Self-Limited Accumulation of Colloids in Porous Media

Soft matter physics of the ground beneath our feet

The soft part of the Earth's surface - the ground beneath our feet - constitutes the basis for life and natural resources, yet a general physical understanding of the ground is still lacking. In this critical time of climate change, cross-pollination of scientific approaches is urgently needed to better understand the behavior of our planet's surface. The major topics in current research in this area cross different disciplines, spanning geosciences, and various aspects of engineering, material sciences, physics, chemistry, and biology. Among these, soft matter physics has emerged as a fundamental nexus connecting and underpinning many research questions. This perspective article is a multi-voice effort to bring together different views and approaches, questions and insights, from researchers that work in this emerging area, the soft matter physics of the ground beneath our feet. In particular, we identify four major challenges concerned with the dynamics in and of the ground: (I) modeling from the grain scale, (II) near-criticality, (III) bridging scales, and (IV) life. For each challenge, we present a selection of topics by individual authors, providing specific context, recent advances, and open questions. Through this, we seek to provide an overview of the opportunities for the broad Soft Matter community to contribute to the fundamental understanding of the physics of the ground, strive towards a common language, and encourage new collaborations across the broad spectrum of scientists interested in the matter of the Earth's surface.

Role of Ripening in the Deposition of Fragments: The Case of Micro- and Nanoplastics

Particulate contaminants, such as microplastics (1 μm to 5 mm) and nanoplastics (<1 μm), are disseminated in many terrestrial environments. However, it is still unclear how particles' properties drive their mobility through soils and aquifers due to (i) poor environmental relevance of the model particles that are studied (e.g., spherical and monodisperse) and (ii) the use of packed bed experiments which do not allow a direct observation of deposition dynamics. Using transparent 2D porous media, this study analyzes deposition dynamics of rough polystyrene fragments with irregular shapes and with a size continuum (≈10 nm to 5 μm). Using in situ and ex situ measurements, particle deposition as a function of size was monitored over time under repulsive conditions. In the absence of natural organic matter (NOM), micrometric particles rapidly deposit and promote the physical interception of smaller nanoparticles by creating local porous roughness or obstacles. In the presence of NOM, differences according to particle size were no longer observed, and all fragments were more prone to being re-entrained, thereby limiting the growth of deposits. This work demonstrates the importance of pore surface roughness and porosity of the pore surface for the deposition of colloidal particles, such as microplastics and nanoplastics, under repulsive conditions.

3D pore-scale characterization of colloid aggregation and retention by confocal microscopy: Effects of fluid structure and ionic strength

Understanding the mechanisms of colloid transport and retention as well as the spatial distribution of colloids in porous media is an important topic for contamination transport and remediation in subsurface environments. Utilizing advanced three-dimensional visualization experiments, we effectively capture the intricate distribution characteristics of colloids in the 3D pore space and quantify the size of colloid clusters that aggregate at fluid-fluid interfaces and solid surfaces during two-phase flow. Our experimental results reveal the influence of pore-scale events, such as Haines jumps and pinch-off, on colloid retention. Our results also indicate that large drainage rates can facilitate colloid retention on solid surfaces, especially under the condition of high ionic strength. This can be attributed to the migration of colloids from the fluid-fluid interface to the solid surface, propelled by transients in the local fluid structure. The findings reveal a synergistic effect of the ionic strength and hydrodynamic conditions on colloid transport and retention during two-phase flow and provide important insights for predicting the fate and transport of contaminants in soil and groundwater environments involving multiple fluid phases.

Inkjet printing on hydrophobic surfaces: Controlled pattern formation using sequential drying

Inkjet-printed micro-patterns on hydrophobic surfaces have promising applications in the fabrication of microscale devices such as organic thin-film transistors. The low wettability of the surface prevents the inkjet-printed droplets from spreading, connecting to each other, and forming a pattern. Consequently, it is challenging to form micro-patterns on surfaces with low wettability. Here, we propose a sequential printing and drying method to form micro-patterns and control their shape. The first set of droplets is inkjet-printed at a certain spacing and dried. The second set of droplets is printed between these dry anchors on the surface with low wettability. As a result, a stable bridge on the surface with low wettability forms. This printing method is extended to more complicated shapes such as triangles. By implementing an energy minimization technique, a simple model was devised to predict the shape of the inkjet-printed micro-patterns while confirming that their equilibrium shape is mainly governed by surface tension forces. The gradient descent method was utilized with parametric boundaries to emulate droplet pinning and wettability of the anchors and to prevent convergence issues from occurring in the simulations. Finally, the energy minimization based simulations were used to predict the required ink to produce dry lines and triangles with smooth edges.

In-Plane Rotation of Prolate Colloids Adhered to a Planar Substrate in the Presence of Flow

Micron-size spherical polystyrene colloidal particles are mechanically stretched to a prolate geometry with desirable aspect ratios. The particles in an aqueous medium with specific ionic concentration are then introduced into a microchannel and allowed to settle on a glass substrate. In the presence of unidirectional flow, the loosely adhered particles in the secondary minimum of surface interaction potential are easily washed off, but the remnant in the strong primary minimum preferentially aligns with the flow direction and exercises in-plane rotation. A rigorous theoretical model is constructed to account for filtration efficiency in terms of hydrodynamic drag, intersurface forces, reorientation of prolate particles, and their dependence on flowrate and ionic concentration.

Three-Dimensional Visualization Reveals Pore-Scale Mechanisms of Colloid Transport and Retention in Two-Phase Flow

Colloids are ubiquitous in the natural environment, playing an important role in facilitating the transport of absorbed contaminants. However, due to the complexities arising from two-phase flow and difficulties in three-dimensional observations, the detailed mechanisms of colloid transport and retention under two-phase flow are still not well understood. In this work, we visualize the colloid transport and retention during immiscible two-phase flow based on confocal microscopy. We find that the colloid transport and retention behaviors depend strongly on the flow rate and pore/grain size. At low levels of saturation (high flow rate) with the wetting liquid mainly present as pendular rings, the colloids can aggregate at the liquid filaments in small-grain packings and are uniformly distributed in large-grain packings. Through theoretical analysis of the pendular ring geometry, we elucidate the mechanism responsible for the strong dependence of colloid clogging behavior on solid grain size. Our results further demonstrate that even at dilute concentrations, colloids can alter the flow paths and the wetting fluid topology, suggesting a strong two-way coupling dynamics between immiscible two-phase flow and colloid transport and calling for improved predictive models to incorporate the overlooked clogging behavior.

Dynamic NMR Relaxometry as a Simple Tool for Measuring Liquid Transfers and Characterizing Surface and Structure Evolution in Porous Media

Porous media containing voids which can be filled with gas and/or liquids are ubiquitous in our everyday life: soils, wood, bricks, concrete, sponges, and textiles. It is of major interest to identify how a liquid, pushing another fluid or transporting particles, ions, or nutriments, can penetrate or be extracted from the porous medium. High-resolution X-ray microtomography, neutron imaging, and magnetic resonance imaging are techniques allowing us to obtain, in a nondestructive way, a view of the internal processes in nontransparent porous media. Here we review the possibilities of a simple though powerful technique which provides various direct quantitative information on the liquid distribution inside the porous structure and its variations over time due to fluid transport and/or phase changes. It relies on the analysis of the details of the NMR (nuclear magnetic resonance) relaxation of the proton spins of the liquid molecules and its evolution during some process such as the imbibition, drying, or phase change of the sample. This rather cheap technique then allows us to distinguish how the liquid is distributed in the different pore sizes or pore types and how this evolves over time; since the NMR relaxation time depends on the fraction of time spent by the molecule along the solid surface, this technique can also be used to determine the specific surface of some pore classes in the material. The principles of the technique and its contribution to the physical understanding of the processes are illustrated through examples: imbibition, drying or fluid transfers in a nanoporous silica glass, large pores dispersed in a fine polymeric porous matrix, a pile of cellulose fibers partially saturated with bound water, a softwood, and a simple porous inclusion in a cement paste. We thus show the efficiency of the technique to quantify the transfers with a good temporal resolution.

Effect of Colloidal Interactions and Hydrodynamic Stress on Particle Deposition in a Single Micropore

Clogging is ubiquitous. It happens in a wide range of material processing and causes severe performance degradation or process breakdown. In this study, we investigate clogging dynamics in a single micropore by controlling the surface property of the particle and processing condition. Microfluidic observation is conducted to investigate particle deposition in a contraction microchannel where polystyrene suspension is injected as a feed solution. The particle deposition area is quantified using the images taken using a CCD camera in both upstream and downstream of the microchannel. Pressure drop across the microchannel is also measured. When the particle interaction is repulsive, the deposition occurs mostly in downstream, while an opposite tendency is identified when the particle interaction is attractive. More complex deposition characteristics are found as the flow rate is changed. Particle flux density and the ratio of lift force to colloidal force are introduced to explain the clogging dynamics. This study provides a useful insight to alleviate clogging issues by controlling the colloidal interaction and hydrodynamic stress.

Diffusion in Heterogenous Media and Sorption—Desorption Processes

We investigate particle diffusion in a heterogeneous medium limited by a surface where sorption–desorption processes are governed by a kinetic equation. We consider that the dynamics of the particles present in the medium are governed by a diffusion equation with a spatial dependence on the diffusion coefficient, i.e., K(x) = D|x|−η, with −1 < η and D = const, respectively. This system is analyzed in a semi-infinity region, i.e., the system is defined in the interval [0,∞) for an arbitrary initial condition. The solutions are obtained and display anomalous spreading, that is, the dynamics may be viewed as anomalous diffusion, which in turn is related, and hence, the model can be directly applied to several complex systems ranging from biological fluids to electrolytic cells.

Capture efficiency of magnetic nanoparticles through the compaction effect of a microparticles column

When a magnetic nanoparticle solution flows through a porous medium formed by iron microparticles packed in a microfluidic channel, the nanoparticles get trapped within the column in the presence of a magnet. A complex interplay between magnetic and fluid forces within the magnetized porous medium governs the trapping of nanoparticles. However, how does the packing state of the microparticles affect the trapping of nanoparticles? Will more nanoparticles be trapped on a loose or a tight packing? In this work, we present experiments that show that the capture of nanoparticles is determined by the total volume occupied by the column, independent of its packing density. We present a simple analytical model based on the competition of drag and magnetic forces that shows that our system can be useful to develop and test more complete and accurate models. We also developed a technique to measure the columns' minute mass and its packing density, which consists of injecting polydimethylsiloxane into the acrylic microfluidic device. Our work can help with the optimization of environmental and biomedical applications based on high-gradient magnetic nanoparticle separation.

Particle Deposition in Drying Porous Media

The drying of porous media is a ubiquitous phenomenon in soils and building materials. The fluid often contains suspended particles. Particle deposition may modify significantly the final material, as it could be pollutants or clogging the pores, decreasing the porosity, such as in salt, in which particles and drying kinetics are coupled. Here, we used SEM and X-ray microtomography to investigate the dried porous media initially saturated by nanoparticle suspensions. As the suspensions were dried, nanoparticles formed a solid deposit, which added to the initial solid matrix and decreased the porosity. We demonstrate that since the drying occurred through the top surface, the deposit is not uniform as a function of depth. Indeed, the particles were advected by the liquid flow toward the evaporative surface; the deposit was significant over a depth that depended on the initial volume fraction, but the pore size was affected over a very narrow length. These findings were interpreted in the frame of a physical model. This study may help to design better porous media and take into account particle influence in drying processes.

Reconfiguring confined magnetic colloids with tunable fluid transport behavior

Collective dynamics of confined colloids are crucial in diverse scenarios such as self-assembly and phase behavior in materials science, microrobot swarms for drug delivery and microfluidic control. Yet, fine-tuning the dynamics of colloids in microscale confined spaces is still a formidable task due to the complexity of the dynamics of colloidal suspension and to the lack of methodology to probe colloids in confinement. Here, we show that the collective dynamics of confined magnetic colloids can be finely tuned by external magnetic fields. In particular, the mechanical properties of the confined colloidal suspension can be probed in real time and this strategy can be also used to tune microscale fluid transport. Our experimental and theoretical investigations reveal that the collective configuration characterized by the colloidal entropy is controlled by the colloidal concentration, confining ratio and external field strength and direction. Indeed, our results show that mechanical properties of the colloidal suspension as well as the transport of the solvent in microfluidic devices can be controlled upon tuning the entropy of the colloidal suspension. Our approach opens new avenues for the design and application of drug delivery, microfluidic logic, dynamic fluid control, chemical reaction and beyond.

Directional clogging and phase separation for disk flow through periodic and diluted obstacle arrays

We model collective disk flow though a square array of obstacles as the flow direction is changed relative to the symmetry directions of the array. At lower disk densities there is no clogging for any driving direction, but as the disk density increases, the average disk velocity decreases and develops a drive angle dependence. For certain driving angles, the flow is reduced or drops to zero when the system forms a heterogeneous clogged state consisting of high density clogged regions coexisting with empty regions. The clogged states are fragile and can be unclogged by changing the driving angle. For large obstacle sizes, we find a uniform clogged state that is distinct from the collective clogging regime. Within the clogged phases, depinning transitions can occur as a function of increasing driving force, with intermittent motion appearing just above the depinning threshold. The clogging is robust against the random removal or dilution of the obstacle sites, and the disks are able to form system-spanning clogged clusters even under increasing dilution. If the dilution becomes too large, however, the clogging behavior is lost.

Dynamics of progressive pore clogging by colloidal aggregates

The flow of a suspension through a bottleneck often leads to its obstruction. Such a continuous flow to clogging transition has been well characterized when the constriction width to particle size ratio, W/D, is smaller than 3-4. In such cases, the constriction is either blocked by a single particle that is larger than the constriction width (W/D < 1), or there is an arch formed by several particles that try to enter it together (2 < W/D < 4). For larger W/D ratios, 4 < W/D < 10, the blockage of the constriction is presumed to be due to the successive accumulations of particles. Such a clogging mechanism may also apply to wider pores. The dynamics of this progressive obstruction remains largely unexplored since it is difficult to see through the forming clog and we still do not know how particles accumulate inside the constriction. In this paper, we use particle tracking and image analysis to study the clogging of a constriction/pore by stable colloidal particles. These techniques allow us to determine the shape and the size of all the objects, be they single particles or aggregates, captured inside the pore. We show that even with the rather monodisperse colloidal suspension we used individual particles cannot clog a pore alone. These individual particles can only partially cover the pore surface whilst it is the very small fraction of aggregates present in the suspension that can pile up and clog the pore. We analyzed the dynamics of aggregate motion up to the point of capture within the pore, which helps us to elucidate why the probability of aggregate capture inside the pore is high.

Microstructure of the near-wall layer of filtration-induced colloidal assembly

This paper describes an experimental study of filtration of a colloidal suspension using microfluidic devices. A suspension of micrometer-scale colloids flows through parallel slit-shaped pores at fixed pressure drop. Clogs and cakes are systematically observed at pore entrance, for variable applied pressure drop and ionic strength. Based on image analysis of the layer of colloids close to the device wall, global and local studies are performed to analyse in detail the near-wall layer microstructure. Whereas global porosity of this layer does not seem to be affected by ionic strength and applied pressure drop, a local study shows some heterogeneity: clogs are more porous at the vicinity of the pore than far away. An analysis of medium-range order using radial distribution function shows a slightly more organized state at high ionic strength. This is confirmed by a local analysis using two-dimension continuous wavelet decomposition: the typical size of crystals of colloids is larger for low ionic strength, and it increases with distance from the pores. We bring these results together in a phase diagram involving colloid-colloid repulsive interactions and fluid velocity.

Transport of Colloidal Particles in Microscopic Porous Medium Analogues with Surface Charge Heterogeneity: Experiments and the Fundamental Role of Single-Bead Deposition

Understanding colloid transport in subsurface environments is challenging because of complex interactions among colloids, groundwater, and porous media over several length scales. Here, we report a versatile method to assemble bead-based microfluidic porous media analogues with chemical heterogeneities of different configurations. We further study the transport of colloidal particles through a family of porous media analogues that are randomly packed with oppositely charged beads with different mixing ratios. We recorded the dynamics of colloidal particle deposition at the level of single grains. From these, the maximum surface coverage (θ_max = 0.051) was measured directly. The surface-blocking function and the deposition coefficient (k_pore = 3.56 s^-1) were obtained. Using these pore-scale parameters, the transport of colloidal particles was modeled using a one-dimensional advection-dispersion-deposition equation under the assumption of irreversible adsorption between oppositely charged beads and colloids, showing very good agreement with experimental breakthrough curves and retention profiles at the scale of the entire porous medium analogue. This work presents a new approach to fabricate chemically heterogeneous porous media in a microfluidic device that enables the direct measurement of pore-scale colloidal deposition. Compared with the conventional curve-fitting method for deposition constant, our approach allows quantitative prediction of colloidal breakthrough and retention via coupling of direct pore-scale measurements and an advection-dispersion-deposition model.

Multiscale dynamics of colloidal deposition and erosion in porous media

Diverse processes-e.g., environmental pollution, groundwater remediation, oil recovery, filtration, and drug delivery-involve the transport of colloidal particles in porous media. Using confocal microscopy, we directly visualize this process in situ and thereby identify the fundamental mechanisms by which particles are distributed throughout a medium. At high injection pressures, hydrodynamic stresses cause particles to be continually deposited on and eroded from the solid matrix-notably, forcing them to be distributed throughout the entire medium. By contrast, at low injection pressures, the relative influence of erosion is suppressed, causing particles to localize near the inlet of the medium. Unexpectedly, these macroscopic distribution behaviors depend on imposed pressure in similar ways for particles of different charges, although the pore-scale distribution of deposition is sensitive to particle charge. These results reveal how the multiscale interactions between fluid, particles, and the solid matrix control how colloids are distributed in a porous medium.

Nanoparticle Tracking to Probe Transport in Porous Media

From the granular and fractured subsurface environment to highly engineered polymer membranes used in pharmaceutical purification, porous materials are ubiquitous in nature and industrial applications. In particular, porous media are used extensively in processes including water treatment, pharmaceutical sterilization, food/beverage processing, and heterogeneous catalysis, where hindered mass transport is either essential to the process or a necessary but undesirable limitation. Unfortunately, there are currently no universal models capable of predicting mass transport based on a description of the porous material because real porous materials are complex and because many coupled dynamic mechanisms (e.g., adsorption, steric effects, hydrodynamic effects, electrostatic interactions, etc.) give rise to the observed macroscopic transport phenomena.While classical techniques, like nuclear magnetic resonance and dynamic light scattering, provide useful information about mass transport in porous media at the ensemble level, they provide limited insight into the microscopic mechanisms that give rise to complex phenomena such as anomalous diffusion, hindered pore-space accessibility, and unexpected retention under flow, among many others. To address this issue, we have developed refractive index matching imaging systems, combined with single-particle tracking methods, allowing the direct visualization of single-particle motion within a variety of porous materials.In this Account, we summarize our recent efforts to advance the understanding of nanoparticle transport in porous media using single-particle tracking methods in both fundamental and applied scenarios. First, we describe the basic principles for two-dimensional and three-dimensional single-particle tracking in porous materials. Then, we provide concrete examples of nanoparticle transport in porous materials from two perspectives: (1) understanding fundamental elementary particle transport processes in porous media, including pore accessibility and cavity escape, which limit transport in porous media, and (2) facilitating applications in industrial processes, e.g., by understanding the mechanisms of particle fouling and remobilization in filtration membranes. Finally, we provide an outlook of opportunities associated with investigating other types of mass transport in confined environments using single-particle tracking methods, including electrophoretic and self-propelled motion.