds number.

A numerical study of microtube geometry effect on flow boiling using the volume of fluid method

Other than pursuing high heat flux, pressure drop also plays a key role in microtube applications as the power and efficiency of a pump are determined in terms of pressure drop. In the literature, only a few studies focus on how tube geometry influences pressure drop. This study numerically investigates the geometry effect on microtube flow boiling and pressure drop using the volume of fluid (VOF) method. Three types of geometries are used in this study: divergent, normal, and convergent microtubes with different lengths and hydraulic diameter ratios. The transient developments of vapor formation, heat flux, and pressure drops are presented within 200 ms. It is shown that the total pressure drop in the divergent microtube is the lowest. The heat flux is decreased as the massive vapor bubbles clog the tube. However, the shortened divergent microtube can increase the heat flux up to 38713.1 W/m2 and reduce the pressure drop down to 214.24 Pa, compared to the normal one under certain flow conditions, while the tube-clogging effect is not dominant. A larger inflow mass flux can delay the vapor bubble formation on the heated wall, which is beneficial to prevent the tube clogging and leads to a higher heat flux. On the other hand, higher heat flux can be achieved in the convergent microtube due to the increasing velocity inside the tube, although it induces the highest total pressure drop. This study provides a better fundamental understanding of the microtube geometry effect on flow boiling and relevant physical insight for the future design of microscale heat transfer applications.

Heat transfer enhancement of two-phase droplet flow in microtube: a phase-field simulation study

Heat transfer enhancement of two-phase droplet flow in microtube: a phase-field simulation study

Cooling of a lithium-ion battery using microchannel heatsink with wavy microtubes in the presence of nanofluid

The cooling process is important for the thermal management of lithium-ion batteries, and maintaining their operating temperature in the optimal range is essential because high temperatures, in addition to reducing efficiency, can damage the batteries. In recent years, many studies have been conducted to achieve an efficient thermal management system (TMS) and the effect of coolant flow distribution in mini-channels, but simultaneous utilization of wavy microchannels and microtubes in a cooling system is a new topic that is addressed in the present work. In this study, silver-water/ethylene glycol nanofluid is considered as a biologically synthesized working fluid, and the effect of nanoparticle volume fraction (ϕ), Reynolds number (Re), and inlet and outlet arrangement on thermal performance and battery temperature changes are examined. The results demonstrate that the use of HS in all cases reduces the temperature of the battery surface and the use of nanofluid in this cooling system keeps its temperature within a safe operating range. Also, counter flow in microchannel and microtube creates a more uniform temperature profile on the battery surface, keeping the battery temperature in the range of 300 to 310 K. For parallel flow, the battery temperature is in the range of 303 to 312 K. In all cases, the temperature difference between different points on the battery surface is less than 5°. Besides, an increment in Re and ϕ enhances the entropy generation of the system.

Heat Transfer of Turbulent Gaseous Flow in Microtubes With Constant Wall Temperature

Abstract In this paper, we report on experimental results to measure the total temperature of nitrogen gas at the inlet and outlet of microtubes with constant wall temperature and to quantitatively determine the heat transfer rates. Experiments were conducted with nitrogen gas flowing in a stainless steel microtube with a diameter of 524 μm and a copper microtube with a diameter of 537 μm. The temperature differences between the inlet and the wall were maintained at 3, 5, and 10 K by circulating water around the inlet and the wall. The stagnation pressures were also controlled so that the flow, with atmospheric back pressure, could reach Reynolds numbers as high as 26,000. To measure the total temperature, a polystyrene tube with a thermally insulated exterior wall containing six plastic baffles was attached to the outlet. Heat transfer rates were obtained from the gas enthalpy difference by using the pressures and the total temperatures measured at the inlet and outlet. Heat transfer rates were also compared with those obtained from the ideal gas enthalpy using the measured total temperatures and from the Nusselt number of incompressible flows. It was found that the measured total temperature at the microtube outlet was higher than the wall temperature. Also, the heat transfer rates calculated from the total temperature difference were higher than the values obtained from the incompressible flow theory.

Non-isothermal rarefied gas flow in microtube with constant wall temperature

In this paper, pressure-driven gas flow through a microtube with constant wall temperature is considered. The ratio of the molecular mean free path and the diameter of the microtube cannot be negligible. Therefore, the gas rarefaction is taken into account. A solution is obtained for subsonic as well as slip and continuum gas flow. Velocity, pressure, and temperature fields are analytically attained by macroscopic approach, using continuity, Navier-Stokes, and energy equations, with the first order boundary conditions for velocity and temperature. Characteristic variables are expressed in the form of perturbation series. The first approximation stands for solution to the continuum flow. The second one reveals the effects of gas rarefaction, inertia, and dissipation. Solutions for compressible and incompressible gas flow are presented and compared with the available results from the literature. A good matching has been achieved. This enables using proposed method for solving other microtube gas flows, which are common in various fields of engineering, biomedicine, pharmacy, etc. The main contribution of this paper is the integral treatment of several important effects such as rarefaction, compressibility, temperature field variability, inertia, and viscous dissipation in the presented solutions. Since the solutions are analytical, they are useful and easily applicable.

Effect of Nanoparticle Shape and Volume Fraction on Nanofluid Flow in Serpentine Microtube

The nanofluid flow in serpentine microtube was numerically investigated in this study. The study has been carried out in three-dimensional laminar flow (750≤Re≤2000) condition. Al2O3 – water nanofluid with different nanoparticle volume fractions (1.0%, 2.0%, 3.0%) have been used as the working fluid in the numerical analyzes. In addition, studies were carried out for blade, platelet and cylindrical nanoparticle shapes. The average Nusselt numbers and the average Darcy friction factors have been used to estimate the flow and heat transfer performance of nanofluid flow in serpentine microtubes. Velocity and temperature distributions inside the microtube were also examined for different cases. Numerical results of the study have been presented as the variation of average Nusselt number and average Darcy friction factor with Reynolds number, nanoparticle shape and nanoparticle volume fraction. As a result, the highest convective heat transfer performance has been obtained for platelet nanoparticle shape of the Al2O3-water nanofluid with 3.0% nanoparticle volume fraction.

Resolved CFD-DEM simulation of blood flow with a reduced-order RBC model

Mathematical modeling of the blood flow with a resolved description of biological cells mechanics such as red blood cell (RBC) has been a challenge in the past decades as it involves physical complexities and demands high computational costs. In the present study, we propose an approach for efficient simulation of blood flow with several suspended RBCs. In this approach, we employ our previously proposed reduced-order model for deformable particles (Nair et al. in Comput Part Mech 7:593–601, 2020) to mimic the mechanical behavior of an individual RBC as a cluster of overlapping spheres interconnected by flexible mathematical bonds. This discrete element method-based model is then coupled with a fluid flow solver using the immersed boundary method with continuous forcing in the context of computational fluid dynamics-discrete element method (CFD-DEM) coupling. The present computational method is tested with a couple of validation cases in which the single RBC dynamics, as well as the blood flow with several RBCs, were tested in comparison with existing literature date. First, the RBC deformation index in shear flow at different shear rates is studied with a good accuracy. Then, the blood flow in micro-tubes of different diameters and hematocrits was simulated. The key characteristics of blood flow such as cell-free layer (CFL) thickness, Fahraeus effect and the relative apparent viscosity are used as the validation metrics. The proposed approach can predict the formation of the migration of RBC toward the tube center-line and the CFL thickness in good agreement with previous measurement and simulations. Furthermore, the model is employed to study the CFL enhancement for plasma separation based on channel constriction. The simulation results compute the CFL thickness downstream of the channel constriction in good agreement with the experiments in a wide range of flow rates and constriction lengths. The original contribution of this study lies in proposing an efficient resolved CFD-DEM simulation method for blood flows with many RBCs which can be employed for numerical investigation of bio-microfluidic applications.

Numerical and experimental studies on flow condensation in hydrophilic microtubes

• A parametric study was performed to investigate the flow condensation in microtubes. • The dynamic contact angle was used to obtain wall temperature and shear stresses. • The effect of diameter, inlet vapor quality, and vapor mass flux was assessed. • A non-dimensional analysis was performed to define flow regime transition criteria. • A flow map for condensing flow in microtubes with 250 μm < D h ≤ 900 μm was obtained. Microchannels have increasingly been used to miniaturize heat transfer equipment, improve energy efficiency, and minimize heat transfer fluid inventory. A fundamental understanding of condensation in microscale will yield far-reaching benefits for the different areas of industry. In this study, microtubes with inner diameters of 250, 500, 600, and 900 µm were used to investigate the effect of microtube diameter, inlet quality, and mass flux on the liquid/vapor interface near the wall boundaries in condensing flow. After validation with the experimental results, a transient numerical model (based on the Volume of Fluid approach) was developed to investigate the hydrothermal properties of condensing such as bubble dynamics, flow map transitions, transient interface shear force, and temperature on flow condensation performance in terms of heat transfer coefficient and pressure drop. The liquid film thickness, slug velocity, and location of transition from annular flow to slug flow inside the microtube were characterized for different microtubes, and the resultant alteration in condensation flow heat transfer and pressure drop is discussed in detail. Using non-dimensional analysis, a flow map was constructed and compared with the available flow maps for flow condensation in microchannels. The obtained results indicated that the interfacial characteristics of condensing flow in microtubes with hydraulic diameters lower than 500 µm are majorly different from those with D > 500 µm.

Axisymmetric lattice Boltzmann model with slip boundary conditions for liquid flows in microtube

Lattice Boltzmann (LB) method, which is a mesoscopic numerical method, has been considered as a powerful tool to study microscale gas and liquid flows. Boundary slip phenomenon, which is a significant feature of both microscale gas and liquid flows, has been extensively studied by the LB method in the past decade. However, most of the previous works have focused on the microchannel flows and studies on the microtube flows are very rare. In this paper, we investigate the widely used slip boundary conditions, i.e., combined bounce-back and specular-reflection (BS) scheme, combined Maxwell-diffusion and specular-reflection (MS) scheme, and combined Maxwell-diffusion and bounce-back (MB) scheme, for the axisymmetric LB model with multi-relaxation-time (MRT) in detail. In order to realize the Navier slip boundary condition for liquid flows, we put forward to a reasonable strategy for determining the combination coefficients and the relaxation time. The proposed boundary schemes are validated by some numerical tests including the Hagen–Poiseuille flow, axisymmetric Womersley flow, Poiseuille flow in a circular annulus, and Womersley flow in a circular annulus. Numerical results are consistent with the analytical solutions, which demonstrate that the proposed boundary schemes are suitable for microscale liquid flows in microtube.

Kinetic boundary schemes of axisymmetric multi-relaxation-time lattice Boltzmann model for microscale gas flows in microtube

Because of its mesoscopic nature and distinctive computing features, lattice Boltzmann method (LBM) is shown as a promising tool to simulate microscale gas flows. However, studies on the microtube flows are rare, and some fundamental problems for LBM to such flows still remain unsolved. In this work, three widely used kinetic boundary schemes, i.e., combined bounce-back and specular-reflection scheme, combined Maxwell-diffusion and specular-reflection scheme, and combined Maxwell-diffusion and bounce-back scheme, for the axisymmetric lattice Boltzmann equation (LBE) with multi-relaxation-time (MRT) are investigated. The discrete effects of the three boundary schemes in the axisymmetric MRT-LBE are observed by analyzing the micro-scale Hagen-Poiseuille flow, and the strategies of adjusting the parameters in the boundary schemes are put forward to implement the no-slip boundary condition and the second-order slip boundary condition. Some numerical tests are implemented to validate the proposed correction strategies for kinetic boundary schemes. Our analysis also shows that the kinetic boundary schemes of the axisymmetric Bhatnagar-Gross-Krook (BGK) LBE cannot realize the no-slip boundary condition and are also inapplicable to microscale gas flows with even some moderate Knudsen numbers (). Therefore, the axisymmetric MRT-LBE is superior to the axisymmetric BGK-LBE in realizing both the no-slip and slip boundary conditions.

Advanced Constitutive Modeling of the Thixotropic Elasto-Visco-Plastic Behavior of Blood: Steady-State Blood Flow in Microtubes.

The present work focuses on the in-silico investigation of the steady-state blood flow in straight microtubes, incorporating advanced constitutive modeling for human blood and blood plasma. The blood constitutive model accounts for the interplay between thixotropy and elasto-visco-plasticity via a scalar variable that describes the level of the local blood structure at any instance. The constitutive model is enhanced by the non-Newtonian modeling of the plasma phase, which features bulk viscoelasticity. Incorporating microcirculation phenomena such as the cell-free layer (CFL) formation or the Fåhraeus and the Fåhraeus-Lindqvist effects is an indispensable part of the blood flow investigation. The coupling between them and the momentum balance is achieved through correlations based on experimental observations. Notably, we propose a new simplified form for the dependence of the apparent viscosity on the hematocrit that predicts the CFL thickness correctly. Our investigation focuses on the impact of the microtube diameter and the pressure-gradient on velocity profiles, normal and shear viscoelastic stresses, and thixotropic properties. We demonstrate the microstructural configuration of blood in steady-state conditions, revealing that blood is highly aggregated in narrow tubes, promoting a flat velocity profile. Additionally, the proper accounting of the CFL thickness shows that for narrow microtubes, the reduction of discharged hematocrit is significant, which in some cases is up to 70%. At high pressure-gradients, the plasmatic proteins in both regions are extended in the flow direction, developing large axial normal stresses, which are more significant in the core region. We also provide normal stress predictions at both the blood/plasma interface (INS) and the tube wall (WNS), which are difficult to measure experimentally. Both decrease with the tube radius; however, they exhibit significant differences in magnitude and type of variation. INS varies linearly from 4.5 to 2 Pa, while WNS exhibits an exponential decrease taking values from 50 mPa to zero.

Prediction of flow characteristics for micro-tube gas flow by temperature recovery factor

Prediction of flow characteristics for micro-tube gas flow by temperature recovery factor

Average Friction Factors of Choked Gas Flow in Microtubes

A micro-tube passage is a basic and important element in the design of micro heat exchangers and for this reason during the last decade a series of investigations have been made with the aim to clarify the main scaling effects playing an important role in microtubes. In this paper, a combined analysis of numerically and experimentally obtained average friction factors in microtubes under the situation of under-expanded (choked) gas flow is presented. The working fluid (nitrogen) passes through the microtube and discharges into the atmosphere under an increasing inlet pressure. Experiments and numerical computations are performed for microtubes with 249 and 528.9 mm in diameter, by varying the aspect ratio (i.e. length/diameter) from 100 to 200. The numerical methodology to solve the governing equations is based on the Arbitrary-Lagrangian-Eulerian (ALE) method. In order to capture the under-expansion characteristics of the flow during choking, the computational domain is extended in the downstream region beyond the microtube outlet. Both experimental and numerical results were obtained for a wide range of Mach number and Reynolds number. In the previous study, it was demonstrated how the outlet Mach number can be expressed as a function of the tube diameter under choked conditions. In this paper, a data reduction procedure for the estimation of the average friction factor between the inlet and the outlet of the microtube is proposed for choked flows in which the outlet gas temperature and pressure are obtained by using the outlet Mach number calculated numerically as a function of the microtube diameter. It is demonstrated how this data reduction method allows an accurate calculation of the average friction factors in microtubes by using a limited number of parameters which are easy to measure. The results obtained in this way are in good agreement with the numerical predictions as well as with the most common empirical correlations.

A simplified quasi-2D model for gas flow in microchannels and microtubes

The analytic equations of mass flow rate for gas flow in microchannels or microtubes developed in the 1990s have been widely validated by experimental results for slow-speed flow, but the applicability for high-speed flow might be constrained. A new model for analyzing the modified Navier–Stokes equations of the gas flow in 2D microchannels and microtubes is proposed in this study, named the simplified quasi-2D (SQ2D) model. The applicability of the SQ2D model can be in the range from slow-speed flow to high-speed flow with no-slip boundary conditions or high-order slip boundary conditions. The flows in 2D microchannels and microtubes, with hydraulic diameters sized from 5 µm to 100 µm and various hydraulic-diameter-to-length ratios, were analyzed by the SQ2D model under different pressure conditions. The mass flow rates calculated by the SQ2D model meet the data computed by the computational fluid dynamics-based method better than the analytic equations in the high Mach number region. The results were also compared with the numerical or experimental data from other studies, good agreements could be reached. Some particular characteristics of micro gas flow were also identified and briefly discussed with the data computed by the SQ2D model.

The electroviscous flow of non-Newtonian fluids in microtubes and implications for nonlinear flow in porous media

This paper aims to interpret the low-velocity nonlinear flow occurring in low-permeability reservoirs based on the theories of electrokinetic transport and non-Newtonian rheology of fluids. To achieve this end, we simulate the steady-state electroviscous flow of Bingham-Papanastasiou (BP) fluids in circular microtubes by simultaneously solving the Poisson-Boltzmann and the modified Navier-Stokes equations. The induced electrical field strength Es, velocity profiles, and the transport capacity of the non-Newtonian fluid under the effects of various factors (such as capillary radius R, zeta potential ζ, yield stress τ0, and stress growth index m) were examined. The results show that the generated Es of the BP fluid is highly affected by the fluid rheology, which is quite different from that of the Newtonian liquid. The velocity profiles become lower and flatter as m or τ0 increases, and this is more remarkable in smaller microtubes. The apparent viscosity of non-Newtonian fluid declines monotonically with increasing c∞, yet non-monotonically with R, m, τ0, and ζ. In addition, the low-velocity nonlinear flow in microtubes can be successfully captured when considering the electrokinetic flow of the non-Newtonian fluid rheology. While for the Newtonian fluid, only involving the electroviscous effect fails to generate the nonlinear flow behavior. The contributions of electrokinetic parameters versus rheological properties to the degree of flow nonlinearity are also discussed. The impact of electrokinetic parameters (ζ, c∞) on the flow characteristics is significant at high-pressure gradients and becomes trivial when the pressure gradient is relatively low. In contrast, the fluid rheological parameters (m, τ0) greatly determine the magnitude of the flow nonlinearity occurring at the low-pressure gradients. In sum, the electroviscous flow of BP fluids in microchannels provides a possible explanation of the low-velocity non-Darcy flow in porous media.