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An alternative model is proposed for hydrodynamic stability of plane parallel flow of an incompressible Newtonian fluid with suspended solid particles. For heavy particle-laden dusty gases with negligible particle volume fraction, the effective complex-form mean velocity in the modified Orr-Sommerfeld equation derived by the present model is showed to be essentially identical to the well-known Saffman's classical results. In the limit cases of small or large Stokes number of particles, simple formulas are derived for the effective Reynolds number ratio of the particle-laden suspension to the clear fluid without particles under otherwise identical conditions. The derived formula for particles of finite particle-to-fluid density ratio and small Stokes number is verified by comparing predicted results with known data, although a comparison of the derived formula with known results for particles of finite density ratio and large Stokes number cannot be made here due to the lack of available data. It is hoped that the present work could offer a conceptually novel and relatively simplified model for hydrodynamics of solid particle-fluid suspensions. [ABSTRACT FROM AUTHOR]

Particle suspension and deposition dynamics are significant factors affecting the level of mixing quality in solid-liquid two-phase stirring processes. In general, the ability to increase the suspension rate and minimize deposition effects is instrumental in improving the uniformity of particle mixing, accelerating the reaction of involved solid-liquid two-phase, and improving the efficiency of production operations. In this work, suspension and deposition indicator based on the Betti number and a uniformity indicator are introduced and obtained by means of image analysis. The influence of the blade type, rotation speed, blade diameter and blade bottom height on the particle suspension/deposition characteristics and mixing uniformity are carefully investigated. The experimental results show that the two-phase motion region can be divided into three local regions, including a bottom motion along the wall, a low-degree suspension region under the blade and a high suspension region above the blade. The best degree of particle suspension is attained by the double-inclined blade paddle at a speed of 270 r/min, a paddle diameter ratio of 0.414, and a height-diameter ratio of 0.086. The double-inclined blade paddle has a better effect on promoting particle suspension and solid-liquid two-phase mixing uniformity. [ABSTRACT FROM AUTHOR]

This study evaluated the suspension stability of passion fruit nectar formulated with different concentrations of carboxymethyl cellulose (CMC). Passion fruit nectars with 0, 0.02, 0.1 and 0.2% (w/v) CMC were placed at rest in test tubes at room temperature (~25 °C) to measure the phase separation height for 87 h. Passion fruit nectars with 0 and 0.02% (w/v) CMC showed notable phase separation, while those with 0.1 and 0.2% (w/v) CMC were relatively stable suspensions. The analysis of sedimentation kinetics revealed that passion fruit nectars with 0 and 0.02% (w/v) CMC presented respectively: maximum sedimentation velocity of 0.426 m/s and 0.260 m/s, equilibrium sedimentation index of 46.494% and 20.434%, and sedimentation rate speed of 0.0362 and 0.0556%/s. A concentration of 0.2% (w/v) CMC is recommended in passion fruit nectar to maintain the appearance of a stable suspension, which is a characteristic desired by the consumer.

The bubbling flow plays a key role in gas–liquid–solid fluidized beds. To understand the intrinsic fluidization behaviors at the discrete bubble and particle scale, coupled simulations with the volume of fluid model and the discrete element method are performed to investigate the effects of the gas inlet velocity, particle properties and two-orifice bubbling flow on particle fluidization. Three-dimensional simulations are carried out to accurately capture the dynamic changes in the bubble shape and trajectory. A bubbling flow with a closely packed bed is simulated to study the onset of particle fluidization. The obvious phenomena of particle fluidization are presented by both the experiment and simulation. Although an increasing gas inlet velocity promotes particle fluidization, the good fluidization of particles cannot be achieved solely by increasing the gas inlet velocity. When the channel is packed with more particles, the bubbles take a longer time to pass through the higher particle bed, and the bubbles grow larger in the bed. The increase in particle density also extends the time needed for the bubbles to escape from the bed, and it is more difficult to fluidize the particles with a larger density. Even if more particles are added into the channel, the percentage of suspended particles is not significantly changed. The percentage of suspended particles is not increased with a decrease in the particle diameter. The particle suspension is not significantly improved by the bubbling flow with two orifices, while the particle velocity is increased due to the more frequent bubble–particle collisions. The findings from this study will be beneficial in guiding the enhancement of particle fluidization in multiphase reactors. [ABSTRACT FROM AUTHOR]

The main objective of the present article is to investigate the hydromagnetic particle Reiner-Rivlin fluid flow in an asymmetric (divergent) channel. The non-dimensionalized equations solved by the shooting method. The graphs are intended to examine how different developing parameters affect the thermal and velocity fields. The effects of various parameters on skin friction and the rate of heat transmission along channel walls are investigated using tabular data. The current results are in admirable agreement with the published data. The fluid velocity delineates in the first portion of the channel and rockets up in the second when the inelastic parameter increases. An increase in cross-flow Reynolds number is accompanied by an increasing tendency in particle temperature. Several areas, like metal steam resistors, fiber suspension in paper manufacture, etc., are significantly impacted by the magnetic field's action on Reiner-Rivlin fluid through asymmetric channels. [ABSTRACT FROM AUTHOR]

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Particle suspension is considered powerful and perspective in enhancing heat transfer, but the unclear nature of particle‐loaded flow limits further understanding of particle suspension. Therefore, in this paper, orthogonal experiments and the arbitrary Lagrangian‐Eulerian method were used to investigate the heat transfer characteristics of particle‐loaded flow. Results indicate that when the particle is at the inlet of the microchannel, the factors arranged in important order are the Reynolds number, blockage ratio, particle initial position, specific heat capacity, and thermal conductivity. When the particle is far from the microchannel inlet, the factors arranged in important order are the Reynolds number, blockage ratio, particle initial position, thermal conductivity, and specific heat capacity. [ABSTRACT FROM AUTHOR]

Biomechanics is a field for mechanical study of the structure and function of living organisms, which finds many applications in various fields such as engineering, medicine and biology. Research in blood, systems showed that the blood volume is effectively changed by the strength and direction of shear stress on the vessel wall, also inducing changes in the vessel diameter. Most studies about wall shear stress in bends or branches are based on macroscopic single-phase flow, and more studies should be necessary to investigate wall shear stress distribution by multi-phase flow considering blood as a suspension. In this study, we focused on the flow characteristics of particle suspension, and aimed to analyze a flow field with asymmetrical differences in the shear stress on each wall of a two-dimensional (2D) parallel plates flow, i.e., a flow field with an asymmetric velocity profile. A 2D curvilinear channel was used to reproduce this flow field, and the regularized lattice Boltzmann method and the virtual flux method were used as the computational methods. Our results confirmed that the equilibrium positions were either two asymmetric points or a single point, depending on the radius of curvature of the channel and Reynolds number. The radial pressure gradient was found to be a major factor for the presence of a single equilibrium position. Furthermore, when the radius of curvature was decreased, the equilibrium position shifted closer to the inner wall side, and the relative viscosity of the suspension became higher because of the decreasing the distance between the particle and the inner wall.

Suspensions of monodisperse spherical particles under shear flow were simulated using a solid-liquid two-phase model based on coupled lattice Boltzmann method (LBM) and discrete element method (DEM). Evaluating the shear stresses due to the viscous behavior of the bulk fluid, the hydrodynamic interaction between particles and fluid, and the physical contact between particles, the contribution of each factor to the suspension viscosity was investigated. The results showed that in the range of low to moderate particle volume fractions, the viscosity of suspensions is mainly determined by the action of the fluid, and that the contribution of particle contact increases with increasing particle volume fraction. In particular, the flow behavior of dense suspensions should be viewed not as a fluid motion but as the motion of a group of particles. From these results, in order to predict and control the rheological properties of particle suspensions, it is important to understand that the main factors increasing viscosity vary with the concentration range of interest. [ABSTRACT FROM AUTHOR]

The goal of the current investigation is to examine the impact of magnetic field and heat source effects on a Reiner–Rivlin particulate flow through an asymmetric channel (convergent channel). The transformed governing equations are solved by employing the shooting technique with the RK4 method. To check the convergence of the computational results, a grid independence test has been performed. The impact of influential parameters on fluid as well as particle phases of velocity and temperature fields have been analyzed graphically. The present results exactly match previously published results in some limited cases. As the Reynolds number and magnetic parameter increase, the fluid phase velocity increases on the left side and decreases on the right part of the channel. Different fields, including metal steam resistors, paper production, and fibre suspension, are significantly impacted by the magnetic field’s effect on Reiner–Rivlin fluid through asymmetric channels. [ABSTRACT FROM AUTHOR]

Predictions of clarified layer depth and solids suspension in a draft tube reactor were investigated at a moderate solids loading of 16% v/v using both a RANS approach (k − ε) and a scale-resolving approach using Stress Blended Eddy Simulation (SBES). The multiphase flow was modelled using an Algebraic Slip model and the impact of drag law, turbulent particle diffusion and number of particle size classes was examined. The inclusion or exclusion of turbulent particle diffusion is found to dominate the RANS results, with resulting poor prediction of clarified layer depth and solids suspension under some conditions. In contrast, the SBES model is found to give good agreement with experimental data and the results show there is no need for a modelled turbulent dispersion force in this system if the large-scale turbulence structures responsible for particle transport are explicitly resolved. [Display omitted] • Clarified layer depth and solids suspension in a draft tube reactor studied. • RANS and Stress Blended Eddy Simulation (SBES) predictions compared. • Impact of modelled turbulent dispersion force investigated. • SBES predictions superior to RANS and in close agreement with experimental data. [ABSTRACT FROM AUTHOR]

[Display omitted] The vacuum method is a widely adopted technique for eliminating bubbles from polymers containing particles. To investigate the influence of bubbles on the behavior of particles and the concentration distribution in high-viscosity liquids under negative pressure, experimental and numerical methods have been employed. The experimental findings demonstrated a positive correlation between the diameter and rising velocity of bubbles and the negative pressure. As the negative pressure increased from − 10 kPa to − 50 kPa, the position of the region where the particles were concentrated in the vertical direction was elevated. Furthermore, when the negative pressure exceeded − 50 kPa, the particle distribution became sparse and layered locally. The Lattice Boltzmann method (LBM) integrated with the discrete phase model (DPM) was utilized to investigate the phenomenon, and the outcomes revealed that rising bubbles have an inhibitory effect on particle sedimentation, and the extent of inhibition was determined by the negative pressure. In addition, vortexes generated by differences in the rising velocity between bubbles resulted in a particle distribution that was sparse and layered locally. This research provides a reference for achieving desired particle distributions using a vacuum defoaming approach and should be further studied to extend its applicability to suspensions containing particles with different viscosities. [ABSTRACT FROM AUTHOR]

The shear rheology of particle suspensions in shear-thinning polymeric fluids is studied experimentally using parallel plate measurements and numerically using fully resolved, 3D finite volume simulations with the Giesekus fluid model. We show in our experiments that the steady shear viscosity and first normal stress difference coefficient of the suspension evolve from shear-thickening to substantially shear-thinning as the degree of shear-thinning of the suspending fluid increases. Moreover, in highly shear-thinning fluids, the suspension exhibits greater shear-thinning of the viscosity than the suspending fluid itself. Our dilute body-fitted simulations show that in the absence of hydrodynamic interactions, shear-thinning can arise from the particle-induced fluid stress (PIFS), which ceases to grow with increasing shear rate at low values of β (solvent viscosity ratio) and finite values of α (the Giesekus drag coefficient). In a Giesekus suspending fluid, the polymers surrounding the suspended particle are unable to stretch sufficiently at high Weissenberg numbers (Wi) and the reduced polymer stress results in a lower PIFS. When coupled with the shear-thinning stresslet, this effect creates an overall shear-thinning of the viscosity. We then explore the effects of particle-particle interactions on the suspension rheology using immersed boundary simulations. We show that multiparticle simulations are necessary to obtain the shear-thinning behavior of the per-particle viscosity of suspensions in shear-thinning fluids at moderate values of β. Particle-particle interactions lead to a substantial decrease in the PIFS and an enhancement of the shear-thinning of the stresslet compared to the single particle simulations. This combination leads to the shear-thinning of the per-particle viscosity seen in experiments. We also find that very low values of β and finite values of α have opposing effects on the per-particle viscosity that can lead to a nonmonotonic per-particle viscosity versus shear rate in a highly shear-thinning fluid. Overall, the addition of rigid particles to highly shear-thinning fluids, such as joint synovial fluid, leads to increased viscosity and also increased shear-thinning at high shear rates. [ABSTRACT FROM AUTHOR]

We study the effect of varying polymer concentration, measured by the dimensionless polymer viscosity partition function β , on the steady shear rheology of rigid particle suspensions using direct numerical simulation of the Oldroyd-B model. We compare the bulk rheology using immersed boundary simulations at Φ = 2.5 % and 5 % to body-fitted single-particle simulations and find that the per-particle viscosity and first normal stress difference coefficient are always shear-thickening at all values of β considered. However, as β decreases, the polymer stress transforms the flow field near each particle from closed concentric streamlines to helical streamlines that advect stretched polymers away from the particle surface. At low β , the polymer stress is diffuse, where the distribution of the particle induced fluid stress (PIFS) caused by the stretched polymers is spread out in the simulation domain rather than concentrated near the particle surface. Therefore in multiparticle simulations, the polymer stress can be significantly affected by particle-particle interactions. The stress generated by a given particle is disrupted by the presence of particles in its vicinity, leading to a significantly lower PIFS than that of the single-particle simulation. In addition, at increased volume fractions and low values of β , the polymer stress distribution on the particle surface shifts so as to increase the magnitude of the polymer stress moments, resulting in a shear-thickening stresslet contribution to the viscosity that is not seen in single particle or high β simulations. This result indicates that for suspensions in highly viscoelastic suspending fluids that are characterized by a low β parameter, hydrodynamic interactions are significant even at modest particle concentrations and fully resolved multiparticle simulations are necessary to understand the rheological behavior. [ABSTRACT FROM AUTHOR]

In the chemical and water treatment industries, it is necessary to achieve maximum contact between the solid and liquid phase, thus promoting the mass and heat transfer, to obtain a homogeneous solution. Increasing stirring speed is the most recommended solution in different types of reactors: stirred tank, column, and tubular. However, this inadvertently increases the energy consumption of the industry. Determination of the minimum speed, labeled the just suspended speed (Njs) and crucial to attaining homogeneity, has been widely investigated. Numerous studies have been carried out to assess formulas for determining the solid particle speed in various reactor types. Given the limitations of the existing formulations based on a generalization of a unique equation for computing Njs for all soil classifications, it appears that most formulas can only approximate complex phenomena that depend on several parameters. A novel formula was developed, and the results given in this paper demonstrate the effectiveness of generating significant uncertainties for the estimation of Njs. The purpose of this study was the elaboration of experiment-based data-driven formulas to calculate Njs for different particle size classes. Nonlinear multiple regression (MNLR) models were used to generate the new formulas. The gradient descent optimization algorithm was employed to solve the hyperparameters of each novel equation, utilizing supervised learning. A comparison of the data indicated that the unique formulas presented in this study outperformed empirical formulas and provide a useful means for lowering energy consumption, while increasing the heat and mass transfer in torus type reactors. [ABSTRACT FROM AUTHOR]

Heat transfer characteristics of random suspensions of 0.25 aspect ratio (AR) cylinders are investigated for Reynolds numbers (Re) between 10 and 300 and solid fraction (φ) ranging from 0.1 to 0.3 using particle resolved simulations. The effect of particle inclination with respect to flow and particle clustering on heat transfer is investigated. The Nusselt number decreases with an increase in inclination angle and the dependence becomes stronger as φ and Re increase. On the other hand, while prolate ellipsoid suspensions of AR 2.5 follow the same trend, the Nusselt number increases with inclination angle as AR increases to 5 and 10 and as φ increases. Local particle clustering nominally decreases the Nusselt number because of the dominance of thermal wakes. At low φ⁠, this effect is felt only at low Re⁠, but as φ increases, the effect spreads to higher Re⁠. Similar but weaker trends are also found in suspensions of prolate ellipsoids of AR 2.5, 5, and 10. High AR, low Re prolate ellipsoids exhibit the greatest dependence of Nusselt number on local solid fraction. Implementation of two independent definitions of reference length, i.e., volume equivalent sphere diameter deq for ellipsoids and diameter dp of the cylindrical particle in the correlation of Tavassoli et al. (2015, "Direct Numerical Simulation of Fluid-Particle Heat Transfer in Fixed Random Arrays of Non-Spherical Particles," Chem. Eng. Sci., 129, pp. 42-48) provides good estimates of the respective suspension mean Nusselt numbers. [ABSTRACT FROM AUTHOR]

A coupled method of discrete element method (DEM) and volume of fluid (VOF) is applied to study the particle suspension in top‐sealed solid–liquid tanks with a free‐surface. VOF is used to track the gas–liquid free‐surface, and DEM is used to calculate the movement and interaction of particles. As the air between the cover and free‐surface in a sealed tank is very limited, the free‐surface evolution process that a big vortex is generated quickly and then shrinks to a smaller one in sealed stirred tanks is reported first in this paper. In addition, the effects of pitched blade turbine (PBT) with different blade pitched angles (including 30°, 45°, 60°, 75°, and 90°) on solid suspension, free‐surface, and power number are investigated. Finally, the relationships between particle motion and fluid flow during the stirring are studied carefully. Fluid flow plays a dominant role during the start‐up of the stirring; and then, due to the contact of particles, some particles could obtain the larger velocity than the fluid. The results obtained here are helpful to design the sealed stirred tanks with PBT. [ABSTRACT FROM AUTHOR]

In the chemical and water treatment industries, it is necessary to achieve maximum contact between the solid and liquid phase, thus promoting the mass and heat transfer, to obtain a homogeneous solution. Increasing stirring speed is the most recommended solution in different types of reactors: stirred tank, column, and tubular. However, this inadvertently increases the energy consumption of the industry. Determination of the minimum speed, labeled the just suspended speed (Njs) and crucial to attaining homogeneity, has been widely investigated. Numerous studies have been carried out to assess formulas for determining the solid particle speed in various reactor types. Given the limitations of the existing formulations based on a generalization of a unique equation for computing Njs for all soil classifications, it appears that most formulas can only approximate complex phenomena that depend on several parameters. A novel formula was developed, and the results given in this paper demonstrate the effectiveness of generating significant uncertainties for the estimation of Njs. The purpose of this study was the elaboration of experiment-based data-driven formulas to calculate Njs for different particle size classes. Nonlinear multiple regression (MNLR) models were used to generate the new formulas. The gradient descent optimization algorithm was employed to solve the hyperparameters of each novel equation, utilizing supervised learning. A comparison of the data indicated that the unique formulas presented in this study outperformed empirical formulas and provide a useful means for lowering energy consumption, while increasing the heat and mass transfer in torus type reactors.

[Display omitted] • A scheme was proposed to realize the harmless motion and accumulation of particles. • The particle suspension was effectively suppression, improving product quality and production efficiency. • The research can provide a basis of field productions concerning control technologies of particles. Particle suspension in a turbulent flow can seriously affect the performance of manufactured products in many industrial processes in which the motion of particles cannot be modeled using the numerical method because of the enormous number of particles. Therefore, in this study, a full-scale computational fluid dynamics (CFD) simulation and a 1/5 scaled-down water model experiment were employed to investigate the flow pattern and dynamic behavior of particles in a continuously stirred vessel system. Based on the understanding of the suspension mechanism of settling particles, a particle-suppression device was designed to realize the harmless movement and deposition of particles. The results showed that the flow guidance and division mechanisms of the particle-suppression device led to the inhibition of particle suspensions. In addition, the optimal parameter combination for the device from the water model experiment combined with the orthogonal experimental design, resulted in a 98.3% reduction in the concentration of suspended particles. The suspension of particles was effectively suppressed, which improves product quality and production efficiency. Reliable results can be achieved by combining CFD simulations and water model experiments. [ABSTRACT FROM AUTHOR]

The suspension of a heavy sphere by an upward jet is a classical fluid mechanics experiment to demonstrate the fluid forces acting on an object. In the range of the parameter space where the sphere can be suspended, the dynamics can either be regular, i.e., with oscillations around an equilibrium position, or chaotic, with extreme events leading to large deviations from that equilibrium region. The existence and characteristics of suspension regimes of several heavy spheres in such flow configurations remain open questions. Spheres compete for the equilibrium position and come very close to each other, resulting in large local particle concentrations that prevent direct imaging. Relatively high speed X-ray radiography along with the radioSphereanalysis technique is leveraged here to study the time-resolved 3D trajectory of each individual sphere in a vertical jet. radioSphereis an X-ray analysis method that retrieves the 3D information out of a single 2D radiography using a priori knowledge of the imaging geometry (E. Andò et al., 2021), which due to the imaging modality imposes no limitations on the optical properties of the water. The 3D ＋ time kinematics yield the evolution of the statistics of the position and velocity of the spheres as a function of the number of spheres and for two jet Reynolds numbers. Drastic changes in behavior occur when many spheres are present, leaving a clear signature on the temporal dynamics and on the exploration of the flow volume, where spheres can remain on the bottom of the vessel for long periods of time, resulting in only partial suspension. In addition to the suspension capacity, the interactions between spheres are explored with statistics of pair separation distances, which, together, allow for quantitative arguments to introduce suspension regimes of a collection of spheres in an upward vertical jet. • The suspension dynamics of heavy spheres in an upward vertical jet are studied. • Time-resolved radiography combined with the radioSphere method yields 4D kinematics. • Statistics of the spheres' position and velocity and temporal dynamics are explored. • The interactions between spheres drastically change the dynamics and flow sampling. • Collective suspension regimes are introduced quantitatively based on interactions. [ABSTRACT FROM AUTHOR]

Multiphase displacement in porous media can be adjusted by micro/nanoparticle suspensions, which is widespread in many scientific and industrial contexts. Direct visualization of suspension flow dynamics and corresponding multiphase patterns is crucial to understanding displacement mechanisms and eventually optimizing these processes in geological, biological, chemical, and other engineering systems. However, suspension flow inside the opaque realistic porous media makes direct observation challenging. The advances in microfluidic experiments have provided us with alternative methods to observe suspension influence on the interface and multiphase flow behaviors at high temporal and spatial resolutions. Macroscale processes are controlled by microscale interfacial behaviors, which are affected by multiple physical factors, such as particle adsorption, capillarity, and hydrodynamics. These properties exerted on the suspension flow in porous media may lead to interesting interfacial phenomena and new displacement consequences. As an underpinning science, understanding and controlling the suspension transport process from interface to flow patterns in porous media is critical for a lower operating cost to improve resource production while reducing harmful emissions and other environmental impacts. This review summarizes the basic properties of different micro/nanoparticle suspensions and the state-of-the-art microfluidic techniques for displacement research activities in porous media. Various suspension transport behaviors and displacement mechanisms explored by microfluidic experiments are comprehensively reviewed. This review is expected to boost both experimental and theoretical understanding of suspension transport and interfacial interaction processes in porous media. It also brings forward the challenges and opportunities for future research in controlling complex fluid flow in porous media for diverse applications. [Display omitted] • A comprehensive review of progress on microfluidic experiments for micro/nanoparticles suspension-related multiphase displacement mechanism. • The microscopic particle kinetics and the basic properties of different micro/nanoparticle suspensions are summarized. • The state-of-the-art microfluidic techniques for displacement research activities in porous media are reviewed. • Various suspension transport behaviors and corresponding displacement mechanisms in porous media are summarized and discussed. [ABSTRACT FROM AUTHOR]