Dynamics Of Suspensions Research Articles

Spatiotemporal Dynamics of Dilute Red Blood Cell Suspensions in Low-Inertia Microchannel Flow

Microfluidic technologies are commonly used for the manipulation of red blood cell (RBC) suspensions and analyses of flow-mediated biomechanics. To enhance the performance of microfluidic devices, understanding the dynamics of the suspensions processed within is crucial. We report novel, to our knowledge, aspects of the spatiotemporal dynamics of RBC suspensions flowing through a typical microchannel at low Reynolds number. Through experiments with dilute RBC suspensions, we find an off-center two-peak (OCTP) profile of cells contrary to the centralized distribution commonly reported for low-inertia flows. This is reminiscent of the well-known “tubular pinch effect,” which arises from inertial effects. However, given the conditions of negligible inertia in our experiments, an alternative explanation is needed for this OCTP profile. Our massively parallel simulations of RBC flow in real-size microfluidic dimensions using the immersed-boundary-lattice-Boltzmann method confirm the experimental findings and elucidate the underlying mechanism for the counterintuitive RBC pattern. By analyzing the RBC migration and cell-free layer development within a high-aspect-ratio channel, we show that such a distribution is co-determined by the spatial decay of hydrodynamic lift and the global deficiency of cell dispersion in dilute suspensions. We find a cell-free layer development length greater than 46 and 28 hydraulic diameters in the experiment and simulation, respectively, exceeding typical lengths of microfluidic designs. Our work highlights the key role of transient cell distribution in dilute suspensions, which may negatively affect the reliability of experimental results if not taken into account.

Influence of a Vibration Isolation System on Planar Dynamics of a Motorcycle

This paper examines a model to investigate the impact of a vibration isolation system on the planar (in-plane) dynamics of a motorcycle. While it is not very common, a vibration isolation system is used in some motorcycles to mitigate vibrations resulting from the shaking forces of the engine. For such layouts, the powertrain is assembled to the frame through the vibration isolation system that typically consists of two to four isolators. It is critical to comprehend the influence of the isolation system on the overall dynamic characteristics of the motorcycle due to the coupled dynamics of the rear suspension, the isolation system, and the rear unsprung mass. The influence of a vibration isolation system on the in-plane dynamics is analysed by using a relatively simple model that has been developed in this study. This model has been used to evaluate the influence of the isolation system on natural modes, transmissibility, and ride comfort. Results indicate that the use of a vibration isolation system couples the rear unsprung hop to the pitch motion of the powertrain with a slight increase in the corresponding natural frequency. Results indicate that the use of a vibration isolation system directly affects handling of the motorcycle. Furthermore, results indicate that the pitch of the sprung mass and the hop of the rear unsprung mass are particularly influenced by the vibration isolation system. The model presented in this paper could be useful in the early stages of the design process to compare the rigidly mounted powertrain to different layouts of the vibration isolation system.

Shear thickening in dense non-Brownian suspensions: Viscous to inertial transition

We present an experimental study on the viscous to inertial mode of shear thickening in dense non-Brownian suspensions. We design a model suspension consisting of monosized spherical particles within a Newtonian suspending fluid. We develop a protocol for the rheological characterization of dense suspensions using the conventional rheometry technique. Our results provide constitutive laws for suspensions with solid volume fractions close to jamming when both viscous and inertial effects at the particle scale are present. We perform atomic force microscopy to measure forces between the particles immersed in the suspending fluid and show that our system of study corresponds to the frictionless regime of dense suspensions in which viscous and collisional forces dissipate the energy. Finally, we show that the proposed empirical constitutive laws, when approaching jamming, predict the dynamics of dense suspensions in a transient boundary driven flow.

Monte Carlo sensitivity analysis of vehicle suspension energy harvesting in frequency domain

Regenerative shock absorbers (RSAs) have still not entered production lines despite the promising potentials in energy efficiency and emission reduction. Vibration energy harvesting from vehicle dampers has been replicating the dynamics of passive viscous dampers. An accurate frequency-based analysis of the harvestable energy and dynamics for vehicle suspensions under typical operating conditions is essentially needed for designing functional Vibratory Regenerative Dampers (VRDs). This paper proposes frequency-based parametrical bandwidth sensitivity analyses of both the vehicular suspension dynamics and energy harvesting potentiality in accordance with the Monte Carlo sensitivity simulations. This provides insights into which suspension parameter could highly broaden the harvestable power magnitude, which contributes positively to conceptualizing an efficient design of a wide broad-banded energy harvesting damper leading to improved harvesting efficiencies in different road conditions. The conducted sensitivity analysis included the change in both frequency and amplitude bandwidth of the dissipative damping power, body acceleration, dynamic tire load, and suspension deflection. During the sensitivity simulations, a 2-DOFs (degrees-of-freedom) quarter-car model is considered, being excited by harmonic excitations. The selected suspension parameters were normally randomized according to the Gaussian probability distribution based on their nominal values and a 30% SD (standard deviation) with respect to the uniformly randomized excitation frequency. The results inferred higher sensitivity change in the harvestable power bandwidth versus the excitation parameters, damping rate, and tire properties. Conversely, the harvestable power hardly broadened with respect to the body and wheel masses and the spring stiffness.

Condensate formation and multiscale dynamics in two-dimensional active suspensions.

The collective effects of microswimmers in active suspensions result in active turbulence, a spatiotemporally chaotic dynamics at mesoscale, which is characterized by the presence of vortices and jets at scales much larger than the characteristic size of the individual active constituents. To describe this dynamics, Navier-Stokes-based one-fluid models driven by small-scale forces have been proposed. Here, we provide a justification of such models for the case of dense suspensions in two dimensions (2D). We subsequently carry out an in-depth numerical study of the properties of one-fluid models as a function of the active driving in view of possible transition scenarios from active turbulence to large-scale pattern, referred to as condensate, formation induced by the classical inverse energy cascade in Newtonian 2D turbulence. Using a one-fluid model it was recently shown [M. Linkmann et al., Phys. Rev. Lett 122, 214503 (2019)10.1103/PhysRevLett.122.214503] that two-dimensional active suspensions support two nonequilibrium steady states, one with a condensate and one without, which are separated by a subcritical transition. Here, we report further details on this transition such as hysteresis and discuss a low-dimensional model that describes the main features of the transition through nonlocal-in-scale coupling between the small-scale driving and the condensate.

Stochastic failure process of railway vehicle dampers and the effects on suspension and vehicle dynamics

Railway vehicle dampers undergo degradation and failure after long-term service. Bench tests in this paper indicate a stochastic failure process, in which damping characteristics follow bimodal random distributions between normal and failure; failure probability increases in the ageing process until it becomes deterministic. This failure mode may be neglected due to the probabilistic absence of failure, which poses great risk to reliability. Then, nonlinear suspension dynamics with stochastic failure is modelled; Itô stochastic differential rule and cumulant-neglect closure are adopted to derive moment equations. The scheme of progressive iteration is proposed to obtain fast-convergent and stable solutions for analysing the effect of stochastic failure process on vibration response. Further, numerical simulation of a vehicle with stochastic failure is performed for failure effects analysis on dynamical performance. The results demonstrate that the deterioration of failure probability and damping reduction amplitude leads to larger vibrations. The stochastic failure of secondary lateral damper and anti-yaw damper is harmful for lateral vehicle dynamics, while that of secondary vertical damper has negative effects on vertical ride quality. It is of great importance to pay full attention to the stochastic failure process of dampers for reliability and security of railway vehicles.

Elimination of friction-induced vibration of a propulsion shafting system by auxiliary electromagnetic suspension

This paper focuses on the problem of eliminating self-excited vibration in a propulsion shafting system induced by the friction of the water-lubricated rubber bearing. A new scenario involving electromagnetic suspension is proposed to change the condition of instability. To explore the mechanism of elimination of self-excited vibration, a dynamic model of the shafting system is established on the basis of Hamilton’s principle, the velocity-dependent friction model as well as the dynamics of the electromagnetic suspension. Influence of the electromagnetic force on the self-excited vibration of the system is evaluated. Transient responses of the system are obtained by using the Runge–Kutta fourth-order method. Numerical results indicate that the electromagnetic force can reduce the load on the rubber bearing and correspondingly the friction force on the interface. The occurrence of self-excited vibration will be delayed as the electromagnetic force increases, and once the suspension force increases to a critical value, instability of the system will be eliminated and vibration responses are damped exponentially.

The first normal stress difference of non-Brownian hard-sphere suspensions in the oscillatory shear flow near the liquid and crystal coexistence region.

We carry out a numerical study to investigate the dynamics of non-Brownian hard-sphere suspensions near the liquid and crystal coexistence region in small to large amplitude oscillatory shear flow. The first normal stress difference (N1) and related rheological functions are carefully analyzed, focusing on the strain stiffening phenomenon, which occurs in the large strain amplitude region. Under oscillatory shear, we observe several unique behaviors of N1. A negative nonzero mean value of N1 (N1,0) is observed for the applied strain amplitudes. The change of the sign, from negative to positive, at the maximum value of N1 (N1,max) is observed at a specific point, which is not consistent with the critical strain amplitude (γ0,c) at which the modulus begins to deviate from linear viscoelasticity. The behavior of N1 in the oscillatory shear flow is different from that of N1 in steady shear flow, that is, the characteristics of N1 in strain stiffening and shear thickening are quite distinguished from each other. We also perform structural analysis to confirm the relationship between the rheological properties and microstructure of the suspension. A strong correlation is observed between the global bond order parameter (Ψ6) and the distortions in both nonlinear shear and normal stresses. The most noticeable characteristic is captured through the maximum of the global bond order parameter (Ψ6,max). The strain amplitude at the slope change of Ψ6,max corresponds to the point where a unique behavior of N1 is observed, i.e. the change of the sign in N1,max, but a strong correlation is not captured at γ0,c. This demonstrates that the normal stress responds to particle ordering more sensitively than other rheological functions based on shear stress like dynamic moduli. As far as we are concerned, the behavior of N1 has rarely been fully explored and related with the strain stiffening of non-Brownian suspensions so far. Therefore, this study has significance as the first report to strictly analyze strain stiffening along with the first normal stress difference N1.

Driven dynamics in dense suspensions of microrollers.

We perform detailed computational and experimental measurements of the driven dynamics of a dense, uniform suspension of sedimented microrollers driven by a magnetic field rotating around an axis parallel to the floor. We develop a lubrication-corrected Brownian dynamics method for dense suspensions of driven colloids sedimented above a bottom wall. The numerical method adds lubrication friction between nearby pairs of particles, as well as particles and the bottom wall, to a minimally-resolved model of the far-field hydrodynamic interactions. Our experiments combine fluorescent labeling with particle tracking to trace the trajectories of individual particles in a dense suspension, and to measure their propulsion velocities. Previous computational studies [B. Sprinkle et al., J. Chem. Phys., 2017, 147, 244103] predicted that at sufficiently high densities a uniform suspension of microrollers separates into two layers, a slow monolayer right above the wall, and a fast layer on top of the bottom layer. Here we verify this prediction, showing good quantitative agreement between the bimodal distribution of particle velocities predicted by the lubrication-corrected Brownian dynamics and those measured in the experiments. The computational method accurately predicts the rate at which particles are observed to switch between the slow and fast layers in the experiments. We also use our numerical method to demonstrate the important role that pairwise lubrication plays in motility-induced phase separation in dense monolayers of colloidal microrollers, as recently suggested for suspensions of Quincke rollers [D. Geyer et al., Phys. Rev. X, 2019, 9(3), 031043].

Modeling chemo-hydrodynamic interactions of phoretic particles: A unified framework

A theoretical framework based on the method of reflections for Laplace's and Stokes' equations is developed to systematically determine multibody chemohydrodynamic interactions of autophoretic colloids. This approach is an efficient alternative to full numerical simulations of suspension dynamics.

Modeling deswelling, thermodynamics, structure, and dynamics in ionic microgel suspensions.

Ionic microgel particles in a good solvent swell to an equilibrium size determined by a balance of electrostatic and elastic forces. When crowded, ionic microgels deswell owing to a redistribution of microions inside and outside the particles. The concentration-dependent deswelling affects the interactions between the microgels and, consequently, the suspension properties. We present a comprehensive theoretical study of crowding effects on thermodynamic, structural, and dynamic properties of weakly cross-linked ionic microgels in a good solvent. The microgels are modeled as microion- and solvent-permeable colloidal spheres with fixed charge uniformly distributed over the polymer gel backbone, whose elastic and solvent-interaction free energies are described using the Flory-Rehner theory. Two mean-field methods for calculating the crowding-dependent microgel radius are investigated and combined with calculations of the net microgel charge characterizing the electrostatic part of an effective microgel pair potential, with charge renormalization accounted for. Using this effective pair potential, thermodynamic and static suspension properties are calculated, including the osmotic pressure and microgel pair distribution function. The latter is used in our calculations of dynamic suspension properties, where we account for hydrodynamic interactions. Results for diffusion and rheological properties are presented over ranges of microgel concentration and charge. We show that deswelling mildly enhances self- diffusion and collective diffusion and the osmotic pressure, lowers the suspension viscosity, and significantly shifts the suspension crystallization point to higher concentrations. This paper presents a bottom-up approach to efficiently computing suspension properties of crowded ionic microgels using single-particle characteristics.

Short and Soft: Multidomain Organization, Tunable Dynamics, and Jamming in Suspensions of Grafted Colloidal Cylinders with a Small Aspect Ratio.

The yet virtually unexplored class of soft colloidal rods with a small aspect ratio is investigated and shown to exhibit a very rich phase and dynamic behavior, spanning from liquid to nearly melt state. Instead of the nematic order, these short and soft nanocylinders alter their organization with increasing concentration from isotropic liquid with random orientation to small domains with preferred local orientation and eventually a multidomain arrangement with a local orientational order. The latter gives rise to a kinetically suppressed state akin to structural glass with detectable terminal relaxation, which, on further increasing concentration, reveals features of hexagonally packed order as in ordered block copolymers. The respective dynamic response comprises four regimes, all above the overlapping concentration of 0.02 g/mL:(I) from 0.03 to 0.1 g/mol, the system undergoes a liquid-to-solidlike transition with a structural relaxation time that grows by 4 orders of magnitude. (II) From 0.1 to 0.2 g/mL, a dramatic slowing-down is observed and is accompanied by an evolution from isotropic to a multidomain structure. (III) Between 0.2 and 0.6 g/mol, the suspensions exhibit signatures of shell interpenetration and jamming, with the colloidal plateau modulus depending linearly on concentration. (IV) At 0.74 g/mL, in the densely jammed state, the viscoelastic signature of hexagonally packed cylinders from microphase-separated block copolymers is detected. These properties set short and soft nanocylinders apart from long colloidal rods (with a large aspect ratio) and provide insights for fundamentally understanding the physics in this intermediate soft colloidal regime and for tailoring the flow properties of nonspherical soft colloids.

Coupling of long-wavelength density fluctuations to orientations in cellulose nanocrystal suspensions under external fields.

Motivated by the development of cellulose-based functional materials, we investigate the microscopic dynamics of suspensions of cellulose nanocrystals (CNCs) at different ionic strengths, both in the absence and in the presence of AC electric fields and for various temperatures. A concentration of 5 wt% of the CNCs is chosen for which the dispersions are in the full chiral-nematic state at low ionic strengths. Dynamic light scattering is used to characterize the wave vector-dependent decay rates of number-density fluctuations. Contrary to an isotropic suspension, the dispersion relations (the wave vector dependence of the correlation-function decay rates) as obtained by means of depolarized light scattering are found to exhibit anomalous behavior. The dispersion relations, both without and with an external field, exhibit minima at small wave vectors, which is attributed to coupling of translational motion to the orientation of the CNCs, shown in the chiral-nematic state. The location of the minima is found to weakly depend on ionic strength and shifts significantly towards larger wave vectors upon applying an external electric field for sufficiently high ionic strengths. Finally, preliminary results are presented for smaller length-scale density fluctuations (at larger wave vectors) as a function of temperature, revealing the anisotropic mobilities in the chiral-nematic state of CNCs.

Spherically symmetric stationary flows of a gas suspension

The dynamics of an isothermal gas suspension is studied. A spherically symmetric stationary submodel is derived and partially integrated. In a barochronous case, this submodel is fully integrated and results are discussed. Different modes of motion are analytically described in the barochronous case. The interpretation of the solutions is proposed. We highlight three essentially different modes of motion. In the first mode, we have a dispersion of gas suspension from the origin with a relaxation of velocities and leading to the uniform motion. In the second mode, phases focus in the origin with finite nonzero velocities and infinitely increasing densities. In the third mode, phases are interpenetrating to each other and decelerating due to the friction force, that leads to an accumulation of particles and an unlimited increase of densities in different nonzero raduises with zero velocities.

Direct numerical simulations of viscous suspensions with variably shaped crystals

Our ability to numerically model and understand the complex flow behavior of solid-bearing suspensions has increased significantly over the last couple of years, partly due to direct numerical simulations that compute flow around individual immersed particles. Direct numerical simulations hence resolve suspension dynamics in unprecedented detail. While most previous studies focus on spherical particles, we develop a direct numerical approach to also capture rectangular particles. Our approach uses distributed Lagrange multipliers to enforce rigid-body motion in the solid domain in combination with an immersed boundary method to correctly enforce the no-slip constraint on the solid-fluid interfaces. An important component of our model is an efficient particle collision scheme that prevents overlap between particles of different shapes and allows for the transfer of both translational and angular momentum during particle collision. We verify and validate our numerical method through several benchmark cases. Applied to particulate suspensions, we test the hypothesize that particle rotations alter the aggregated dynamics of the suspension even if the relative rotational energy of the particles remains small as compared to the translational energy. At low solid fraction, we reproduce experimental observations of strongly nonlinear coupling between rectangular particles that is reminiscent of particle aggregation in the inertial regime but occurs at zero Reynolds number as a result of the long-range interaction between non-spherical particles. At intermediate solid fraction, we show that particle rotations can destabilize force chains. The dynamic consequences include the delayed onset of jamming and strong nonlinear coupling to the flow field in the fluid domain, which channelizes more strongly for rectangular as compared to spherical particles. Our model was motivated specifically by the need to better understand hazardous, crystal-bearing lava flows, but our insights generalize to viscous suspension flow in other scientific or engineering contexts.

Suspension Dynamics in an Optical Field

Suspension Dynamics in an Optical Field

Research of the impact of geometric unevenness of the railway track on the dynamic parameters of the railway rolling stock with two-stage spring suspension

The paper studies the possibility of using previously developed by the authors spatial mathematical model of the modern diesel train DPKr-2 for parameters determination, with the help of which the dynamic properties of the mechanical part are evaluated. The dependences of maximum accelerations of the body in the vertical and horizontal planes, the coefficients of vertical and horizontal dynamics both in the primary and in the secondary suspension on the speed of the car movement, the amplitude and the length of geometrical unevenness of the railway track were obtained. It is established at what speeds, depending on the parameters of geometrical unevenness of the railway track, the phenomenon of resonance and danger for the diesel train car movement appears. For a particular length of geometrical unevenness, the maximum permissible value of its amplitude over the entire range of speed movement, where the coefficients of vertical and horizontal dynamics in the primary suspension do not exceed permissible limits, has been studied. The adequacy of the mathematical model is checked by comparing the results obtained during calculations with the experimental ones.

Mesoscale simulation of soft particles with tunable contact angle in multicomponent fluids.

Soft particles at fluid interfaces play an important role in many aspects of our daily life, such as the food industry, paints and coatings, and medical applications. Analytical methods are not capable of describing the emergent effects of the complex dynamics of suspensions of many soft particles, whereas experiments typically either only capture bulk properties or require invasive methods. Computational methods are therefore a great tool to complement experimental work. However, an efficient and versatile numerical method is needed to model dense suspensions of many soft particles. In this article we propose a method to simulate soft particles in a multicomponent fluid, both at and near fluid-fluid interfaces, based on the lattice Boltzmann method, and characterize the error stemming from the fluid-structure coupling for the particle equilibrium shape when adsorbed onto a fluid-fluid interface. Furthermore, we characterize the influence of the preferential contact angle of the particle surface and the particle softness on the vertical displacement of the center of mass relative to the fluid interface. Finally, we demonstrate the capability of our model by simulating a soft capsule adsorbing onto a fluid-fluid interface with a shear flow parallel to the interface, and the covering of a droplet suspended in another fluid by soft particles with different wettability.

Hydrodynamics in unbaffled liquid-solid stirred tanks with free surface studied by DEM-VOF method

DEM-VOF simulations of particle suspension dynamics in unbaffled liquid-solid stirred tanks with free surface were performed in conjunction with RSM turbulence model. The two-way coupling of particle and fluid was achieved by solving Gidaspow’s drag force, non-drag force and source term in the momentum equation. The calculation of particle volume in the fluid was realized by the porous model. Particle-particle and particle-wall interactions were also considered. A four-blade 45° pitched blade turbine was used, and the sliding-grid has been adopted to simulate impeller rotating. DEM-VOF coupling method was validated by theories and experiments. The effects of tank geometries, impeller rotating speed, particle density, diameter and volume fraction on the free surface vortex, flow patterns and particle suspension dynamics were investigated by DEM-VOF method for the first time. Results indicate that the particle-fluid interaction has important effects on the flow field and particle distribution. The modifications of tank geometries substantially influence flow patterns and particle suspension behaviors. The profiled bottom could eliminate sharp flow diversions completely. It can give rise to off-bottom suspension of particles and an elimination of the surface vortex due to particle-fluid interaction for large solid holdup and large particle diameter. Furthermore, the base of the profiled bottom tank was optimized. The reported research data has important guiding significance for the design of stirred tanks.

Traveling band formation in feedback-driven colloids.

Using simulation and theory we study the dynamics of a colloidal suspension in two dimensions subject to a time-delayed repulsive feedback that depends on the positions of the colloidal particles. The colloidal particles experience an additional potential that is a superposition of repulsive potential energies centered around the positions of all the particles a delay time ago. Here we show that such a feedback leads to self-organization of the particles into traveling bands. The width of the bands and their propagation speed can be tuned by the delay time and the range of the imposed repulsive potential. The emerging traveling band behavior is observed in Brownian dynamics computer simulations as well as microscopic dynamic density functional theory. Traveling band formation also persists in systems of finite size leading to rotating traveling waves in the case of circularly confined systems.