Particle Volume Concentration Research Articles

Use of hollow silica and titanium dioxide microparticles in solar reflective paints for daytime radiative cooling applications in a tropical region

Passive radiative cooling provides an energy-saving method for heat management in buildings. Solar reflective paints are versatile and scalable formats that can be readily applied for this cooling technology. We investigate solar reflective paints consisting of hollow silica (SiO2) and hollow titanium dioxide (TiO2) microparticles as pigments and methyltrimethoxysilane as a binder. The hollow microparticles are synthesized via sol-gel and etching methods to control their diameter. Paint formulation is optimized for high total solar reflectance, measured by a UV-visible-near infrared photospectrometer, without exceeding the critical particle volume content. By introducing air volume into the particles and selecting optimal particle size, solar reflectance of the dry paints is significantly improved. Compared to TiO2 microparticle samples, paints with hollow SiO2 microparticles are more effective at rejecting solar irradiation on average while also requiring less particle volume content. Thermal and spectral emissivity measurement also indicates that the hollow SiO2 microparticle paint has the highest broadband infrared emission, followed by a commercial paint and a TiO2 sample. Outdoor experiment in a tropical climate demonstrates that the paint with hollow SiO2 microparticles has better cooling performance than a commercial cooling paint product. The results suggest the potential of hollow SiO2 microparticles for improving radiative cooling paints.

Flow and Heat Transfer Property of Oldroyd-B-Fluid-Based Nanofluids Containing Cylindrical Particles in a Pipe

Flow and heat transfer property of Oldroyd-B-fluid-based nanofluids containing cylindrical particles are studied in a pipe with circular cross-section in the range of Reynolds number (Re) from 100 to 2000, Weissenberg number (We) from 0.1 to 2, particle aspect ratio (β) from 2 to 16 and particle volume concentration (Φ) from 0.1% to 2.5%. The motion equation of Oldroyd-B fluid with particles, the equation for probability density function of particle orientation and convection-diffusion equation for particles are solved numerically. The numerical method used in the simulation is validated by comparing with the available results. The effects of Re, We, β and Φ on the friction factor (f), Nusselt number (Nu) and ratio of energy performance evaluation criterion (PECt/PECf) for Oldroyd-B-fluid-based nanofluids to that for Oldroyd-B fluids are discussed. The results showed that the values of f and Nu of Oldroyd-B-fluid-based nanofluids are larger than that of water-based nanofluids and that of pure Oldroyd-B fluids. The values of f increase with increasing Re, We and Φ, but with decreasing β. The values of Nu and PECt/PECf are enhanced with increasing Re, We, β and Φ. The increase of f is larger than that of Nu at lower Re, but is less than that of Nu at higher Re. It is more effective to use Oldroyd-B-fluid-based nanofluids with cylindrical nanoparticles to improve the heat transfer at the conditions of higher Re, We, β and Φ. Finally, the correlation formula of PECt/PECf as a function of Re, We, β and Φ is derived.

Wear Characteristics of Dense Fine Particles Solid-Liquid Two-Phase Fluid Centrifugal Pump with Open Impellers

The demand for a centrifugal pump with open impellers for conveying dense fine particles in solid-liquid two-phase flow has increased significantly in actual engineering. The wear of dense fine particles on the centrifugal pump is also exceedingly prominent, which affects the engineering efficiency and economic benefits. The two-phase flow in the open centrifugal pump is three-dimensional and unsteady; the movement of high-volume concentration particles in the centrifugal pump and its mutual influence on the two-phase flow, which results in the calculation of wear, are very intricate. To study the wear characteristics of the centrifugal pump with open impeller with high-volume concentration particles more accurately, numerical simulation and experimental comparison are carried out for the impeller wear of dense fine particles transported by the centrifugal pump with open impellers. Considering the relationship between particles and walls, we used the Fluent 18.0 built-in rebound function and wear model. The RNG k-ε model and the DDPM model were adopted in the numerical simulation, and the numerical solution for centrifugal pump wear was performed under flow rate (9.6 m3·h−1, 12.8 m3·h−1, 16 m3·h−1, and 19.2 m3·h−1), different particle sizes (0.048 mm, 0.106 mm, 0.15 mm, 0.27 mm, and 0.425 mm), and different particle volume concentrations (10%, 15%, 20%, 25%, and 30%), respectively. By comparing the serious wear positions of the impeller, the experimental results correspond well with the numerical simulation, which can be used to predict and study the wear characteristics of the impeller. The results show that the most serious area of blade wear is the middle part of the pressure surface, followed by the middle part of the upper part of the blade. The wear of the impeller is greatly affected by relevant parameters, such as pump flow rate, particle diameter, and particle volume concentration. These results can provide some basis for the wear-resistant design of dense fine particle impeller.

Performance Analysis of FPSC using hybrid nanofluid of Aluminum oxide and Titanium oxide

An experimental study was conducted to see the effect of using Aluminum oxide and Titanium oxide hybrid nano fluid on FPSC results. Experimentation was carried out by using nano fluid of size 30-50 nm and particle volume concentration at 0.25, 0.5, 0.75 and 1%. It has been found that by using nanofluid optimum efficiency is obtained at 0.75% concentration of nano fluid maximum 62%.

Experimental Insights on the Propagation of Fine‐Grained Geophysical Flows Entering Water

AbstractGranular flows that propagate down a mountainside, then reach the sea, a lake or a river and finally, travel underwater, is a common event on the Earth's surface. To help the description of such events, laboratory experiments on gas‐fluidized granular flows entering water are performed, analyzed, and compared to those propagating in air. The originality of this study lies in the fluidization process, which improves the laboratory modeling of geophysical flows by taking their high mobility into account. Qualitatively, the presence of the water body promotes the generation of a granular jet over the water surface, a leading and largest wave, and a particle‐driven gravity current underwater. Hydrodynamic forces mainly play a dissipative role by slowing and reducing the spreading of the granular mass underwater, but a low amount of grains are still transported by the turbulent fluid as a gravity current far away. The temporal evolution of the granular jet and the particle‐driven gravity current are well described by ballistic motion theory and scaling laws of homogeneous gravity currents, respectively. Most currents propagate with a constant flow‐front velocity along the horizontal bottom, which is controlled by the flow height depending on the water depth. In contrast, the bulk volume concentration of particles in the current is estimated to be nearly constant, interpreted as a critical concentration above which the excess of particles cannot be maintained by the turbulent fluid. This experimental study highlights the complexity of the dynamics and deposits of granular masses when they encounter a water body.

Evaluating the potential of Azadirachta indica–assisted zinc oxide particles as efficacious nanofluids by convective experiments with twisted tape annexed circular tube

To cater to the needs of energy sustainability and conservation, reuse of decomposed leaves from trees could reap benefits to biosynthesize nanoparticles that might play a very significant role in the convective performance of nanofluids. Azadirachta indica (neem) possesses capping and reducing agents can assist in fluid stability besides providing good thermal transport behavior in nanofluids. Hence, the synthesis of neem-assisted zinc oxide (ZnOneem) nanoparticles aids in evaluating the role of neem in the thermo-hydraulic behavior as nanofluids. The synthesized particles were 36 nm in size as per the Debye Scherrer relation. Nanofluid samples under particle volume concentrations, ϕ (%) of 0.05, 0.2, and 0.6 with ethylene glycol:water (50:50) as base fluid, were prepared. The optimized stability without surfactants was retrieved by stirring and sonicating at different periods. Convective experiments were done by pumping the fluid turbulently (Re=5000 to 10000) through a circular tube with twisted tape inserts (twist ratio, Y=6, 8, and 10) annexed within it. It was evident that the highest performance evaluation factor (PEF) for ZnOneem was 1.385 while the ZnOpure was 1.289. Though the trade-off existed between the convective performance and frictional drag with ϕ =0.05% ZnOpure nanofluid, it did not exist in the case of ZnOneem nanofluid.

Numerical Assessment of Nanofluids in Recharging Microchannel: Thermo-Hydrodynamic and Entropy Generation Analysis

Abstract Three-dimensional numerical study is presented in this work that deals with thermo-hydrodynamic and entropy generation analysis of water-based nanofluids in recharging microchannel (RMC). Four different water-based nanofluids (Al2O3, CuO, SiO2, and ZnO) are considered with volume concentrations of 1–5% and nanoparticle diameters of 10–50 nm to understand their effect on thermo-hydrodynamic performance and entropy generation. Substrate bottom surface is subjected to a constant wall heat flux of 100 W/cm2 while coolant with Reynolds number range of 100–500 flows through the RMC. It is revealed that among all the nanofluids under investigation, water/Al2O3 provides enhanced thermal performance with higher effectiveness parameter (η), and it also shows reduced entropy generation. With increasing volume concentration of water/Al2O3 nanofluid, heat transfer coefficient increases, effectiveness parameter increases, and entropy generation reduces. Water/Al2O3 nanofluid with smaller nanoparticle diameter shows enhanced heat transfer coefficient and reduced entropy generation, whereas it shows decreased effectiveness parameter. This is attributed to increased pressure drop with decreasing particle diameter. This study suggests that an optimized combination of particle diameter and volume concentration should be chosen for using nanofluid-based coolants for high heat flux removal.

Experimental study on heat transfer, friction factor, entropy and exergy efficiency analyses of a corrugated plate heat exchanger using Ni/water nanofluids

In the present study, the heat transfer, entropy, friction factor, exergy efficiency, pumping power, and performance index ratio of nickel/water nanofluids flow in a corrugated plate heat exchanger are investigated experimentally. The nickel nanoparticles were synthesized using the chemical precipitation method and characterized by various techniques. The stable water based nickel nanofluids were prepared with particle volume concentrations of 0.1%, 0.3%, and 0.6%. The experiments were conducted at nanofluids Reynolds numbers ranged from 300 to 1000. The properties of nickel nanofluid are evaluated experimentally as well. The thermal conductivity and viscosity enhancements are 33.92%, and 67.45% at a temperature of 60 °C compared to the base fluid data. The increase of nanoparticle loadings and Reynolds number leads to an augmentation of the overall heat transfer coefficient, heat transfer coefficient, and Nusselt number. The overall heat transfer coefficient, convective heat transfer, and Nusselt number enhanced by 38.60%, 57.35%, and 42.68% at 0.6 vol % of nanofluid and a Reynolds number of 707, respectively compared to water data. The thermal entropy generation is decreased by 15.70%, while frictional entropy generation and pumping power are increased by 68.29% and 61.77%, respectively at 0.6 vol % of nanofluid and a Reynolds number of 707 against water data. The exergy efficiency was enhanced by 42.27% at 0.6 vol % of nanofluid and a Reynolds number of 303 compared to water data. The performance index ratio is decreased with the use of nanofluids due to the increase of viscosity, friction factor, pressure drop, and pumping power.

Solar energy absorbed thermosyphon flat plate collector analysis using Cu/H2O nanofluid – An experimental study

An experimental investigation was conducted aiming to determine the heat transfer, friction and instantaneous collector thermal efficiency of a thermosyphon (natural circulation) solar water heating system using as working fluids of water and the Cu/H2O nanofluid. The Cu nanoparticles were synthesized using the chemical reduction method and characterized by the x-ray diffraction and transmission electron microscopy techniques. The stable Cu/H2O nanofluid was prepared for the volume concentrations of 0.1% and 0.3%. The empirical correlations developed for Nusselt number and friction factor for the Cu/H2O nanofluid fit the experimental data with a deviation of less than ±3.5% and ±2.5%, respectively. The results of present experimental investigation were presented at various Reynolds number and particle volume concentrations under thermosyphon conditions. The comparison indicates that the heat transfer enhancement obtained with the Cu/H2O nanofluid for the thermosyphon is higher than that for the plain tube collector and increases with the increase of particle volume concentration. The overall thermal performance of the thermosyphon increases when the operating fluid is Cu/H2O nanofluid as compared to water.

Numerical Simulation of Fine Particle Solid-Liquid Two-Phase Flow in a Centrifugal Pump

To study the effect of fine particle size and volume concentration on the performance of solid-liquid two-phase centrifugal pump, the mixture multiphase flow model, RNG k-ε turbulence model, and SIMPLEC algorithm were used to simulate the two-phase flow of the centrifugal pump. The effects of particle size and volume concentration on internal pressure distribution, solid volume distribution, and external characteristics were analyzed. The results show that under the design discharge conditions, with the increase of particle size and volume concentration, the internal pressure of the flow field will decrease, and the volume fraction of solid phase in the impeller passage will also decrease as a whole. The solid particles gradually migrate from the suction surface to the pressure surface, and the particles in the volute channel are mainly concentrated in the flow channel near the outlet side of the volute. With the increase of particle size and volume concentration, the negative pressure value at the inlet of centrifugal pump increases, the total pressure difference at the inlet and outlet decreases, and the head and efficiency decrease accordingly.

Thermophysical properties using ND/water nanofluids: An experimental study, ANFIS-based model and optimization

The research work was achieved to optimize the experimentally determined thermophysical properties of water based nanodiamond nanofluids using the Adaptive network-based fuzzy inference system model. The thermophysical properties were determined at various temperatures (20 °C to 60 °C) and various particle volume concentrations (0.2% to 1.0%). The stability of nanodiamond nanofluids was measured based on the dynamic light scattering method. Results indicated that the zeta potential of all the prepared nanodiamond/water nanofluids is above −30 mV. The thermophysical properties like thermal conductivity and viscosity augments are 22.86% and 79.16% at ϕ = 1.0 vol% compared to the water data at a temperature of 60 °C. Fuzzy logic is one of the artificial intelligence tools that have been used to analyze the optimized property value. The optimization process was applied in a single objective and a multi-objective procedure using a new and efficient optimizer, namely, the marine predators' algorithm. In a single objective, the lowest density and highest thermal conductivity values were found at 0.23% with 54.81o C and 1% with 60 °C, respectively. However, the viscosity and specific heat showed improvements only in the absence of the nanodiamond material and temperatures of 35.99 and 60 °C, respectively. In the multi-objective process, the optimizer confirmed that the thermophysical properties' optimal values could be obtained when no nanomaterial was added, and the best values were found at a temperature of 59.48 °C. This optimal point is found as close to the experimental data.

Recent Progress on Stability and Thermo-Physical Properties of Mono and Hybrid towards Green Nanofluids.

Many studies have shown the remarkable enhancement of thermo-physical properties with the addition of a small quantity of nanoparticles into conventional fluids. However, the long-term stability of the nanofluids, which plays a significant role in enhancing these properties, is hard to achieve, thus limiting the performance of the heat transfer fluids in practical applications. The present paper attempts to highlight various approaches used by researchers in improving and evaluating the stability of thermal fluids and thoroughly explores various factors that contribute to the enhancement of the thermo-physical properties of mono, hybrid, and green nanofluids. There are various methods to maintain the stability of nanofluids, but this paper particularly focuses on the sonication process, pH modification, and the use of surfactant. In addition, the common techniques to evaluate the stability of nanofluids are undertaken by using visual observation, TEM, FESEM, XRD, zeta potential analysis, and UV-Vis spectroscopy. Prior investigations revealed that the type of nanoparticle, particle volume concentration, size and shape of particles, temperature, and base fluids highly influence the thermo-physical properties of nanofluids. In conclusion, this paper summarized the findings and strategies to enhance the stability and factors affecting the thermal conductivity and dynamic viscosity of mono and hybrid of nanofluids towards green nanofluids.

Thermosyphon Flat Plate Collector with Nanodiamond-Water Nanofluids: Properties, Friction Factor, Heat Transfer, Thermal Efficiency, and Cost Analysis

Thermal efficiency, friction factor, heat transfer, and cost analysis of a flat plate collector operates with water-based nanodiamond nanofluids under thermosyphon (natural circulation) conditions are investigated experimentally at 0.2%, 0.4%, 0.6%, 0.8%, and 1.0% particle volume concentrations. The thermophysical properties of the working fluids are analyzed as well. Results show that the maximum thermal conductivity and viscosity enhancements are obtained by using 1.0 vol% concentration of nanofluid and found to be 22.86% and 79.16%, respectively, compared to water at a temperature of 60 °C. The maximum increases in Nusselt number are 19.53% and 36.17% using 1.0 vol% concentration of nanofluid compared to water at Reynolds number of 140 and 345, respectively. The maximum increases of friction factor are attained by using 1.0 vol% concentration of nanofluid and found to be 1.14 times and 1.25 times of water friction factor at Reynolds number of 143 and 345, respectively. The collector thermal efficiency increases from 57.15% using water to 69.85% using nanofluid with a concentration of 1.0%. The collector cost decreases approximately by 18.18% for 1.0 vol% nanofluid compared to water. The relative deviations of the equations developed to evaluate Nusselt number and friction factor are within ± 2.5%.

Cooling performance of an impinging synthetic jet in a microchannel with nanofluids: An Eulerian approach

Numerical investigations of heat transfer enhancement in a three-dimensional micro-channel with a single synthetic jet were conducted using Al2O3-water, CuO-water and TiO2-water nanofluids. The effects of different types of nanoparticles at particle volume concentrations of 1%, 2% and 5% on the thermal performance in the micro-channel were examined. The numerical tool was validated against existing experimental data on the heat transfer characteristic of nanofluids in micro-channel. Heat transfer enhancement using nanofluids based on the Eulerian single-phase model was assessed for the cases with and without the operation of the synthetic jet. In general, the overall thermal performance was greatly influenced by the thermal conductivity and dynamic viscosity of the working nanofluids. The former corresponds to thermal enhancement by conduction whilst the latter corresponds to convective enhancement due to the periodic oscillation of the synthetic jet diaphragm. As the particle volume concentration of a nanofluid increased, effectiveness of the synthetic jet to provide convective cooling became poorer on account of higher viscosity. Nevertheless, in some cases, this can be overcome by the enhancement in thermal conductivity, depending on the Peclet number of the working fluid. Synthetic jet microchannel with Al2O3-water nanofluid at φ = 5% showed the best overall cooling performance whereas TiO2-water nanofluid at φ = 5% failed to improve the thermal performance.

A method to approach constant isotropic permeabilities and demagnetization factors of magneto-rheological elastomers

The use of non-conventional materials is nowadays of much interest in scientific community. Magneto-rheological elastomers are hybrid materials, which in presence of magnetic fields state a change in their mechanical properties. They are composed by an elastomeric matrix with embedded magnetic particles. One of the most attractive features of these materials is that as soon as the magnetic field is removed from the material, the original mechanical properties are completely recovered, with negligible differences in comparison to the original state. This paper focuses on the study of magnetic characteristics of these smart materials, such as relative permeability and demagnetizing factors, for samples with different volume concentration of ferromagnetic particles.

Analysis of quasistatic squeeze behavior of magnetorheological fluid from the microstructure variations

Magnetorheological fluid is a novel functional material, of which quasistatic squeeze behavior needs to be quantitatively controlled in industrial applications. Since the quasistatic squeeze behavior has a close relation with microstructure variations, thus it is modeled from a microscopic approach. By analyzing compression of single chains, aggregation from single chains to BCT structure and compression of BCT structure, the initial stress [Formula: see text], yield stress [Formula: see text], yield strain [Formula: see text], and stress in post-yield stage [Formula: see text] are respectively modeled. It is found that they have an exponential dependence on magnetic field strength H and particle volume concentration [Formula: see text], including [Formula: see text], [Formula: see text], and [Formula: see text], etc. By comparing predicted results with measured results, the micro-macro stress model on quasistatic squeeze behavior is well validated. This model can be used to design, manufacture, and control industrial magnetorheological devices.

Reproducing pyroclastic density current deposits of the 79 CE eruption of the Somma–Vesuvius volcano using the box-model approach

Abstract. We use PyBox, a new numerical implementation of the box-model approach, to reproduce pyroclastic density current (PDC) deposits from the Somma–Vesuvius volcano (Italy). Our simplified model assumes inertial flow front dynamics and mass deposition equations and axisymmetric conditions inside circular sectors. Tephra volume and density and total grain size distribution of EU3pf and EU4b/c, two well-studied PDC units from different phases of the 79 CE Pompeii eruption, are used as input parameters. Such units correspond to the deposits from variably dilute, turbulent PDCs. We perform a quantitative comparison and uncertainty quantification of numerical model outputs with respect to the observed data of unit thickness, inundation areas and grain size distribution as a function of the radial distance to the source. The simulations consider (i) polydisperse conditions, given by the total grain size distribution of the deposit, or monodisperse conditions, given by the mean Sauter diameter of the deposit; (ii) axisymmetric collapses either covering the whole 360∘ (round angle) or divided into two circular sectors. We obtain a range of plausible initial volume concentrations of solid particles from 2.5 % to 6 %, depending on the unit and the circular sector. Optimal modelling results of flow extent and deposit thickness are reached on the EU4b/c unit in a polydisperse and sectorialized situation, indicating that using total grain size distribution and particle densities as close as possible to the real conditions significantly improves the performance of the PyBox code. The study findings suggest that the simplified box-model approach has promise for applications in constraining the plausible range of the input parameters of more computationally expensive models. This could be done due to the relatively fast computational time of the PyBox code, which allows the exploration of the physical space of the input parameters.

The influence of laser treatment of aluminum-magnesium alloy surface on the ”self-assembly” of nanoparticles during the evaporation of colloidal solution

Establishing the characteristics of the self-assembly of micron and sub-micron particles when colloidal solution droplets evaporate from solid surfaces is an urgent problem. This is explained by the possibility of using these structures obtained by droplet technologies to create and optimize the production of direct and indirect liquid cooling devices, electronic and sensor working boards, current-conducting coatings, optical crystals, and chemo sensors. The method used in this study for processing of metals and alloys by laser radiation is prospective for controlling the processes at the liquid/gas/solid interface. This article aims to analyze the effect of laser processing of the widely used in the industry aluminum-magnesium alloy on the formation of a layer of particles during the droplet evaporation of colloidal solutions. The samples’ surfaces were processed by two methods: polished by tumbling and nanosecond laser pulses. The geometric parameters of the droplets of colloidal solutions evaporating from the samples’ surfaces were determined by the shadow method. To process the obtained shadow images, the Young — Laplace method was used. Using a scanning electron microscope, the authors have received the images of the particles’ layers formed due to the droplet evaporation of colloidal solutions. The experimental studies reveal the effect of texture formed on aluminum-magnesium alloy sample on the morphology of the layer of polystyrene nanoparticles during the droplet evaporation of colloidal solutions. Due to the self-assembly of particles, solid ring-like sediments are formed, which are elongated under the action of the capillary force parallel to the motion vector of the laser beam (when creating the texture). When the solvent evaporated from the solution droplet on the textured surface, in addition to the rings, a homogeneous layer of polystyrene particles was formed. This refers to the droplet evaporation of the solution. The results show that with an increase in the concentration of particles in the solution, the sizes of radial cracks on the rings formed due to particle deposition increase. There were no cracks on the rings at a relatively low volume concentration of particles.

Performance of –Vacuum Pump Oil Nanofluid in Tube with Wire Coil Inserts

The thermal performance of high-Prandtl-number –vacuum pump oil (VPO) nanofluid with wire coil (WC) inserts is experimentally studied under laminar flow conditions. The volume concentrations of the nanoparticles considered are 0.05, 0.2, and 0.5%. The study also investigates different values of the ratio of the pitch to diameter () of the WC inserts; those include 1.79, 2.54, and 3.24. Mass flow rates of the base fluid and the nanofluids considered in the experimental tests are 0.0416, 0.083, 0.12, 0.166, and , and their corresponding Reynolds numbers are 63.3, 126.6, 189.9, 253.2, and 316.5. The results show that heat transfer enhancement is increased as the particle volume concentration increases. Also the results show that the heat transfer process can be improved with the use of WC inserts, and this improvement becomes higher at smaller ratio values. For instance, when 0.5 vol.% of nanofluid flows in a tube with a WC insert of , the Nusselt number increases by 20.52% over that of a plain tube. It was also found that the presence of nanoparticles and the use of the WC insert increase the pressure drop, causing the friction factor to increase. The study found that the combined effect switches in favor of using the WC inserts and –VPO nanofluid because the resulted heat transfer enhancement outweighs the increase in the friction factor.

Dynamics of self-organizing single-line particle trains in the channel flow of a power-law fluid

The formation of self-organizing single-line particle train in a channel flow of a power-law fluid is studied using the lattice Boltzmann method with power-law index 0.6 ≤ n ≤ 1.2, particle volume concentration 0.8% ≤ Φ ≤ 6.4%, Reynolds number 10 ≤ Re ≤ 100, and blockage ratio 0.2 ≤ k ≤ 0.4. The numerical method is validated by comparing the present results with the previous ones. The effect n, Φ, Re and k on the interparticle spacing and parallelism of particle train is discussed. The results showed that the randomly distributed particles would migrate towards the vicinity of the equilibrium position and form the ordered particle train in the power-law fluid. The equilibrium position of particles is closer to the channel centerline in the shear-thickening fluid than that in the Newtonian fluid and shear-thinning fluid. The particles are not perfectly parallel in the equilibrium position, hence IH is used to describe the inclination of the line linking the equilibrium position of each particle. When self-organizing single-line particle train is formed, the particle train has a better parallelism and hence benefit for particle focusing in the shear-thickening fluid at high Φ, low Re and small k. Meanwhile, the interparticle spacing is the largest and hence benefit for particle separation in the shear-thinning fluid at low Φ, low Re and small k.