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Mixing dynamics in flows are governed by the coupled action of diffusion and stretching by velocity gradients. This leads to the development of elongated lamellar structures in scalar fields where concentration fluctuations exist at scales set by the Batchelor scale. Because the latter is generally too small to be resolved experimentally, observation of these mechanisms remains an outstanding challenge. Here we present high-resolution experiments allowing for the precise quantification of the evolution of concentration distributions at the scale of a single lamella experiencing diffusion, stretching and aggregation with other lamellae. Quantitative agreement is found with analytical predictions for the lamella’s concentration profile, Batchelor time, Batchelor length scale, and concentration distribution for a large range of Péclet numbers and without adjustable parameter. This benchmark configuration is used to set the experimental spatial resolution required to quantify the concentration probability density functions (PDFs) of scalar mixtures in fluids. The diffusive coalescence of two nearby lamellae, the mechanism by which scalar mixtures ultimately reach uniformity, is shown to induce a complex transient evolution of the concentration PDFs.

The effect of pore size distribution on the flow kinematics and transport properties within a three‐dimensional porous medium is investigated through numerical simulations using the Smoothed Particle Hydrodynamics (SPH) method. The method is first validated for a model porous medium within a monodisperse random spherical packing, for which the velocity distribution of the fluid flowing through the pores (i.e., the interstitial fluid velocity) and the dispersion process are found to be in both qualitative and quantitative agreement with previous experimental results. When varying the pore size distribution of the porous medium by using polydisperse beads (of different diameters), the interstitial fluid velocity distributions get narrower, and the streamlines' tortuosity decreases. This is interpreted as a result of the narrower pore size distribution reported for polydisperse microstructures. Although the dispersion process remains qualitatively the same among the investigated microstructures, with an initial ballistic trend followed by a transient seemingly anomalous regime and eventually a Fickian regime, the transverse dispersion process is found to be quantitatively reduced for polydisperse microstructure (i.e., with a narrower pore size distribution), consistently with the reported decrease in streamlines' tortuosity.

Forcing dense suspensions of non-cohesive particles through constrictions might result in a continuous flow, an intermittent one, or indefinite interruption of flow, i.e. a clog. While one of the most important (and obvious) controlling parameters in such a system is the neck-to-particle size ratio, the role of the liquid driving method is not so straightforward. On the one hand, widespread volume-controlled systems such as syringe pumps result in pressure and local liquid velocity increases upon eventual clogs. On the other hand, pressure-controlled systems result in a decrease of the flow through the constriction when a clog is formed. The root of the question therefore lies in the role of interparticle liquid flow and hydrodynamic forces on both the formation and stability of an arch blocking the particle transport through a constriction. In this work, we study experimentally a suspension of non-cohesive particles flowing through a constricted channel (with neck-to-particle size ratio $3.03\\leq D/d\\leq 5.26$) in an intermittent fashion, in which they are most sensitive to parametric changes. Due to the stochastic nature of the intermittency, we make use of statistical distributions of arrest times and of discharged particles, and surprisingly, we find that the transport of non-cohesive suspensions through constrictions actually follows a ‘slower is faster’ principle under pressure-controlled driving: low imposed pressures yield intermittent non-persistent clogs, while high imposed pressures result in longer-lasting clogs, eventually becoming everlasting, and thus reducing the net particle transport rate.

Using index matching and particle tracking, we measure the three-dimensional velocity field in an isotropic porous medium composed of randomly packed solid spheres. This high-resolution experimental dataset provides new insights into the dynamics of dispersion and stretching in porous media. Dynamic-range velocity measurements indicate that the distribution of the velocity magnitude,$U$, is flat at low velocity (probability density function$(U)\\propto U^{0}$). While such a distribution should lead to a persistent anomalous dispersion process for advected non-diffusive point particles, we show that the dispersion of non-diffusive tracers nonetheless becomes Fickian beyond a time set by the smallest effective velocity of the tracers. We derive expressions for the onset time of the Fickian regime and the longitudinal and transverse dispersion coefficients as a function of the velocity field properties. The experimental velocity field is also used to study, by numerical advection, the stretching histories of fluid material lines. The mean and the variance of the line elongations are found to grow exponentially in time and the distribution of elongation is log-normal. These results confirm the chaotic nature of advection within three-dimensional porous media. By providing the laws of dispersion and stretching, the present study opens the way to a complete description of mixing in porous media.

We experimentally investigate mixing in sheared particulate suspensions by measuring a crucial kinematic quantity of the flow: the stretching laws of material lines in the suspending liquid. High-resolution particle image velocimetry (PIV) measurements in the fluid phase are performed to reconstruct, following the Diffusive Strip Method (Meunier & Villermaux, J. Fluid Mech., vol. 662, 2010, pp. 134–172), the stretching histories of the fluid material lines. In a broad range of volume fractions $20\\,\\%\\leqslant \\unicode[STIX]{x1D719}\\leqslant 55\\,\\%$ , the nature of the elongation law changes drastically from linear, in the absence of particles, to exponential in the presence of particles: the mean and the standard deviation of the material line elongations are found to grow exponentially in time and the distribution of elongations converges to a log-normal. A multiplicative stretching model, based on the distribution of local shear rates and on their persistence time, is derived. This model quantitatively captures the experimental stretching laws. The presence of particles is shown to accelerate mixing at large Péclet numbers ( ${\\gtrsim}10^{5}$ ). However, the wide distribution of stretching rates results in heterogeneous mixing and, hence, broadly distributed mixing times, in qualitative agreement with experimental observations.

Forcing dense suspensions of non-cohesive particles through constrictions might either result in a continuous flow, an intermittent one, or indefinite interruption of flow, i.e., a clog. While one of the most important (and obvious) controlling parameters in such a system is the neck-to-particle size ratio, the role of the liquid driving method is not so obvious. On the one hand, wide-spread volume-controlled systems result in pressure and local liquid velocity increases upon eventual clogs. On the other hand, pressure-controlled systems result in a decrease of the flow through the constriction when a clog is developed. The root of the question therefore lies on the role of interparticle liquid flow and hydrodynamic forces on both the formation and stability of an arch blocking the particle transport through a constriction. In this work, we experimentally analyse a suspension of non-cohesive particles in channels undergoing intermittent regimes, in which they are most sensitive to parametric changes. By exploring the statistical distribution of arrest times and of discharged particles, we surprisingly find that the transport of non-cohesive suspensions through constrictions actually follows a \"slower is faster\" principle under certain conditions.

When suspended particles are pushed by liquid flow through a constricted channel they might either pass the bottleneck without trouble or encounter a permanent clog that will stop them forever. However, they may also flow intermittently with great sensitivity to the neck-to-particle size ratio D/d. In this work, we experimentally explore the limits of the intermittent regime for a dense suspension through a single bottleneck as a function of this parameter. To this end, we make use of high time- and space-resolution experiments to obtain the distributions of arrest times T between successive bursts, which display power-law tails with characteristic exponents. These exponents compare well with the ones found for as disparate situations as the evacuation of pedestrians from a room, the entry of a flock of sheep into a shed or the discharge of particles from a silo. Nevertheless, the intrinsic properties of our system i.e. channel geometry, driving and interaction forces, particle size distribution seem to introduce a sharp transition from a clogged state to a continuous flow, where clogs do not develop at all. This contrasts with the results obtained in other systems where intermittent flow, with power-law exponents above two, were obtained.

When objects are forced to flow through constrictions their transport can be frustrated temporarily or permanently due to the formation of arches in the region of the bottleneck. While such systems have been intensively studied in the case of solid particles in a gas phase being forced by gravitational forces, the case of solid particles suspended in a liquid phase, forced by the liquid itself, has received much less attention. In this case, the influence of the liquid flow on the transport efficiency is not well understood yet, leading to several apparently trivial, but yet unanswered questions, e.g., would an increase of the liquid flow improve the transport of particles or worsen it? Although some experimental data is already available, it lacks enough detail to give a complete answer to such a question. Numerical models would be needed to scrutinize the system deeper. In this paper, we study this system making use of an advanced discrete particle solver (MercuryDPM) and an approximated numerical model for the liquid drag and compare the results with experimental data.

When a drop of a volatile liquid is deposited on a uniformly heated wettable, thermally conducting substrate, one expects to see it spread into a thin film and evaporate. Contrary to this intuition, due to thermal Marangoni contraction the deposited drop contracts into a spherical-cap-shaped puddle, with a finite apparent contact angle. Strikingly, this contracted droplet, above a threshold temperature, well below the boiling point of the liquid, starts to spontaneously move on the substrate in an apparently erratic way. We describe and quantify this self-propulsion of the volatile drop. It arises due to spontaneous symmetry breaking of thermal-Marangoni convection, which is induced by the non-uniform evaporation of the droplet. Using infra-red imaging, we reveal the characteristic interfacial flow patterns associated with the Marangoni convection in the evaporating drop. A scaling relation describes the correlation between the moving velocity of the drop and the apparent contact angle, both of which increase with the substrate temperature.

Cells have evolved efficient strategies to probe their surroundings and navigate through complex environments. From metastatic spread in the body to swimming cells in porous materials, escape through narrow constrictions - a key component of any structured environment connecting isolated micro-domains - is one ubiquitous and crucial aspect of cell exploration. Here, using the model microalgae Chlamydomonas reinhardtii, we combine experiments and simulations to achieve a tractable realization of the classical Brownian narrow escape problem in the context of active confined matter. Our results differ from those expected for Brownian particles or leaking chaotic billiards and demonstrate that cell-wall interactions substantially modify escape rates and, under generic conditions, expedite spread dynamics.