Hydrodynamic interactions in a suspension of spherical particles confined between two parallel planar walls are studied under creeping-flow conditions. The many-particle friction matrix in this system is evaluated using our novel numerical algorithm based on transformations between Cartesian and spherical representations of Stokes flow. The Cartesian representation is used to describe the interaction of the fluid with the walls and the spherical representation is used to describe the interaction with the particles. The transformations between these two representations are given in a closed form, which allows us to evaluate the coefficients in linear equations for the induced-force multipoles on particle surfaces. The friction matrix is obtained from these equations, supplemented with the superposition lubrication corrections. We have used our algorithm to evaluate the friction matrix for a single sphere, a pair of spheres, and for linear chains of spheres. The friction matrix exhibits a crossover from a quasi-two-dimensional behavior (for systems with small wall separation H) to the three-dimensional behavior (when the distance H is much larger than the interparticle distance L). The crossover is especially pronounced for a long chain moving in the direction normal to its orientation and parallel to the walls. In this configuration, a large pressure buildup occurs in front of the chain for small values of the gapwidth H, which results in a large hydrodynamic friction force. A standard wall superposition approximation does not capture this behavior.
We have shown [J.\ Fluid Mech.\ {\bf 592}, 447 (2007)] that swapping (reversing) trajectories in confined suspension flows prevent collisions between particles approaching each other in adjacent streamlines. Here we demonstrate that by inducing layering this hydrodynamic mechanism changes the microstructure of suspensions in a confined Couette flow. Layers occur either in the near-wall regions or span the whole channel width, depending on the strength of the swapping-trajectory effect. While our theory focuses on dilute suspensions, we postulate that this new hydrodynamic mechanism controls fo…
We run numerical simulations of strongly confined suspensions of model spherical swimmers called "squirmers". Because of the confinement, the Stokeslet dipoles generated by the particles are quickly screened and the far-field flow is dominated by the source dipole for all the different kinds of squirmers. However, we show that the collective behavior of the suspension still depends on the self-propelling mechanism of the swimmers as polar states can only be observed for neutral squirmers. We demonstrate that the near-field hydrodynamic interactions play a crucial role in the alignment of the o…
Hydrodynamic interactions between particles confined in a liquid-filled linear channel are known to be screened beyond a distance comparable to the channel width. Using a simple analytical theory and lattice-Boltzmann simulations, we show that the hydrodynamic screening is qualitatively modified when the time-dependent response and finite compressibility of the host liquid are taken into account. Diffusive compression modes in the confined liquid cause the particles to have velocity correlations of unbounded range, whose amplitude decays with time only as $t^{-3/2}$.
A mechanistic theory is developed to describe segregation in confined multicomponent suspensions such as blood. It incorporates the two key phenomena arising in these systems at low Reynolds number: hydrodynamic pair collisions and wall-induced migration. In simple shear flow, several regimes of segregation arise, depending on the value of a "margination parameter" M. Most importantly, there is a critical value of M below which a sharp "drainage transition" occurs: one component is completely depleted from the bulk flow to the vicinity of the walls. Direct simulations also exhibit this transit…
Strongly confined active liquids are subject to unique hydrodynamic interactions due to momentum screening and lubricated friction by the confining walls. Using numerical simulations, we demonstrate that 2D dilute suspensions of fore-aft asymmetric polar swimmers in a Hele-Shaw geometry can exhibit a rich variety of novel phase behaviors depending on particle shape, including: coherent polarized density waves with global alignment, stationary asters, persistent counter-rotating vortices, density shocks and rarefaction waves. We also explain these phenomena using a linear stability analysis 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…
Flowing blood displays a phenomenon called margination, in which leukocytes and platelets are preferentially found near blood vessel walls, while erythrocytes are depleted from these regions. Here margination is investigated using direct hydrodynamic simulations of a binary suspension of stiff (s) and floppy (f) capsules, as well as a stochastic model that incorporates the key particle transport mechanisms in suspensions -- wall-induced hydrodynamic migration and shear-induced pair collisions. The stochastic model allows the relative importance of these two mechanisms to be directly evaluated …
We study theoretically the velocity cross-correlations of a viscous fluid confined in a slit between two viscoelastic media. We analyze the effect of these correlations on the motions of particles suspended in the fluid. The compliance of the confining boundaries gives rise to a long-ranged pair correlation, decaying only as $1/r$ with the interparticle distance $r$. We show how this long-ranged effect may be used to extract the viscoelastic properties of the confining media without embedding tracer particles in them. We discuss the remarkable robustness of such a potential technique with resp…
Similarly to their biological counterparts, suspensions of chemically-active autophoretic swimmers exhibit nontrivial dynamics involving self-organization processes as a result of inter-particle interactions. Using a kinetic model for a dilute suspension of autochemotactic Janus particles, we analyse the effect of a confined pressure-driven flow on these collective behaviours and the impact of chemotactic aggregation on the effective viscosity of the active fluid. Four dynamic regimes are identified when increasing the strength of the imposed pressure-driven flow, each associated with a differ…
Low Reynolds number direct simulations of large populations of hydrodynamically interacting swimming particles confined between planar walls are performed. The results of simulations are compared with a theory that describes dilute suspensions of swimmers. The theory yields scalings with concentration for diffusivities and velocity fluctuations as well as a prediction of the fluid velocity spatial autocorrelation function. Even for uncorrelated swimmers, the theory predicts anticorrelations between nearby fluid elements that correspond to vortex-like swirling motions in the fluid with length s…
Concentrated suspensions of swimming microorganisms and other forms of active matter are known to display complex, self-organized spatio-temporal patterns on scales large compared to those of the individual motile units. Despite intensive experimental and theoretical study, it has remained unclear the extent to which the hydrodynamic flows generated by swimming cells, rather than purely steric interactions between them, drive the self-organization. Here we utilize the recent discovery of a spiral-vortex state in confined suspensions of \textit{B. subtilis} to study this issue in detail. Those …
We consider extensional flows of a dense layer of spheres in a viscous fluid and employ force and torque balances to determine the trajectory of particle pairs that contribute to the stress. In doing this, we use Stokesian dynamics simulations to guide the choice of the near-contacting pairs that follow such a trajectory. We specify the boundary conditions on the representative trajectory, and determine the distribution of particles along it and how the stress depends on the microstructure and strain rate. We test the resulting predictions using the numerical simulations. Also, we show that th…
Intricate fluid displacement patterns, arising from the unstable growth of interfacial perturbations, can be driven by fluid viscoelasticity and surface tension. A soft glassy suspension ages, $i.e.$ its mechanical moduli evolve with time, due to the spontaneous formation of suspension microstructures. The shear and time-dependent rheology of an aging suspension can be exploited to generate a wide variety of interfacial patterns during its displacement by a Newtonian fluid. Using video imaging, we report a rich array of interfacial pattern morphologies: dense viscous, dendritic, viscoelastic f…
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 …
We present experimental observations of the spatial distribution of large inertial particles suspended in a turbulent swirling flow at high Reynolds number. The plastic particles, which are tracked using several high speed cameras, are heavier than the working fluid so that their dynamics results from a competition between gravitational effects and turbulent agitation. We observe two different regimes of suspension. At low rotation rate, particles are strongly confined close to the bottom and are not able to reach the upper region of the tank whatever their size or density. At high rotation ra…
Phoretic particles self-propel using self-generated physico-chemical gradients at their surface. Within a suspension, they interact hydrodynamically by setting the fluid around them into motion, and chemically by modifying the chemical background seen by their neighbours. While most phoretic systems evolve in confined environments due to buoyancy effects, most models focus on their interactions in unbounded flows. Here, we propose a first model for the interaction of phoretic particles in Hele-Shaw confinement and show that in this limit, hydrodynamic and phoretic interactions share not only t…
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 …
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…
A Modified Suspension-Balance Model for Deformable Particle Suspensions: Application to Blood Flows with Cell-Free Layer
FAMU–FSU College of Engineering（FAMU-FSU工程学院）；University of New Mexico（新墨西哥大学）；Sandia National Laboratories（桑迪亚国家实验室）；Institute for Successful Longevity, Florida State University（佛罗里达州立大学成功长寿研究所）
We combine experiments, large scale simulations and continuum models to study the emergence of coherent structures in a suspension of magnetically driven microrollers sedimented near a floor. Collective hydrodynamic effects are predominant in this system, leading to strong density-velocity coupling. We characterize a uniform suspension and show that density waves propagate freely in all directions in a dispersive fashion. When sharp density gradients are introduced in the suspension, we observe the formation of a shock. Unlike Burgers' shock-like structures observed in other active and driven …
Small-scale effects of turbulent mixing are numerically investigated by applying the map-based, stochastic, one-dimensional turbulence (ODT) model to confined planar jets. The model validation is carried out for the momentum transport by comparing ODT results to available reference data for the bulk Reynolds numbers $Re=20\,000$ and $40\,000$. Various pointwise statistical quantities are computed and compared to the available reference data. We show that these quantities can be captured well, or at least to a reasonable extent, by the stand-alone model formulation and for fixed model parameter…
Clogging can occur whenever a suspension of particles flows through a confined system. The formation of clogs is often correlated to a reduction in the cross-section of the channel. In this study, we consider the clogging by bridging, i.e., through the formation of a stable arch of particles at a constriction that hinders the transport of particles downstream of the clog. To characterize the role of the volume fraction of the suspension on the clogging dynamics, we study the flow of particulate suspensions through 3D-printed millifluidic devices. We systematically characterize the bridging of …
We have studied experimentally particle suspension when injecting a gas at the bottom of an immersed granular layer confined in a Hele-Shaw cell. This work focuses on the dynamics of particles slightly denser than the surrounding fluid. The gas, injected at constant flow-rate, rises through the granular bed then forms bubbles which entrain particles in the above liquid layer. The particles settle down on the edges of the cell, avalanche on the crater formed at the granular bed free surface, and are further entrained by the continuous bubbling at the center. We report the existence of a station…
The distribution of Red Blood Cells in a confined channel flow is inhomogeneous and shows a marked depletion near the walls due to a competition between migration away from the walls and shear-induced diffusion resulting from interactions between particles. We investigated the lift of RBCs in a shear flow near a wall and measured a significant lift velocity despite the tumbling motion of cells. We also provide values for the collective and anisotropic shear-induced diffusion of a cloud of RBCs, both in the direction of shear and in the direction of vorticity. A generic down-gradient subdiffusi…
We derive a minimal continuum model to investigate the hydrodynamic mechanism behind the fingering instability recently discovered in a suspension of microrollers near a floor [Driscoll et al. Nature Physics, 2016]. Our model, consisting of two continuous lines of rotlets, exhibits a linear instability driven only by hydrodynamics interactions, and reproduces the lengthscale selection observed in large scale particle simulations and in experiments. By adjusting only one parameter, the distance between the two lines, our dispersion relation exhibits quantitative agreement with the simulations a…
We experimentally examine pressure-driven flows of 1%, 3%, and 5% dilute suspensions over and through a porous media model. The flow of non-colloidal, non-Brownian suspensions of rigid and spherical particles suspended in a Newtonian fluid is considered at very low Reynolds numbers. The model of porous media consists of square arrays of rods oriented across the flow in a rectangular channel. Systematic experiments using high-spatial-resolution planar particle image velocimetry (PIV) and index-matching techniques are conducted to accurately measure the velocity measurements of both very dilute …
The presence and the microscopic origin of normal stress differences in dense suspensions under simple shear flows are investigated by means of inertialess particle dynamics simulations, taking into account hydrodynamic lubrication and frictional contact forces. The synergic action of hydrodynamic and contact forces between the suspended particles is found to be the origin of negative contributions to the first normal stress difference $N_1$, whereas positive values of $N_1$ observed at higher volume fractions near jamming are due to effects that cannot be accounted for in the hard-sphere limi…
We theoretically describe the dynamics of swimmer populations confined in thin liquid films. We first demonstrate that hydrodynamic interactions between confined swimmers only depend on their shape and are independent of their specific swimming mechanism. We also show that due to friction with the walls, confined swimmers do not reorient due to flow gradients but the flow field itself. We then quantify the consequences of these microscopic interaction rules on the large-scale hydrodynamics of isotropic populations. We investigate in details their stability and the resulting phase behavior, hig…
The dynamics of an adhesive two-dimensional vesicle doublet under various flow conditions is investigated numerically using a high-order, adaptive-in-time boundary integral method. In a quiescent flow, two nearby vesicles move slowly towards each other under the adhesive potential, pushing out fluid between them to form a vesicle doublet at equilibrium. A lubrication analysis on such draining of a thin film gives the dependencies of draining time on adhesion strength and separation distance that are in good agreement with numerical results. In a planar extensional flow we find a stable vesicle…
The interplay of inertia and deformability has a substantial impact on the transport of soft particles suspended in a fluid. However, to date a thorough understanding of these systems is still missing and only a limited number of experimental and theoretical studies is available. We combine the finite-element, immersed-boundary and lattice-Boltzmann methods to simulate three-dimensional suspensions of soft particles subjected to planar Poiseuille flow at finite Reynolds numbers. Our findings confirm that the particle deformation and inclination increase when inertia is present. We observe that…
Driven or active suspensions can display fascinating collective behavior, where coherent motions or structures arise on a scale much larger than that of the constituent particles. Here, we report experiments and numerical simulations revealing that red blood cells (RBCs) assemble into regular patterns in a confined shear flow. The order is of pure hydrodynamic and inertialess origin, and emerges from a subtle interplay between (i) hydrodynamic repulsion by the bounding walls which drives deformable cells towards the channel mid-plane and (ii) intercellular hydrodynamic interactions which can b…
We analyze a dilute suspension of active particles confined between walls and subjected to fields that can modulate particle speed as well as orientation. Generally, the particle distribution is different in the bulk compared to near the walls. In the bulk, particles tend to accumulate in the regions of low speed, but in the presence of an orienting field, particles rotate to align with the field and accumulate downstream in the field direction. At the walls, particles tend to accumulate pointing into the walls and thereby exert pressure on walls. But the presence of strong orienting fields ca…
