Dynamics Of Suspensions Research Articles

Dispersion and particle pressure in sedimenting suspensions with hydrodynamic interactions and particle inertia

Particle inertia is a feature of suspension dynamics that is often neglected. However, its neglect changes the order of the governing equations of particle motion. In this work, we examine the impact of the inertia of particles over their velocity fluctuations and the resulting stresses. In order to observe effects of particle inertia, we consider dusty-gas suspensions of spherical weakly Brownian microparticles sedimenting in a Newtonian fluid at low Reynolds numbers. We first investigate the motion of a single spherical particle. The simulations for this simple case allow us to define the appropriate physical parameters of the flow and to validate the numerical calculation of velocity statistics over a range of Péclet and Stokes numbers. Next, we perform Langevin dynamics simulations with periodic boundary conditions to integrate the equations governing the translational and rotational motions of N hydrodynamically interacting particles suspended in the viscous fluid. The first aim of this paper is to examine the behavior of the velocity variance of inertial particles, with small fluctuations produced by Brownian motion at the moderate Péclet numbers. The interplay between mild Brownian forces and hydrodynamic interactions decreases the anisotropy of velocity fluctuations observed in non-Brownian suspensions (Pe≫1) of sedimenting particles. The simulation results suggest that particle inertia attenuates the magnitude of velocity fluctuations produced by both Brownian motion and viscous hydrodynamic interactions. Additionally, we study the long-time behavior of the velocity fluctuations by calculating their autocorrelation functions and the particle diffusivities. The numerical simulations show clear evidence of particle pressure arising from the flow disturbance produced by hydrodynamic interactions in a suspension. From the particle velocity variance obtained in the present numerical simulations, we propose a simple model for particle-phase pressure as a linear function of the particle volume fraction ϕ⩽5%, which is usually a closure quantity required in models of more complex particulate systems such as fluidized beds.

The Countoscope: Measuring Self and Collective Dynamics without Trajectories

Driven by physical questions pertaining to quantifying particle dynamics, microscopy can now resolve complex systems at the single-particle level, from cellular organisms to individual ions. Yet, available analysis techniques face challenges reconstructing trajectories in dense and heterogeneous systems where accurately labeling particles is difficult. Furthermore, the inescapable finite field of view of experiments hinders the measurement of collective effects. Inspired by Smoluchowski, we introduce a broadly applicable analysis technique that probes dynamics of interacting particle suspensions based on a remarkably simple principle: counting particles in finite observation boxes. Using colloidal experiments, advanced simulations, and theory, we first demonstrate that statistical properties of fluctuating counts can be used to determine self-diffusion coefficients, so alleviating the hurdles associated with trajectory reconstruction. We also provide a recipe for practically extracting the diffusion coefficient from experimental data at variable particle densities, which is sensitive to steric and hydrodynamic interactions. Remarkably, by increasing the observation box size, counting naturally enables the study of collective dynamics in dense suspensions. Using our novel analysis of particle counts, we uncover a surprising enhancement of collective behavior due to hydrodynamics as well as a new length scale which can be connected with hyperuniform structure. Our counting framework, the “countoscope,” thus enables efficient measurements of self and collective dynamics in dense suspensions and opens the way to quantifying dynamics and identifying novel physical mechanisms in diverse complex systems where single particles can be resolved. Published by the American Physical Society 2024

Tangent hyperbolic MHD nanoliquids on non-isothermal stretched sheets: Analyzing the impact of transport parameters, variable fluid properties and convective boundary conditions

The key focus of this research is to look at how tangent hyperbolic magnetohydrodynamic (MHD) nano-liquids move in a non-isothermal coagulated stretched sheet. In this study, we intend to explore how fluid behavior responds to alternations in transport physical parameters. The coagulated sheet is subjected to two distinct boundary conditions to inspect the heat and mass transport rate of the nano liquid. The convective heat boundary condition (CBC) and mass-convective boundary condition (MCBC) are employed to specify the physical conditions at the boundaries of the problem domain. The boundary conditions, responsible for regulating heat flow and mass transfer rates, play a crucial role in shaping the liquid’s behavior. Using a similarity solution, the partial differential equation describing the flow of mass and heat within the system transforms into an interconnected network of non-linear ordinary differential equations. These mathematical equations are subsequently figured out using a numerical finite difference method. This study additionally examines the correlation between thermophoresis and Brownian motion, two fundamental concepts in the dynamics of colloidal suspensions. The study’s findings indicate that the temperature profile increases in all scenarios when the variable thermal conductivity and variable viscosity parameters are increased. In contrast, for the same parameters, the velocity profile is decreased. Further, increasing wall thickness reduces heat dissipation; consequently, the temperature profile similarly affects the velocity power index. The Biot number improves the rates of temperature transfer. These results underscore the significant influence of these parameters in predicting the behavior of MHD tangent hyperbolic nanofluids. This study elucidates the intricate interaction among different physical parameters in the dynamics of nano liquids, which holds significant implications for various industrial applications.

On bifurcation of non-isolated singular points arising in a problem of two-phase fluid motion in a pipe

The dynamics of gas suspension in a pipe is studied. It is described by a system of three autonomous differential equations, whose equilibrium (singular) points are not isolated, but form several continuous curves. One of these curves belongs to the transonic plane. The dynamics in a neighborhood of this plane is interesting from the physical viewpoint. In this work, the dynamics in a neighborhood of the curves of singular points is investigated. The main tools of this work are the center manifold theorem and the reduction principle. A peculiarity of the system is that the curves of singular points intersect each other. Moreover, at the intersection point a bifurcation occurs. Results of the work are the description of the dynamics in a neighborhood of singular points, the proof that a curve of singular points belongs to a center manifold and the description of the bifurcation, which occurs at the intersection point of the curves of singular points.

A novel robust adaptive control for nonlinear uncertain quarter-vehicle suspension system in presence of unknown time delay actuation

This paper presents a novel robust adaptive control approach for nonlinear uncertain vehicle suspension system with time delayed actuation and bounded disturbances. The uncertainty and disturbance as well as the input delay on the system are all limited and unknown. This paper explores a control-oriented nonlinear model to accurately describe the dynamics of the vehicle suspension which incorporates uncertainty, disturbance and actuator delay. The controller is designed based on robust and adaptive approaches, which along with guaranteeing general goals for the suspension system is able to assure the stability of the closed-loop system in the Lyapunov concept. Also, due to the use of smooth functions in the robust controller structure, sudden changes in the behavior of system states are prevented. The simulation and comparison results in MATLAB environment show the efficiency of the proposed robust adaptive method in covering the effects of uncertainty, disturbance and time-variant actuator delay.

Shape effects on the local dynamics of suspensions of spheroidal particles

The effect of shape on the dynamics of suspensions of non-spherical heavy particles is examined by fully resolved numerical simulations of oblate and prolate spheroids, as well as spheres, for a density ratio of ten, volume fractions ranging from 0.5% to 5%, and Reynolds numbers between 20 and 30. The dynamics is determined both by the interactions of the particles with the fluid as well as by collisions, with the number and importance of collisions increasing with volume fractions. A single isolated oblate or prolate spheroid falling under gravity generally falls broadside on, for the governing parameters examined here, and at low-volume fractions, the majority of particles in a suspension fall that way. At higher-volume fractions, the orientation is more random. The slip velocity decreases as the volume fraction increases for all shapes, as expected, but the effect of the shape is much less than seen for a single particle. This seems to be due to two effects. For all volume fractions, the most deformed particles cluster more than spheres and less deformed particles, which increases their slip velocity. As the concentration increases, the increased particle interactions also causes more particles to fall short side-on, which reduces the frontal area and the resulting drag, increasing the slip velocity. This second effect is, of course, absent for spherical particles.

Numerical Modeling of the Interaction of a Monodisperse Gas Suspension with a Shock Wave Moving at an Angle to the Separation Boundary of a Homogeneous Gas and a Gas Suspension

The work is devoted to the study of the influence of the dispersed phase on the dynamics of gas suspensions during numerical modeling of the dynamics of gas suspensions. In this study, based on the continuum technique of dynamics of inhomogeneous media, the interaction of a shock wave propagating from a homogeneous gas with a gas suspension was numerically simulated. For each of the components of the mixture, a complete hydrodynamic system of equations of motion was solved, which included the equations of conservation of density, the equations of conservation of the spatial components of the momentum of the mixture components, and the equations of conservation of energy of the components. The carrier medium was described as a viscous, compressible heat-conducting gas. The mathematical model took into account interfacial heat transfer. The mathematical model also took into account the interphase exchange of momentum, which included the force of aerodynamic drag, the dynamic force of Archimedes and the force of added masses. The system of equations of the mathematical model was integrated using the finite difference method. To suppress numerical oscillations, a nonlinear correction scheme was used. Large volumetric contents of the dispersed phase were considered. The influence of interfacial interaction on the process of shock wave propagation has been studied.

Magnetic resonance imaging of a stream of bubbles injected into liquid suspensions

Magnetic resonance imaging (MRI) is a powerful tool for characterizing opaque multiphase flows non-invasively. However, MRI has often (i) had low temporal resolution and thus not captured transient dynamics, (ii) only provided 2D slice images of 3D flows and (iii) been limited to flows in narrow (∼30 mm) tubes with significant wall effects. Here, we apply multi-band echo planar imaging (MB-EPI) with a custom-built radiofrequency coil in a full-body MRI scanner to provide fully 3D images of the dynamics of a stream of bubbles rising through a dense suspension with 151 ms resolution in a 178 mm diameter system. Image processing demonstrates that bubble rise and coalescence dynamics vary significantly with (a) initial spacing between bubbles and (b) particle volume fraction. The ability to image bubble dynamics in dense suspensions as well as in full 3D provides future opportunities to characterize complex, non-axisymmetric, multiphase flows.

Dynamics of particle-laden turbulent suspensions: Effect of particle roughness

Dynamics of particle-laden turbulent suspensions: Effect of particle roughness

Porous structures impact on particle dynamics of non-Brownian and noncolloidal suspensions

This study aims to provide valuable insights into the impact of porous structures on particle dynamics in non-Brownian, non-colloidal suspension flows at very low Reynolds numbers. Two experimental approaches, Particle Image Velocimetry (PIV) with refractive index matching and Optical Flow Tracking Velocimetry (OFTV) were employed to analyze very dilute suspensions over various porous media models. The study considered three different porous structures with permeabilities ranging from 0.7 to 0.9 and three different thicknesses ranging from 0.2 cm to 0.5 cm, while the suspension bulk volume fraction was maintained at 3 %. In the PIV analysis, we observed that decreasing the porous permeability resulted in the maximum velocity location within the free flow region moving closer towards the interface between the flow and the porous media. We further quantified the effect of the porous structure on the suspension by characterizing interface properties, such as dimensionless slip velocity, shear rate, and slip length. These interface properties were found to be influenced by both the thickness and permeability of the porous media. Next, we analyzed particle migration due to the presence of porous structures using OFTV for very dilute suspensions of 1 %, 2 %, and 3 %, considering a porous medium with known physical properties and thickness. The study revealed two local concentration maxima: one within the free flow region on top of the rod arrays used to create the porous structure and a second along the rods' centerline inside the porous media model.

Rescaled mode-coupling scheme for the quantitative description of experimentally observed colloid dynamics.

We describe experimentally observed collective dynamics in colloidal suspensions of model hard-sphere particles using a modified mode coupling theory (MCT). This rescaled MCT is capable of describing quantitatively the wave-vector and time-dependent diffusion in these systems. Intermediate scattering functions of liquidlike structured dispersions are determined by means of static and dynamic light-scattering experiments. The structure and short-time dynamics of the systems can be described quantitatively employing a multicomponent Percus-Yevick ansatz for the partial structure factors and an effective, one-component description of hydrodynamic interactions based on the semianalytical δγ expansion. Combined with a recently proposed empirical modification of MCT in which memory functions are calculated using effective structure factors at rescaled number densities, the scheme is able to model the collective dynamics over the entire accessible time and wave-vector range and predicts the volume-fraction-dependence of long-time self-diffusion coefficients and the zero-shear viscosity quantitatively. This highlights the potential of MCT as a practical tool for the quantitative analysis and prediction of experimental observations.

Sheared settling in viscoelastic shear‐thinning fluids: Empirical studies and model development

AbstractThe hydrotransport of settling particles using laminar flow as opposed to the more energy‐ and water‐intensive turbulent flow has remained a tentative option for industries due to the complexity in characterizing particle settling dynamics in opaque non‐Newtonian fluids under sheared conditions. To provide insight into this unknown physics, this study focused on viscoelastic shear‐thinning fluids and developed a semi‐empirical model to characterize the batch‐settling dynamics of dilute suspensions (<5 vol% solids concentration) experiencing a shear field. These suspensions consisted of spherical glass microparticles in aqueous xanthan gum solutions. Settling profiles were measured with Electrical Resistance Tomography (ERT) while a motorized belt generated a cross‐shear field. The data acquired by the ERT showed that introducing cross‐shear fields into such suspensions increased settling rates when compared with static settling contexts. Then, a semi‐empirical model describing the “acceleration phase” of the settling process was developed and validated at accuracies between 81% and 97%.

Fractional-Order PIλDμ Control to Enhance the Driving Smoothness of Active Vehicle Suspension in Electric Vehicles

The suspension system is a crucial part of an electric vehicle, which directly affects its handling performance, driving comfort, and driving safety. The dynamics of the 8-DoF full-vehicle suspension with seat active control are established based on rigid-body dynamics, and the time-domain stochastic excitation model of four tires is constructed by the filtered white noise method. The suspension dynamics model and road surface model are constructed on the Matlab/Simulink simulation software platform, and the simulation study of the dynamic characteristics of active suspension based on the fractional-order PIλDμ control strategy is carried out. The three performance indicators of acceleration, suspension dynamic deflection, and tire dynamic displacement are selected to construct the fitness function of the genetic algorithm, and the structural parameters of the fractional-order PIλDμ controller are optimized using the genetic algorithm. The control effect of the optimized fractional-order PIλDμ controller based on the genetic algorithm is analyzed by comparing the integer-order PID control suspension and passive suspension. The simulation results show that for optimized fractional-order PID control suspension, compared with passive suspension, the average optimization of the root mean square (RMS) of acceleration under random road conditions reaches over 25%, the average optimization of suspension dynamic deflection exceeds 30%, and the average optimization of tire dynamic displacement is 5%. However, compared to the integer-order PID control suspension, the average optimization of the root mean square (RMS) of acceleration under random road conditions decreased by 5%, the average optimization of suspension dynamic deflection increased by 3%, and the average optimization of tire dynamic displacement increased by 2%.

Shape deformation, disintegration, and coalescence of suspension drops: Efficient simulation enabled by graph neural networks

Understanding the behaviors of suspension drops (particle swarms) as they settle in a viscous fluid holds significant importance across various applications. Due to hydrodynamic interactions (HIs), suspension drops would undergo a series of intricate behaviors, including shape deformation, disintegration, and coalescence. This work presents the hydrodynamic interaction graph neural network (HIGNN), developed in our prior work (Ma et al., 2022), as an efficient and accurate modeling framework for simulating the dynamics of suspension drops and investigating the various behaviors they exhibit. The HIGNN effectively incorporates the many-body nature of HIs, a feature lacking in most previous simulations that employ the Stokeslet assumption. In the meanwhile, the HIGNN achieves superior computational efficiency compared to traditional, high-fidelity numerical tools such as Stokesian dynamics and PDE solvers. Moreover, the HIGNN, once trained, is applicable to predicting suspension drops across a range of particle concentrations and under diverse forces (such as gravity and Coulombic interactions). Training the HIGNN only requires the data containing a small number of particles, leading to low training cost. Our results demonstrate that the HIGNN can effectively reproduce the various behaviors of suspension drops that were previously reported in literature. More specifically, a single, initially spherical drop slowly evolves into a torus-shaped drop, as particles escape from its rear and form a tail along the sedimenting direction. Subsequently, the torus breaks into secondary droplets, each undergoing a similar transition (deformation into a torus followed by disintegration), thereby leading to a repeating cascade. Further, we quantitatively analyze the correlation between the drop’s sedimentation velocity and volume fraction. We also propose new scaling laws for evaluating both the leakage rate of particles and the expansion rate of the horizontal radius of a suspension drop. For single suspension drops, we also systematically investigate how their dynamics is affected by their initial shapes and the formed tori’s aspect ratios, as well as with or without Coulombic interactions between particles. For a pair of suspension drops, we study the process of coalescence of two vertically aligned particles and examine the effect of introducing a horizontal offset on the subsequent breakup of the coalesced drop. All simulations were executed on a single GPU, with the computation of velocities for several thousand particles requiring less than five seconds per time step. This computational efficiency enables fast and resource-saving simulations of large suspension drops over extended time scales.

Height control strategy employing AWPSO-fuzzy PID control for electronically controlled air suspension system

Electronically controlled air suspension (ECAS) system has been extensively applied in vehicles to increase driving comfort, fuel economy, and operation safety. However, due to the nonlinear and hysteresis characteristics of the ECAS system, accurately controlling suspension height remains challenging. To tackle this problem, a bench test is conducted on the air spring and solenoid valve to establish their mathematical model for their characteristics. Based on this, a mathematical model of the ECAS system is developed by integrating suspension kinematics and dynamics theories. Then, a height control strategy is devised utilizing a fuzzy proportional-integral-derivative (PID) algorithm, enabling precise control of the vehicle’s body height. Based on this, an adaptive weight particle swarm optimization (AWPSO) algorithm is utilized to optimize the output range of the fuzzy controller. The effectiveness of the proposed model and control strategy is validated through both simulation tests and real-vehicle testing under both no-load and full-load conditions. These tests confirm the proposed approach’s effectiveness in achieving precise suspension height control in ECAS systems.

Emergence of a hexagonal pattern in shear-thickening suspensions under orbital oscillations

A dense particle suspension under shear may lose its uniform state to large local density and stress fluctuations, which challenge the mean-field description of the system. Here, we explore the novel dynamics of a non-Brownian suspension under orbital oscillations, where localized density waves along the flow direction appear beyond an excitation frequency threshold and self-organize into a hexagonal pattern across the system. The spontaneous occurrence of the inhomogeneity pattern arises from a coupling between particle advection and the shear-thickening nature of the suspension. Through linear stability analysis, we show that they overcome the stabilizing effects of particle pressure at sufficient particle volume fraction and oscillation frequency. In addition, the long-standing density waves degenerate into random fluctuations when replacing the free surface with rigid confinement. It indicates that the shear-thickened state is intrinsically heterogeneous, and the boundary conditions are crucial for developing local disturbance.

Estimation of vehicle suspension dynamics with data fusion for correcting measurement errors

This paper presents a novel algorithm that aims to estimate an accurate dynamic model for a vehicle suspension system. The proposed method addresses the uncertainties associated with the system model and unknown road input by incorporating complementary terms. These terms are calculated using information from accelerometers installed on both the sprung and unsprung masses. To correct measurement errors, including bias and noise, the paper suggests fusing the accelerometer data with displacement data. The paper further introduces an adaptive solution for adjusting the estimator coefficients, enabling effective data fusion. An experimental implementation is conducted on a quarter-car suspension platform, equipped with additional sensors to verify the estimated responses. Comparative results with the unknown-input Kalman filter highlight the superior accuracy of the proposed estimator in constructing a precise dynamic model for the system. Additionally, the results demonstrate the effectiveness of data fusion-based adaptive tuning of the estimator coefficients in correcting measurement errors.

Implementation and Validation of a Numerical Method for Concentrated Suspensions in Large Flows Based on the Particle Diffusion Equation

This work presents the development of an OpenFOAM solver aimed at correctly predicting dynamics of concentrated suspensions when subjected to non-uniform shear flows. The newly implemented solver is able to predict the behavior of a heterogeneous mixture whose characteristics depend on the solid particle local concentration. To simulate such behavior, the conservation equation expressing the time variation of the particle volume fraction has been implemented in OpenFOAM; this was achieved by modifying a pre-existing solver, pimpleFoam, which discretizes the Navier–Stokes system of equation through the PIMPLE algorithm. As a first step, the formulation of the momentum equation has been adapted to correctly solve cases with non-Newtonian fluids. Successively, the Krieger’s correlation has been used to model the viscosity variation in the domain to take in account heterogeneous particle distributions. Finally, the iterative cycle for the solution of the migration equation has been included within the time loop. The above-mentioned code has been successfully validated by comparing the numerical results with the measured data provided by experiments reported in literature.

A comprehensive study of large eddy simulation models in capturing the dynamics of gas-particle turbulent suspensions

The particle phase attenuates the fluid fluctuations with an increase in volume fraction, and a sudden collapse in the turbulence is observed at a particular particle volume fraction, called critical particle volume loading (CPVL) [P. Muramulla et al. J. Fluid Mech. 889, A28 (2020)]. The present study reports the capability of two different classes of large eddy simulation (LES), viz. anisotropic and eddy viscosity-based, models to capture the turbulence modulation and the sudden disruption of the fluid fluctuations in the particle-laden vertical channel flows. The simulations are performed at two bulk Reynolds numbers of 3300 and 5600 based on the channel width and the bulk averaged fluid velocity. Our study on different LES models shows that approximate deconvolution (ADM) and scale similarity (SS) models accurately predict the critical loading for the Reynolds number of 3300. However, these models predict the critical loading qualitatively only for the Reynolds number of 5600 in the sense that they fail to predict the discontinuity as shown by the direct numerical simulation (DNS) study. The coherent structure model (CSM) predicts the critical loading with an 80% accuracy at both Reynolds numbers. The energy spectral density, production, and particle-induced dissipation spectra are plotted to analyze the distribution across wavenumbers. For all the LES models, a decrease in more than one order of magnitude is observed in the energy spectrum density at the critical loading compared to the unladen flow. The energy density decreases more in the channel center than in the near-wall region for the same particle volume loading. The mean component of particle-induced dissipation is almost two orders of magnitude larger than the particle dissipation spectra of fluctuating energy. The magnitude of streamwise and spanwise dissipation spectra of fluctuating components is higher in the near-wall region than the channel center. However, the magnitude of wall-normal dissipation spectra is higher in the channel center than near the wall region.

Analytical Study on Mechanical Energy Recovery and Utilization of New Energy Vehicles

The pursuit of energy efficiency and sustainability in the automotive industry has become increasingly urgent in response to growing environmental concerns. Herein, this paper focuses on the critical challenge of energy dissipation in new energy vehicles, particularly during braking and suspension vibrations. The paper presents two innovative energy recovery solutions aimed at reducing energy losses and enhancing sustainability. In the realm of sustainable transportation, this study critically evaluates the optimization strategies for braking energy recovery in new energy vehicles. A key recommendation is the integration of a permanent magnet synchronous motor combined with an advanced fuzzy control system. Such an amalgamation not only heightens energy efficiency but also substantially extends the driving range of electric vehicles. Beyond braking energy, the research casts light on an often-overlooked energy source: the vibrational energy from vehicle suspensions. By introducing an innovative electromagnetic damper design coupled with the strategic incorporation of piezoelectric materials, the study unveils avenues to both improve suspension dynamics and transform vibrational energy into usable electrical power. While there are current technological and economic challenges, the ongoing innovations in the design and control processes of new energy vehicles highlight the profound potential within this domain. The insights offered in this context further emphasize the critical need to expand the horizons of sustainable transportation design and management approaches.