The present study investigates the gravity-driven settling dynamics of non-Brownian suspensions of spherical and cubic particles within a triply periodic domain. The effect of solid volume fraction on the evolving microstructure of a suspension is numerically examined by employing the Rigid MultiBlob method under Stokes flow conditions. Our simulations accurately reproduce macroscopic trends observed in experiments and show strong agreement with established semi-empirical correlations over a wide range of volume fractions. It is observed that the hydrodynamic interactions between particles and the surrounding fluid dominate the settling mechanism at low to moderate solid volume fractions, whereas, frequent collisions between particles in a highly packed space tend to suppress velocity fluctuations at denser regime. The transport properties for dilute suspensions are found to be primarily shaped by an anisotropic microstructure, though this anisotropy decreases as many-body interactions significantly grow at higher volume fractions. Notably, cubic particles exhibit lower anisotropy in velocity fluctuations compared to spheres, due to more effective momentum and energy transfer from the gravity-driven direction to transverse directions. Moreover, cubic particles also display higher velocity fluctuations and particle rebounding after collisions, which may create a transient tendency for cubes to move against gravity more readily than spheres. The distinctive behaviors of cubic and spherical particles can notably influence the efficiency of size segregation in bidisperse mixtures. Interestingly, local velocity fluctuation intensity increases for both particle types in mixed suspensions, affecting the local sedimentation velocity field. Overall, spherical particles are found to settle faster than cubes at low to moderate volume fractions.
Nanoparticle suspensions (also called nanofluids) are often polydisperse and tend to settle with time. Settling kinetics in these systems are known to be complex and hence challenging to understand. In this work, polydisperse spherical alumina (Al2O3) nanoparticles in the size range of ~10-100nm were dispersed in water and examined for aggregation and settling behaviour near its isoelectric point (IEP). A series of settling experiments were conducted and the results were analysed by photography and by Small Angle X-ray Scattering (SAXS). The settling curve obtained from standard bed height mea…
The evolution of suspension drops sedimenting under gravity in a viscous fluid close to a vertical wall was studied experimentally and numerically with the use of the point-force model, in the Stokes flow regime. The fluid inside and outside the drop was identical. The initial distribution of the suspended solid heavy particles was uniform inside a spherical volume. In the experiments and in the simulations, the suspension drops evolved qualitatively in the same way as in an unbounded fluid. However, it was observed, both experimentally and numerically that, on the average, the destabilization…
Dynamic particle-scale numerical simulations are used to show that the shear thickening observed in dense colloidal, or Brownian, suspensions is of a similar nature to that observed in non-colloidal suspensions, i.e., a stress-induced transition from a flow of lubricated near-contacting particles to a flow of a frictionally contacting network of particles. Abrupt (or discontinuous) shear thickening is found to be a geometric rather than hydrodynamic phenomenon; it stems from the strong sensitivity of the jamming volume fraction to the nature of contact forces between suspended particles. The t…
The settling efficiency, and stability with respect to settling, of a dilute suspension of infinite circular cylinders in a quiescent viscoplastic fluid is examined by means of direct numerical simulations with varying solid volume fraction, $ϕ$, and yield number, $Y$ . For $Y$ sufficiently large we find higher settling efficiency for increasing $ϕ$, similar to what is found in shear-thinning fluids and opposite to what is found in Newtonian fluids. The critical yield number at which the suspension is held stationary in the carrier fluid is found to increase monotonically with $ϕ$, while the t…
We propose a unifying mechanism based on the Stribeck curve for the coefficient of friction between the particles to capture the shear thinning - Newtonian plateau - shear thickening - shear thinning rheological behavior at low - intermediate - beyond critical - high shear rates, respectively, for a typical dense non-Brownian suspension. We establish the accuracy of the proposed model by comparing the numerical results with experimental data. The presence of non-DLVO (Derjaguin and Landau, Verwey and Overbeek) forces and a coefficient of friction reducing with asperity deformation explain the …
The settling of heavy spherical particles in a column of quiescent fluid is investigated. The performed experiments cover a range of Galileo numbers ($110 \leq \text{Ga} \leq 310$) for a fixed density ratio of $Γ= ρ_p/ρ_f = 2.5$. In this regime the particles are known (M. Jenny, J. Dušek and G. Bouchet, Journal of Fluid Mechanics 508, 201 (2004).) to show a variety of motions. It is known that the wake undergoes several transitions for increasing $\text{Ga}$ resulting in particle motions that are successively: vertical, oblique, oblique oscillating, and finally chaotic. Not only does this chan…
We present experimental results on dense corn-starch suspensions as examples of non-Brownian, nearly-hard particles that undergo continuous and discontinuous shear thickening (CST and DST) at intermediate and high densities respectively. Our results offer strong support for recent theories involving a stress-dependent effective contact friction among particles. We show however that in the DST regime, where theory might lead one to expect steady-state shear bands oriented layerwise along the vorticity axis, the real flow is unsteady. To explain this, we argue that steady-state banding is generi…
In addition to enabling movement towards environments with favourable living conditions, swimming by microorganisms has also been linked to enhanced mixing and improved nutrient uptake by their populations. Experimental studies have shown that Brownian tracer particles exhibit enhanced diffusion due to the swimmers, while theoretical models have linked this increase in diffusion to the flows generated by the swimming microorganisms, as well as collisions with the swimmers. In this study, we perform detailed simulations based on the force-coupling method and its recent extensions to the swimmin…
Immiscible contaminants are commonly involved in naturally occurring suspensions. The resulting variations of their flow behavior has rarely been evaluated. Here, we investigate the variation of the viscosity of the oil-based two-phase suspension over a period of two years, which is exposed to the ambient air at the production stage. We find that the air's absolute humidity, which strongly varies with the seasons, causes exchanges of water droplets with the suspension, substantially altering its shear-thinning behavior. Only in winter, when the humidity is low, is the latter close to that of i…
Shear thickening appears as an increase of the viscosity of a dense suspension with the shear rate, sometimes sudden and violent at high volume fraction. Its origin for noncolloidal suspension with non-negligible inertial effects is still debated. Here we consider a simple shear flow and demonstrate that fluid inertia causes a strong microstructure anisotropy that results in the formation of a shadow region with no relative flux of particles. We show that shear thickening at finite inertia can be explained as an increase of the effective volume fraction when considering the dynamically exclude…
Orientation and microstructure are investigated in sheared Brownian suspensions of hard dicolloidal particles, with the dicolloids modeled as two fused spheres of varying radii and center to center separations. Two different particle shapes named homonuclear (aspect ratio 1.1) and fused-dumbbells (aspect ratio 1.5) were considered. Hydrodynamic interactions between the particles were computed with a modified lubrication model called Fast Lubrication Dynamics. Studies were conducted for a wide range of volume fractions between $0.3 \leq ϕ\leq 0.5$ and Pèclet numbers between $0 \leq Pe \leq 1000…
Granular fronts are a common yet unexplained phenomenon emerging during the gravity driven free-surface flow of concentrated suspensions. They are usually believed to be the result of fluid convection in combination with particle size segregation. However, suspensions composed of uniformly sized particles also develop a granular front. Within a large rotating drum, a stationary recirculating avalanche is generated. The flowing material is a mixture of a visco-plastic fluid obtained from a kaolin-water dispersion, with spherical ceramic particles denser than the fluid. The goal is to mimic the …
We investigate the stability of the pressure-driven, low-Reynolds flow of Brownian suspensions with spherical particles in microchannels. We find two general families of stable/unstable modes: (i) degenerate modes with symmetric and anti-symmetric patterns; (ii) single modes that are either symmetric or anti-symmetric. The concentration profiles of degenerate modes have strong peaks near the channel walls, while single modes diminish there. Once excited, both families would be detectable through high-speed imaging. We find that unstable modes occur in concentrated suspensions whose velocity pr…
We analyze the angular dynamics of triaxial ellipsoids in a shear flow subject to weak thermal noise. By numerically integrating an overdamped angular Langevin equation, we find the steady angular probability distribution for a range of triaxial particle shapes. From this distribution we compute the intrinsic viscosity of a dilute suspension of triaxial particles. We determine how the viscosity depends on particle shape in the limit of weak thermal noise. While the deterministic angular dynamics depends very sensitively on particle shape, we find that the shape dependence of the intrinsic visc…
The orientation of small anisotropic particles settling in a turbulent fluid determines some essential properties of the suspension. We show that the orientation distribution of small heavy spheroids settling through turbulence can be accurately predicted by a simple Gaussian statistical model that takes into account particle inertia and provides a quantitative understanding of the orientation distribution on the problem parameters when fluid inertia is negligible. Our results open the way to a parameterisation of the distribution of ice-crystals in clouds, and potentially leads to an improved…
Suspensions of non-Brownian rods: droplet pinch-off, onset of heterogeneity and effective extensional viscosity
PMMH, CNRS, ESPCI Paris, Sorbonne Université, Université Paris-Cité（PMHH，法国国家科学研究中心，巴黎高等物理化工学院，索邦大学，巴黎 Cité 大学）；Department of Mechanical Engineering, University of California, Santa Barbara（加州大学圣塔芭芭拉分校机械工程系）；Institute of Physics, University of Amsterdam（阿姆斯特丹大学物理研究所）；Department of Mechanical Engineering, University of Maryland（马里兰大学机械工程系）；Department of Chemical and Biomolecular Engineering, University of Maryland（马里兰大学化学与生物分子工程系）
In this paper, the finite element method is combined with the Brownian Configuration Field (BFC) method to simulate the fibre suspension flow in axisymmetric contraction and expansion passages. In order to solve for the high stress at high concentration, the Discrete Adaptive Viscoelastic Stress Splitting (DAVSS) method is employed. For the axisymmetric contraction and expansion passages with different geometry ratios, the results obtained are compared to available constitutive models and experiments. The predicted vortex length for dilute suspensions agrees well with experimental data in lite…
Particles suspended in a Newtonian fluid raise the viscosity and also generally give rise to a shear-rate dependent rheology. In particular, pronounced shear thickening may be observed at large solid volume fractions. In a recent article (R. Seto, R. Mari, J. F. Morris, and M. M. Denn., Phys. Rev. Lett., 111:218301, 2013) we have considered the minimum set of components to reproduce the experimentally observed shear thickening behavior, including Discontinuous Shear Thickening (DST). We have found frictional contact forces to be essential, and were able to reproduce the experimental behavior b…
Attractive colloidal dispersions, suspensions of fine particles which aggregate and frequently form a space spanning elastic gel are ubiquitous materials in society with a wide range of applications. The colloidal networks in these materials can exist in a mode of free settling when the network weight exceeds its compressive yield stress. An equivalent state occurs when the network is held fixed in place and used as a filter through which the suspending fluid is pumped. In either scenario, hydrodynamic instabilities leading to loss of network integrity occur. Experimental observations have sho…
The Clausius Virial theorem of Classical Kinetic Theory is used to evaluate the pressure of a suspension of small particles at equilibrium in an isotropic homogeneous and stationary turbulent flow. It then follows a similar approach to the way Einstein (1905) evaluated the diffusion coefficient of Brownian particles (leading to the Stokes-Einstein relation) to similarly evaluate the long term diffusion coefficient of the suspended particles. In contrast to Brownian motion, the analogue of temperature in the equation of state which relates pressure to particle density is not the kinetic energy …
We analyze experimentally the behavior of a non-Brownian, iso-dense suspension of spheres submitted to periodic square wave oscillations of the flow in a Hele-Shaw cell of gap $H$. We do observe an instability of the initially homogeneous concentration in form of concentration variation stripes transverse to the flow. The wavelength of these regular spatial structures scales roughly as the gap of the cell and is independent of the particle concentration and of the period of oscillation. This instability requires large enough particle volume fractions $ϕ\geq 0.25$, a gap large enough compared t…
We experimentally investigate particle migration in a non-Brownian suspension sheared in a Taylor-Couette configuration and in the limit of vanishing Reynolds number. Highly resolved index-matching techniques are used to measure the local particulate volume fraction. In this wide-gap Taylor-Couette configuration, we find that for a large range of bulk volume fraction, $ϕ_b \in [20\% - 50\%]$, the fully developed concentration profiles are well predicted by the suspension balance model of Nott \& Brady (J. Fluid Mech., vol. 275, 1994, pp. 157-199). Moreover, we provide systematic measurements o…
The resolution of Brownian motion in simulations of micro-particle suspensions can be crucial to reproducing the correct dynamics of individual particles, as well as providing an accurate characterisation of suspension properties. Including these effects in simulations, however, can be computationally intensive due to the configuration dependent random displacements that would need to be determined at every time step. In this paper, we introduce the fluctuating force-coupling method (FCM) to overcome this difficulty, providing a fast approach to simulate colloidal suspensions at large-scale. W…
Direct numerical simulation of the gravity-induced settling of finite-size particles in triply-periodic domains has been performed under dilute conditions. For a single solid-to-fluid density ratio of 1.5 we have considered two values of the Galileo number corresponding to steady vertical motion (Ga=121) and to steady oblique motion (Ga=178) in the case of one isolated sphere. For the multi-particle system we observe strong particle clustering only in the latter case. The geometry and time scales related to clustering are determined from Voronoi tesselation and particle-conditioned averaging. …
We investigate the development of mobility inversion and fingering when a granular suspension is injected radially between horizontal parallel plates of a cell filled with a miscible fluid. While the suspension spreads uniformly when the suspension and the displaced fluid densities are exactly matched, even a small density difference is found to result in a dense granular front which develops fingers with angular spacing that increase with granular volume fraction and decrease with injection rate. We show that the time scale over which the instability develops is given by the volume fraction d…
The dynamics of macroscopically homogeneous sheared suspensions of neutrally buoyant, non-Brownian spheres is investigated in the limit of vanishingly small Reynolds numbers using Stokesian dynamics. We show that the complex dynamics of sheared suspensions can be characterized as a chaotic motion in phase space and determine the dependence of the largest Lyapunov exponent on the volume fraction $ϕ$. The loss of memory at the microscopic level of individual particles is also shown in terms of the autocorrelation functions for the two transverse velocity components. Moreover, a negative correlat…
Sedimentation in active fluids has come into focus due to the ubiquity of swimming micro-organisms in natural and artificial environments. Here, we experimentally investigate sedimentation of passive particles in water containing various concentrations of the bacterium E. coli. Results show that the presence of living bacteria reduces the velocity of the sedimentation front even in the dilute regime, where the sedimentation velocity is expected to be independent of particle concentration. Bacteria increase the effective diffusion coefficient of the passive particles, which determines the width…
Withdrawing a plate from a suspension leads to the entrainment of a coating layer of fluid and particles on the solid surface. In this article, we study the Landau-Levich problem in the case of a suspension of non-Brownian particles at moderate volume fraction $10\% < ϕ< 41\%$. We observe different regimes depending on the withdrawal velocity $U$, the volume fraction of the suspension $ϕ$, and the diameter of the particles $2\,a$. Our results exhibit three coating regimes. (i) At small enough capillary number $Ca$, no particles are entrained, and only a liquid film coats the plate. (ii) At lar…
A dilute suspension of motile microorganisms subjected to a strong ambient flow, such as algae in the ocean, can be modelled as a population of non-interacting, orientable active Brownian particles (ABPs). Using the Smoluchowski equation (i.e. Fokker-Planck equation in space and orientation), one can describe the non-trivial transport phenomena of ABPs such as taxis and shear-induced migration. This work transforms the Smoluchowski equation into a transport equation, in which the drifts and dispersions can be further approximated as a function of the local flow field. The new model can be appl…
In this work we develop the Spectral Ewald Accelerated Stokesian Dynamics (SEASD), a novel computational method for dynamic simulations of polydisperse colloidal suspensions with full hydrodynamic interactions. SEASD is based on the framework of Stokesian Dynamics (SD) with extension to compressible solvents, and uses the Spectral Ewald (SE) method [Lindbo & Tornberg, J. Comput. Phys. 229 (2010) 8994] for the wave-space mobility computation. To meet the performance requirement of dynamic simulations, we use Graphic Processing Units (GPU) to evaluate the suspension mobility, and achieve an orde…
A study on the spatial organization and velocity fluctuations of non Brownian spherical particles settling at low Reynolds number in a vertical Hele-Shaw cell is reported. The particle volume fraction ranged from 0.005 to 0.05, while the distance between cell plates ranged from 5 to 15 times the particle radius. Particle tracking revealed that particles were not uniformly distributed in space but assembled in transient settling clusters. The population distribution of these clusters followed an exponential law. The measured velocity fluctuations are in agreement with that predicted theoretical…
We study the settling of finite-size rigid spheres in sustained homogeneous isotropic turbulence (HIT) by direct numerical simulations using an immersed boundary method to account for the dispersed solid phase. We study semi-dilute suspensions at different Galileo numbers, Ga. The Galileo number is the ratio between buoyancy and viscous forces, and is here varied via the solid-to-fluid density ratio. The focus is on particles that are slightly heavier than the fluid. We find that in HIT, the mean settling speed is less than that in quiescent fluid; in particular, it reduces by 6%-60% with resp…
Tracer particles immersed in suspensions of biological microswimmers such as E. coli or C. reinhardtii display phenomena unseen in conventional equilibrium systems, including strongly enhanced diffusivity relative to the Brownian value and non-Gaussian displacement statistics. In dilute, 3-dimensional suspensions, these phenomena have typically been explained by the hydrodynamic advection of point tracers by isolated microswimmers, while, at higher concentrations, correlations between pusher microswimmers such as E. coli can increase the effective diffusivity even further. Anisotropic tracers …
We examine the spreading of a suspension of non-Brownian spheres suspended in a Newtonian liquid on a solid substrate. We show that the spreading dynamics is well described by the classical Cox-Voinov law provided the value of the fluid viscosity that arises in the capillary number of the problem is adjusted to a value that depends on particle size and volume fraction in a non-trivial way. We demonstrate that this behavior is a signature of the ability of the particles to approach the contact line close enough to affect dissipation.
