We study the impact between a plate and a drop of non-colloidal solid particles suspended in a Newtonian liquid, with a specific attention to the case when the particle volume fraction, $ϕ$, is close to - or even exceeds - the critical volume fraction, $ϕ_c$, at which the steady effective viscosity of the suspension diverges. We use a specific concentration protocol together with an accurate determination of $ϕ$ for each drop and we measure the deformation $β$ for different liquid viscosities, impact velocities and particle sizes. At low volume fractions, $β$ is found to follow closely an effective Newtonian behavior, which we determine by documenting the low deformation limit for a highly viscous Newtonian drop and characterizing the effective shear viscosity of our suspensions. By contrast, whereas the effective Newtonian approach predicts that $β$ vanishes at $ϕ_c$, a finite deformation is observed for $ϕ>ϕ_c$. This finite deformation remains controlled by the suspending liquid viscosity and increases with increasing particle size, which suggests that the dilatancy of the particle phase is a key factor of the dissipation process close to and above $ϕ_c$.
The dynamics of ideally polarizable spherical particles in concentrated suspensions under the effects of nonlinear electrokinetic phenomena is analysed using large-scale numerical simulations. Particles are assumed to carry no net charge and considered to undergo the combination of dielectrophoresis and induced-charge electrophoresis termed dipolophoresis. Chaotic motion and resulting hydrodynamic diffusion are known to be driven by the induced-charge electrophoresis, which dominates the dielectrophoresis. Up to a volume fraction $ϕ\approx 35\%$, the particle dynamics seems to be hindered by t…
Evolution of a suspension drop entrained by Poiseuille flow is studied numerically at a low Reynolds number. A suspension drop is modelled by a cloud of many non-touching particles, initially randomly distributed inside a spherical volume of a viscous fluid which is identical to the host fluid outside the drop. Evolution of particle positions and velocities is evaluated by the accurate multipole method corrected for lubrication, implemented in the {\sc hydromultipole} numerical code. Deformation of the drop is shown to be smaller for a larger volume fraction. At high concentrations, hydrodynam…
We investigate theoretically and experimentally how the hydrodynamically correlated lateral motion of particles in a suspension confined between two surfaces is affected by the suspension concentration. Despite the long range of the correlations (decaying as 1/r^2 with the inter-particle distance r), the concentration effect is present only at short inter-particle distances for which the static pair correlation is nonuniform. This is in sharp contrast with the effect of hydrodynamic screening present in unconfined suspensions, where increasing the concentration changes the prefactor of the lar…
The response of a suspension under a variety of static or alternating external fields strongly depends on the equilibrium electric double layer that surrounds the colloidal particles in the suspension. The theoretical models for salt-free suspensions can be improved by incorporating non-uniform size effects and orientational ordering of water dipoles neglected in previous mean-field approaches, which are based on the Poisson-Boltzmann approach. Our model including non-uniform size effects and orientational ordering of water dipoles seems to have quite a promising effect because the model can p…
In our recent work on concentrated suspensions of uniformly porous colloidal spheres with excluded volume interactions, a variety of short-time dynamic properties were calculated, except for the rotational self-diffusion coefficient. This missing quantity is included in the present paper. Using a precise hydrodynamic force multipole simulation method, the rotational self-diffusion coefficient is evaluated for concentrated suspensions of permeable particles. Results are presented for particle volume fractions up to 45%, and for a wide range of permeability values. From the simulation results an…
When a droplet is generated, the ligament connecting the drop to the nozzle thins down and eventually pinches off. Adding solid particles to the liquid phase leads to a more complex dynamic, notably by increasing the shear viscosity. Moreover, it introduces an additional length scale to the system, the diameter of the particles, which eventually becomes comparable to the diameter of the ligament. In this paper, we experimentally investigate the thinning and pinch-off of drops of suspensions with two different sizes of particles. We characterize the thinning for different particle size ratios a…
The stability of two-dimensional Poiseuille flow and plane Couette flow for concentrated suspensions is investigated. Linear stability analysis of the two-phase flow model for both flow geometries shows the existence of a convectively driven instability with increasing growth rates of the unstable modes as the particle volume fraction of the suspension increases. In addition it is shown that there exists a bound for the particle phase viscosity below which the two-phase flow model may become ill-posed as the particle phase approaches its maximum packing fraction. The case of two-dimensional Po…
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…
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 …
A new two-phase model for concentrated suspensions is derived that incorporates a constitutive law combining the rheology for non-Brownian suspension and granular flow. The resulting model exhibits a yield-stress behavior for the solid phase depending on the collision pressure. This property is investigated for the simple geometry of plane Poiseuille flow, where an unyielded or jammed zone of finite width arises in the center of the channel. For the steady states of this problem, the governing equations are reduced to a boundary value problem for a system of ordinary differential equations and…
We investigate imbibition of a monodisperse emulsion into a low-aspect ratio microfluidic channel with the height h comparable to the droplet diameter d. For confinement ratio d/h = 1.2, the tightly confined disk-like droplets in the channel move more slowly compared to the average suspension velocity. Behind the meniscus that drives the imbibition, there is a droplet-free region, separated from the suspension region by a sharp concentration front. The suspension exhibits strong droplet density and velocity fluctuations, but on average, the suspension domain remains uniform. For weaker confine…
We investigate the 3D structure and drying dynamics of complex mixtures of emulsion droplets and colloidal particles, using confocal microscopy. Air invades and rapidly collapses large emulsion droplets, forcing their contents into the surrounding porous particle pack at a rate proportional to the square of the droplet radius. By contrast, small droplets do not collapse, but remain intact and are merely deformed. A simple model coupling the Laplace pressure to Darcy's law correctly estimates both the threshold radius separating these two behaviors, and the rate of large-droplet evacuation. Fin…
This paper reports experiments on the shear transient response of concentrated non-Brownian suspensions. The shear viscosity of the suspensions is measured using a wide-gap Couette rheometer equipped with a Particle Image Velocimetry (PIV) device that allows measuring the velocity field. The suspensions made of PMMA particles (31$μ$m in diameter) suspended in a Newtonian index- and density-matched liquid are transparent enough to allow an accurate measurement of the local velocity for particle concentrations as high as 50%. In the wide-gap Couette cell, the shear induced particle migration is …
The deposition of particles on a substrate by drying a colloidal suspension droplet is at the core of applications ranging from traditional printing on paper to printable electronics or photovoltaic devices. The self-pinning induced by the accumulation of particles at the contact line plays an important role in the formation of the deposition. In this paper, we investigate both numerically and theoretically, the effect of friction between the particles and the substrate on the deposition pattern. Without friction, the contact line shows a stick-slip behaviour and a dot-like deposit is left aft…
The impact of drops of concentrated non-Brownian suspensions (cornstarch and polystyrene spheres) onto a solid surface is investigated experimentally. The spreading dynamics and maxi- mal deformation of the droplet of such shear thickening liquids are found to be markedly different from the impact of Newtonian drops. A particularly striking observation is that the maximal de- formation is independent of the drop velocity and that the deformation suddenly stops during the impact phase. Both observations are due to the shear-thickening rheology of the suspensions, as is theoretically explained f…
We experimentally investigated the splashing of dense suspension droplets impacting a solid surface, extending prior work to the regime where the viscosity of the suspending liquid becomes a significant parameter. The overall behavior can be described by a combination of two trends. The first one is that the splashing becomes favored when the kinetic energy of individual particles at the surface of a droplet overcomes the confinement produced by surface tension. This is expressed by a particle-based Weber number $We_p$. The second is that splashing is suppressed by increasing the viscosity of …
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…
We investigate the impact of droplets of dense suspensions onto a solid substrate. We show that a global hydrodynamic balance is unable to predict the splash onset and propose to replace it by an energy balance at the level of the particles in the suspension. We experimentally verify that the resulting, particle-based Weber number gives a reliable, particle size and density dependent splash onset criterion. We further show that the same argument also explains why in bimodal systems smaller particles are more likely to escape than larger ones.
Under an applied traction, highly concentrated suspensions of solid particles in fluids can turn from a state in which they flow to a state in which they counteract the traction as an elastic solid: a shear-jammed state. Remarkably, the suspension can turn back to the flowing state simply by inverting the traction. A tensorial model is presented and tested in paradigmatic cases. We show that, to reproduce the phenomenology of shear jamming in generic geometries, it is necessary to link this effect to the elastic response supported by the suspension microstructure rather than to a divergence of…
In this article, we study the spreading of droplets of density-matched granular suspensions on the surface of a solid. Bidispersity of the particle size distribution enriches the conclusions drawn from monodisperse experiments by highlighting key elements of the wetting dynamics. In all cases, the relation between the dynamic contact angle and the velocity of the contact line follows a similar relation as that of a simple fluid, despite the complexity introduced by the presence of particles. We extract from this relation an apparent wetting viscosity of the suspensions that differs from that m…
We investigate the rheology of strain-hardening spherical capsules, from the dilute to the concentrated regime under a confined shear flow using three-dimensional numerical simulations. We consider the effect of capillary number, volume fraction and membrane inextensibility on the particle deformation and on the effective suspension viscosity and normal stress differences of the suspension. The suspension displays a shear-thinning behaviour which is a characteristic of soft particles such as emulsion droplets, vesicles, strain-softening capsules, and red blood cells. We find that the membrane …
The rheological behaviors of suspension of ideally conductive particles in an electric field are studied using large-scale numerical simulations in the limit of zero-shear-rate flow. Under the action of an electric field, the particles undergo the nonlinear electrokinetic phenomenon termed as dipolophoresis, which is the combination of dielectrophoresis and induced-charge electrophoresis. For ideally conductive particles, the dynamics of the suspension are primarily controlled by induced-charge electrophoresis. To characterize the rheological properties of the suspension, the particle stress t…
We describe and summarize a class of minimal numerical models emerged from recent development of simulation methods for dense particle suspensions in overdamped linear flows. The main ingredients include (i) a frame-invariant, short-range lubrication model for spherical particles, and (ii) a soft-core, stick/slide frictional contact model activated when particles overlap. We implement a version of the model using a modified velocity-Verlet algorithm that explicitly solves the $N$-body dynamical system in $\mathcal{O}(cN)$ operations, where $c$ is a kernel constant depending on the cutoff of pa…
Using absorbance measurements through a Couette cell containing an emulsion of buoyant droplets, volume fraction profiles are measured at various shear rates. These viscous resuspension experiments allow a direct determination of the normal stress in the vorticity direction in connection with the suspension balance model that has been developed for suspensions of solid particles. The results unambigously show that the normal viscosity responsible for the shear-induced migration of the droplets is independant on the capillary number, implying that particle deformation does not play a great role…
A concentrated, vertical monolayer of identical spherical squirmers, which may be bottom-heavy, and which are subjected to a linear shear flow, is modelled computationally by two different methods: Stokesian dynamics, and a lubrication-theory-based method. Inertia is negligible. The aim is to compute the effective shear viscosity and, where possible, the normal stress differences as functions of the areal fraction of spheres $ϕ$, the squirming parameter $β$ (proportional to the ratio of a squirmer's active stresslet to its swimming speed), the ratio $Sq$ of swimming speed to a typical speed of…
Understanding flow patterns and coupled transport phenomena during evaporation of droplets loaded with colloidal particles is central to design technical applications such as organizing proteins/DNA on a solid surface. We review recent reports on evaporating sessile droplets of colloidal suspensions on a solid surface. Starting from the classical mechanism of formation of a ring-like deposit, we discuss the influence of several problem parameters. Notably, thermal or solutal Marangoni effect, particle size, particle concentration, particle shape, substrate wettability, pH of the suspension etc…
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）
Concentrated suspensions may shear-thin when the suspended particles form planar sheets that slide over one another with less friction than if the particles are randomly distributed. In a naïve model the suspension is described by a mean effective viscosity, and particles that collide with each other redistribute the mean density in the shearing direction. This leads to a diffusion equation for the particle density. If the viscosity in the unthinned state is a steeply increasing function of particle density the effective diffusion coefficient is negative and the diffusion equation, meaningful …
The present study deals with the effect of interfacial slip on the deformation and emulsion rheology of a dilute suspension of droplets in a linear flow. The droplets are laden with surfactants that are bulk-insoluble and get transported only along the interface. An asymptotic approach is adopted for the present analysis in order to tackle the nonlinearity present due to deformation of droplets. The analysis is carried out under two different limiting scenarios namely: surface diffusion-dominated-surfactant transport and surface convection-dominated surfactant transport. For either of the limi…
The formation of drops of a complex fluid, for instance including dissolved polymers and/or solid particles, has practical implications in several industrial and biophysical processes. In this Letter, we experimentally investigate the generation of drops of a viscoelastic suspension, made of non-Brownian spherical particles dispersed in a dilute polymer solution. Using high-speed imaging, we characterize the different stages of the detachment. Our experiments show that the particles primarily affect the initial Newtonian necking by increasing the fluid viscosity. In the viscoelastic regime, pa…
Laboratory experiments were conducted to study particle migration and flow properties of non- Brownian, non-colloidal suspensions ranging from 10% to 40% particle volume fraction in a pressure-driven flow over and through a porous structure at low Reynolds number. Particle concentration maps, velocity maps and corresponding profiles were acquired using a magnetic resonance imaging (MRI) technique. The model porous medium consists of square arrays of circular rods oriented across the flow in a rectangular microchannel. It was observed that the square arrays of the circular rods modify the veloc…
Droplet microfluidics, in which micro-droplets serve as individual reactors, has enabled a wide range of high-throughput biochemical processes. Unlike solid wells typically used in current biochemical assays, droplets are subject to instability and can undergo breakup, especially under fast flow conditions. Although the physics of single drops has been studied extensively, the flow of crowded drops or concentrated emulsions, where droplet volume fraction exceeds 80 percent, is relatively unexplored in microfluidics. In this article and the related invited lecture from the 74th Annual Meeting o…
In Stokesian Dynamics, particles are assumed to interact in two ways: through long-range mobility interactions and through short-range lubrication interactions. To speed up computations, in shear-driven concentrated suspensions, often found in rheometric contexts, it is common to consider only lubrication. We show that, although this approximation may provide acceptable results in shear-driven, periodic suspensions, for bidisperse suspensions where the particles are exposed to an external force, it can produce physically unreasonable results. We suggest that this problem could be mitigated by …
The displacement of a suspension of particles by an immiscible fluid in a capillary tube or in a porous media is a canonical configuration that finds application in a large number of natural and industrial applications, including water purification, dispersion of colloids and microplastics, coating and functionalization of tubings. The influence of particles dispersed in the fluid on the interfacial dynamics and on the properties of the liquid film left behind remain poorly understood. Here, we study the deposition of a coating film on the walls of a capillary tube induced by the translation o…
We use experiments and minimal numerical models to investigate the rapidly expanding monolayer formed by the impact of a dense suspension drop against a smooth solid surface. The expansion creates a lace-like pattern of particle clusters separated by particle-free regions. Both the expansion and the development of the spatial inhomogeneity are dominated by particle inertia, therefore robust and insensitive to details of the surface wetting, capillarity and viscous drag.
We analyze fluctuations of particle displacements and stresses in a sheared athermal suspension of elastic capsules (red blood cells). Upon variation of the volume fraction from the dilute up to the highly concentrated regime, our numerical simulations reveal different characteristic power-law regimes of the fluctuation variances and relaxation times. In the jammed phase and at high shear rates, anomalous scaling exponents are found that deviate from pure dimensional predictions. The observed behavior is rationalized via kinetic arguments and a dissipation balance model that takes into account…
A numerical study of suspension plasma spraying (SPS) is presented in the current work. The liquid suspension jet is replaced with a train of droplets containing the suspension particles injected into the plasma flow. Atomization, evaporation, and melting of different components are considered for droplets and particles as they travel towards the substrate. Effect of different parameters on particle conditions during flight and upon impact on the substrate are investigated. Initially, influence of the torch operating conditions such as inlet flow rate and power are studied. Additionally, effec…
We have proposed and investigated a model of drying colloidal suspension drop placed onto a horizontal substrate in which the sol to gel phase transition occurs. The temporal evolution of volume fraction of the solute and the gel phase dynamics were obtained from numerical simulations. Our model takes into account the fact that some physical quantities are dependent on volume fraction of the colloidal particles.
We present a numerical study on the rheology of semi-dilute and concentrated filament suspensions of different bending stiffness and Reynolds number, with the immersed boundary method used to couple the fluid and solid. The filaments are considered as one-dimensional inextensible slender bodies with fixed aspect ratio, obeying the Euler-Bernoulli beam equation. To understand the global suspension behavior we relate it to the filament microstructure, deformation and elastic energy and examine the stress budget to quantify the effect of the elastic contribution. At fixed volume fraction, the vis…
Coalescence event in pendant and sessile drop is distinguished by the formation and evolution of the liquid bridge created upon singular contact. The bridge radius, $R$, is known to evolve as $R\sim t^b$, with power-law exponent, $b$, signifying the dominant governing forces. In this work, we experimentally explore the phenomenon in sub-classes of complex fluids namely, colloidal and non-colloidal suspensions that have particle hydrodynamic interactions as origin of viscoelasticity. Our observations suggest that such fluids have flow dependent thinning response with finite elasticity in shear …
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…
The features of turbulence modulation produced by a heavy loaded suspension of small solid particles or liquid droplets are discussed by using a physically-based regularisation of particle-fluid interactions. The approach allows a robust description of the small scale properties of the system exploiting the convergence of the statistics with respect to the regularisation parameter. It is shown that sub-Kolmogorov particles/droplets modify the energy spectrum leading to a scaling law, $E(k)\propto k^{-4}$, that emerges at small scales where the particle forcing balances the viscous dissipation.…
The statistics of velocity differences between very heavy inertial particles suspended in an incompressible turbulent flow is found to be extremely intermittent. When particles are separated by distances within the viscous subrange, the competition between quiet regular regions and multi-valued caustics leads to a quasi bi-fractal behavior of the particle velocity structure functions, with high-order moments bringing the statistical signature of caustics. Contrastingly, for particles separated by inertial-range distances, the velocity-difference statistics is characterized in terms of a local …
We report experimental observations of turbulent flow with spherical particles in a square duct. Three particle sizes namely: $2H/d_{p}$ = 40, 16 and 9 ($2H$ being the duct full height and $d_{p}$ being the particle diameter) are investigated. The particles are nearly neutrally-buoyant with respect to the suspending fluid. Refractive Index Matched - Particle Image Velocimetry is used for fluid velocity measurement even at the highest particle volume fraction (20%) and Particle Tracking Velocimetry for the particle velocity statistics for the flows seeded with particles of the two largest sizes…
We study the typical collisional velocities in a polydisperse suspension of droplets in two and three-dimensional turbulent flow and obtain precise theoretical estimates of the dependence of the impact velocity of particles-pairs on their relative sizes. These analytical results are validated against data from our direct numerical simulations. We show that the impact velocity saturates exponentially with the inverse of the particle-size ratios. Our results are important to model coalescence or fragmentation (depending on the impact velocities) and will be crucial, for example, in obtaining pre…
