The onset of heterogeneity in the pinch-off of suspension drops.

SignificanceThe pinch-off of a liquid drop extruded from a nozzle is a canonical situation that involves a series of self-similar regimes ending in a finite-time singularity. This configuration allows for exploring capillary flows over a large range of scales. In the case of suspension drops, the presence of particles breaks the self-similarity by introducing a length scale that can be much larger than the particle diameter. This length scale is a signature of the heterogeneities and delimitates a regime, in which a continuum approach of a suspension can be used from a regime where the discrete nature of the particles is involved.

Rheology of debris flow materials is controlled by the distance from jamming.

Debris flows are dense and fast-moving complex suspensions of soil and water that threaten lives and infrastructure. Assessing the hazard potential of debris flows requires predicting yield and flow behavior. Reported measurements of rheology for debris flow slurries are highly variable and sometimes contradictory due to heterogeneity in particle composition and volume fraction ([Formula: see text]) and also inconsistent measurement methods. Here we examine the composition and flow behavior of source materials that formed the postwildfire debris flows in Montecito, CA, in 2018, for a wide range of [Formula: see text] that encapsulates debris flow formation by overland flow. We find that shear viscosity and yield stress are controlled by the distance from jamming, [Formula: see text], where the jamming fraction [Formula: see text] is a material parameter that depends on grain size polydispersity and friction. By rescaling shear and viscous stresses to account for these effects, the data collapse onto a simple nondimensional flow curve indicative of a Bingham plastic (viscoplastic) fluid. Given the highly nonlinear dependence of rheology on [Formula: see text], our findings suggest that determining the jamming fraction for natural materials will significantly improve flow models for geophysical suspensions such as hyperconcentrated flows and debris flows.

Transition to the viscoelastic regime in the thinning of polymer solutions.

In this study, we investigate the transition between the Newtonian and the viscoelastic regimes during the pinch-off of droplets of dilute polymer solutions and discuss its link to the coil-stretch transition. The detachment of a drop from a nozzle is associated with the formation of a liquid neck that causes the divergence of the local stress in a vanishingly small region. If the liquid is a polymer solution, this increasing stress progressively unwinds the polymer chains, up to a point where the resulting increase in the viscosity slows down drastically the thinning. This threshold to a viscoelastic behavior corresponds to a macroscopic strain rate. In the present study, we characterize the variations of with respect to the polymer concentration and molar weight, to the solvent viscosity, and to the nozzle size, i.e., the weight of the drop. We provide empirical scaling laws for these variations. We also analyze the thinning dynamics at the transition and show that it follows a self-similar dynamics controlled by the time scale c-1. This characteristic time is different and always shorter than the relaxation time of the polymer.

Influence of the solid fraction on the clogging by bridging of suspensions in constricted channels.

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 non-Brownian particles in a quasi-bidimensional system in which we directly visualize and track the particles as they flow and form arches at a constriction. We report the conditions for clogging by bridging when varying the constriction width to particle diameter ratio for different concentrations of the particles in suspension. We then discuss our results using a stochastic model to rationalize the influence of solid fraction on the probability of clogging. Understanding the mechanisms and conditions of clog formation is an important step for optimizing engineering design and developing more reliable dispensing systems.

Clog mitigation in a microfluidic array via pulsatile flows.

Clogging is a common obstacle encountered during the transport of suspensions and represents a significant energy and material cost across applications, including water purification, irrigation, biopharmaceutical processing, and aquifer recharge. Pulsatile pressure-driven flows can help mitigate clogging when compared to steady flows. Here, we study experimentally the influence of the amplitude of pulsation 0.25P0 ≤ δP ≤ 1.25P0, where P0 is the mean pressure, and of the frequency of pulsation 10-3 Hz ≤ f ≤ 10-1 Hz on clog mitigation in a microfluidic array of parallel channels using a dilute suspension of colloidal particles. The array geometry is representative of a classical filter, with parallel pores that clog over time, yielding a filter cake that continues to grow and can interact with other pores. We combine flow rate measurements with direct visualizations at the pore scale to correlate the observed clogging dynamics with the changes in flow rate. We observe that all pulsatile amplitudes at 0.1 Hz yield increased throughput compared to steady flows. The rearrangement of particles when subject to a dynamic shear environment can delay the clogging of a pore or even remove an existing clog. However, this benefit is drastically reduced at 10-2 Hz and disappears at 10-3 Hz as the pulsatile timescale becomes too large compared to the timescale associated with the clogging and the growth of the filter cakes in this system. The present study demonstrates that pulsatile flows are a promising method to delay clogging at both the pore and system scale.

Droplet detachment and pinch-off of bidisperse particulate suspensions.

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 and different proportions of small particles. Long before the pinch-off, the thinning rate is that of an equivalent liquid whose viscosity is that of the suspension. Later, when the ligament thickness approaches the size of the large particles, the thinning accelerates and leads to an early pinch-off. We explain how the bidisperse particle size distribution lowers the viscosity by making the packing more efficient, which speeds up the thinning. This result can be used to predict the dynamics of droplet formation with bidisperse suspensions.

Pulsatile Flow in Microfluidic Systems.

This review describes the current knowledge and applications of pulsatile flow in microfluidic systems. Elements of fluid dynamics at low Reynolds number are first described in the context of pulsatile flow. Then the practical applications in microfluidic processes are presented: the methods to generate a pulsatile flow, the generation of emulsion droplets through harmonic flow rate perturbation, the applications in mixing and particle separation, and the benefits of pulsatile flow for clog mitigation. The second part of the review is devoted to pulsatile flow in biological applications. Pulsatile flows can be used for mimicking physiological systems, to alter or enhance cell cultures, and for bioassay automation. Pulsatile flows offer unique advantages over a steady flow, especially in microfluidic systems, but also require some new physical insights and more rigorous investigation to fully benefit future applications.

Dip-coating of suspensions.

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 2a. 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 large capillary number, we observe that the thickness of the entrained film of suspension is captured by the Landau-Levich law using the effective viscosity of the suspension η(φ). (iii) At intermediate capillary numbers, the situation becomes more complicated with a heterogeneous coating on the substrate. We rationalize our experimental findings by providing the domain of existence of these three regimes as a function of the fluid and particles properties.

Accretion Dynamics on Wet Granular Materials.

Wet granular aggregates are common precursors of construction materials, food, and health care products. The physical mechanisms involved in the mixing of dry grains with a wet substrate are not well understood and difficult to control. Here, we study experimentally the accretion of dry grains on a wet granular substrate by measuring the growth dynamics of the wet aggregate. We show that this aggregate is fully saturated and its cohesion is ensured by the capillary depression at the air-liquid interface. The growth dynamics is controlled by the liquid fraction at the surface of the aggregate and exhibits two regimes. In the viscous regime, the growth dynamics is limited by the capillary-driven flow of liquid through the granular packing to the surface of the aggregate. In the capture regime, the capture probability depends on the availability of the liquid at the saturated interface, which is controlled by the hydrostatic depression in the material. We propose a model that rationalizes our observations and captures both dynamics based on the evolution of the capture probability with the hydrostatic depression.

Clogging of microfluidic systems.

The transport of suspensions of microparticles in confined environments is associated with complex phenomena at the interface of fluid mechanics and soft matter. Indeed, the deposition and assembly of particles under flow involve hydrodynamic, steric and colloidal forces, and can lead to the clogging of microchannels. The formation of clogs dramatically alters the performance of both natural and engineered systems, effectively limiting the use of microfluidic technology. While the fouling of porous filters has been studied at the macroscopic level, it is only recently that the formation of clogs has been considered at the pore-scale, using microfluidic devices. In this review, we present the clogging mechanisms recently reported for suspension flows of colloidal particles and for biofluids in microfluidic channels, including sieving, bridging and aggregation of particles. We discuss the technological implications of the clogging of microchannels and the schemes that leverage the formation of clogs. We finally consider some of the outstanding challenges involving clogging in human health, which could be tackled with microfluidic methods.

Drop impact on a flexible fiber.

When droplets impact fibrous media, the liquid can be captured by the fibers or contact then break away. Previous studies have shown that the efficiency of drop capture by a rigid fiber depends on the impact velocity and a threshold velocity was defined below which the drop is captured. However, it is necessary to consider the coupling of elastic and capillary effects to achieve an improved understanding of the capture process for soft substrates. Here, we study experimentally the dynamics of a single drop impacting on a thin flexible fiber. Our results demonstrate that the threshold capture velocity depends on the flexibility of fibers in a non-monotonic way. We conclude that tuning the mechanical properties of fibers can optimize the efficiency of droplet capture.

Drop morphologies on flexible fibers: influence of elastocapillary effects.

Various materials are made of long thin fibers that are randomly oriented to form a complex network in which drops of wetting liquid tend to accumulate at the nodes. The capillary force exerted by the liquid can bend flexible fibers, which in turn influences the morphology adopted by the liquid. In this paper, we investigate through a model situation the role of the fiber flexibility on the shape of a small volume of liquid on a pair of crossed flexible fibers. We characterize the liquid morphologies as we vary the volume of liquid, the angle between the fibers, and the length of the fibers. The drop morphologies previously reported for rigid crossed fibers, i.e., a drop, a column and a mixed morphology, are also observed on flexible crossed fibers with modified domains of existence. In addition, at small tilt angles between the fibers, a new behavior is observed: the fibers bend and collapse. Depending on the volume of liquid, a thin column with or without a drop is reported on the collapsed fibers. Our study suggests that the fiber flexibility adds a rich variety of behaviors that may be important for some applications.

Mechanical tuning of the evaporation rate of liquid on crossed fibers.

We investigate experimentally the drying of a small volume of perfectly wetting liquid on two crossed fibers. We characterize the drying dynamics for the three liquid morphologies that are encountered in this geometry: drop, column, and a mixed morphology, in which a drop and a column coexist. For each morphology, we rationalize our findings with theoretical models that capture the drying kinetics. We find that the evaporation rate significantly depends upon the liquid morphology and that the drying of the liquid column is faster than the evaporation of the drop and the mixed morphology for a given liquid volume. Finally, we illustrate that shearing a network of fibers reduces the angle between them, changes the morphology toward the column state, and therefore, enhances the drying rate of a volatile liquid deposited on it.

Wetting morphologies on an array of fibers of different radii.

We investigate the equilibrium morphology of a finite volume of liquid placed on two parallel rigid fibers of different radii. As observed for identical radii fibers, the liquid is either in a column morphology or adopts a drop shape depending on the inter-fiber distance. However the cross-sectional area and the critical inter-fiber distance at which the transition occurs are both modified by the polydispersity of the fibers. Using energy considerations, we analytically predict the critical inter-fiber distance corresponding to the transition between the column and the drop morphologies. This distance depends both on the radii of the fibers and on the contact angle of the liquid. We perform experiments using a perfectly wetting liquid on two parallel nylon fibers: the results are in good agreement with our analytical model. The morphology of the capillary bridges between fibers of different radii is relevant to the modeling of large arrays of polydisperse fibers.

Wetting morphologies on randomly oriented fibers.

We characterize the different morphologies adopted by a drop of liquid placed on two randomly oriented fibers, which is a first step toward understanding the wetting of fibrous networks. The present work reviews previous modeling for parallel and touching crossed fibers and extends it to an arbitrary orientation of the fibers characterized by the tilting angle and the minimum spacing distance. Depending on the volume of liquid, the spacing distance between fibers and the angle between the fibers, we highlight that the liquid can adopt three different equilibrium morphologies: 1) a column morphology in which the liquid spreads between the fibers, 2) a mixed morphology where a drop grows at one end of the column or 3) a single drop located at the node. We capture the different morphologies observed using an analytical model that predicts the equilibrium configuration of the liquid based on the geometry of the fibers and the volume of liquid.

Deposition and alignment of fiber suspensions by dip coating.

HYPOTHESIS: The dip coating of suspensions made of monodisperse non-Brownian spherical particles dispersed in a Newtonian fluid leads to different coating regimes depending on the ratio of the particle diameter to the thickness of the film entrained on the substrate. In particular, dilute particles dispersed in the liquid are entrained only above a threshold value of film thickness. In the case of anisotropic particles, in particular fibers, the smallest characteristic dimension will control the entrainment of the particle. Furthermore, it is possible to control the orientation of the anisotropic particles depending on the substrate geometry. In the thick film regime, the Landau-Levich-Derjaguin model remains valid if one account for the change in viscosity. EXPERIMENT: To test the hypotheses, we performed dip-coating experiments with dilute suspensions of non-Brownian fibers with different length-to-diameter aspect ratios. We characterize the number of fibers entrained on the surface of the substrate as a function of the withdrawal velocity, allowing us to estimate a threshold capillary number below which all the particles remain in the liquid bath. Besides, we measure the angular distribution of the entrained fibers for two different substrate geometries: flat plates and cylindrical rods. We then measure the film thickness for more concentrated fiber suspensions. FINDINGS: The entrainment of the fibers on a flat plate and a cylindrical rod is primarily controlled by the smaller characteristic length of the fibers: their diameter. At first order, the entrainment threshold scales similarly to that of spherical particles. The length of the fibers only appears to have a minor influence on the entrainment threshold. No preferential alignment is observed for non-Brownian fibers on a flat plate, except for very thin films, whereas the fibers tend to align themselves along the axis of a cylindrical rod for a large enough ratio of the fiber length to the radius of the cylindrical rod. The Landau-Levich-Derjaguin law is recovered for more concentrated suspension by introducing an effective capillary number accounting for the change in viscosity.

Effects of particle size on the electrocoalescence dynamics and arrested morphology of liquid marbles.

HYPOTHESIS: The coalescence of bare droplets when surface tension dominates always results in one larger spherical droplet. In contrast, droplets coated with particles may be stabilized into non-spherical structures after arrested coalescence, which can be achieved by different approaches, such as changing the particle surface coverage. The size of particles coating the initial liquid marbles can be used to control the coalescence dynamics and the resulting morphology of arrested droplets. EXPERIMENT: We characterized the electrocoalescence of liquid marbles coated with particles ranging from hundred nanometers to hundred micrometers. The electrocoalescence was recorded using high-speed imaging. FINDINGS: When the electrocoalescence initiates, particles jam and halt the relaxation of the marbles at different stages, resulting in four possible final morphologies that are characterized using the Gaussian curvature at the neck region. The four regimes are total coalescence, arrested puddle coalescence, arrested saddle coalescence, and non-coalescence. The coalescence is initiated at the center of the contact zone, independent of the particle size. Small particles show little resistance to the coalescence, while marbles coated by large particles demonstrate a viscous-like behavior, indicated by the growth of the liquid bridge and the damping. The present study provides guidelines for applications that involve the formulation of liquid marbles with complex morphologies.

Collapse dynamics of dry granular columns: From free-fall to quasistatic flow.

Gravity-driven collapses involving large amounts of dense granular material, such as landslides, avalanches, or rock falls, in a geophysical context, represent significant natural hazards. Understanding their complex dynamics is hence a key concern for risk assessment. In the present work, we report experiments on the collapse of quasi-two-dimensional dry granular columns under the effect of gravity, where both the velocity at which the grains are released and the aspect ratio of the column are varied to investigate the dynamics of the falling grains. At high release velocity, classical power laws for the final deposit are recovered, meaning those are representative of a free-fall-like regime. For sufficiently high aspect ratios, the top of the column undergoes an overall free-fall-like motion. In addition, for all experiments, the falling grains also spread horizontally in a free-fall-like motion, and the characteristic time of spreading is related to the horizontal extension reached by the deposit at all altitudes. At low release velocity, a quasistatic state is observed, with scaling laws for the final geometry identical to those of the viscous regime of granular-fluid flow. The velocity at which the grains are released governs the collapse dynamics. Between these two asymptotic regimes, higher release velocity correlates with smaller impact on the collapse dynamics. The criterion V[over ¯]≥0.4sqrt[gH_{0}], where H_{0} is the initial height of the column, is found for the mean release velocity V[over ¯] not to influence the granular collapse.

From laboratory experiments to geophysical tsunamis generated by subaerial landslides.

Modeling of tsunami waves generated by subaerial landslides is important to provide accurate hazard and risk assessments in coastal areas. We perform small-scale laboratory experiments where a tsunami-like wave is generated by the gravity-driven collapse of a subaerial granular column into water. We show that the maximal amplitude reached near-shore by the generated wave in our experiments is linked to the instantaneous immersed volume of grains and to the ultimate immersed deposit. Despite the differences in scale and geometry between our small-scale experiments and the larger-scale geophysical events, a rather good agreement is found between the experimental law and the field data. This approach offers an easy way to estimate the amplitude of paleo-tsunamis.