Liquid morphologies and capillary forces between three spherical beads

Numerical Investigation of Funicular Liquid Bridges between Three Spherical Grains in a Bidisperse Particulate System

Appropriate capillary effects are beneficial for controlling the wet powder performance and agglomerate formation. As water content rises, the funicular regime supplants the pendular regime as the predominant state in wet granular media. The displacement of grains leading to the stretching of funicular liquid bridges until rupture is an interesting and common phenomenon. Utilizing Surface Evolver software (an energy minimization approach), this work develops an efficient and accurate numerical model to describe liquid interactions among three spherical grains. The effects of liquid volume, contact angle, grain size ratio, grain-pair gap, and separation distance on the capillary forces and rupture distances are investigated. Notably, we present a modified closed-form equation for predicting the rupture distance of funicular bridges between three grains, which reflects the coupled effects of the contact angle, grain size, and liquid volume on rupture distance. This present study provides insights for incorporating capillary effects into mechanical models relying on microassembly composed of several grains in bidisperse particulate systems. Additionally, the numerical findings confirm some findings regarding the splitting of funicular bridges.

Fates of a Nonwetting Slug in Tapered Microcapillaries under Gravity and Zero Gravity Conditions: Dynamics, Asymptotic Equilibrium Analysis, and Computational Fluid Dynamics Verifications

It has been determined experimentally and numerically that a nonwetting slug in a tapered capillary tube, under the sole action of capillary force, self-propels itself toward the wider end of the tube until an equilibrium state is reached. The aim of this work is to highlight the state of the slug at equilibrium in terms of configuration and location. Furthermore, it turns out that gravity adds richness to this phenomenon, and more fates become possible. A modified Bond number is developed that determines the relative importance of gravity and capillarity for this system. According to the magnitude of the Bond number, three more fates are possible. Therefore, in a tapered capillary tube held vertically upward with its wider end at the top, in the absence of gravity or under microgravity conditions, the nonwetting slug moves upward toward the wider end of the tube until it reaches equilibrium with the two menisci part of a single sphere. The location of the slug at equilibrium in this case represents the farthest fate among the other fates. When gravity exists yet capillarity dominates, the slug still moves upward toward the wider end. However, in this case, the two menisci become parts of two different spheres of different curvatures. For this scenario, the slug climbs upward but reaches a lower level compared to the previous scenario. On the other hand, when gravity dominates, the slug experiences a net downward pull toward the narrower end of the tube and starts to move in the direction of gravity until capillary force establishes a balance, then it stops. When gravity sufficiently dominates, it pulls the slug downward until it completely drains off the tube. A computational fluid dynamics (CFD) analysis is conducted in order to build a framework for verification exercises. Excellent agreements between the results of the developed model and the CFD analysis are obtained. A fate map and a scheme are developed to identify these four fates based on two Bond numbers; namely, the initial Bond number and that associated with the slug when it is at the exit.

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.

Modeling ternary fluids in contact with elastic membranes

We present a thermodynamically consistent model of a ternary fluid interacting with elastic membranes. Following a free-energy modeling approach for the fluid phases, we derive the governing equations for the dynamics of the ternary fluid flow and membranes. We also provide the numerical framework for simulating such fluid-structure interaction problems. It is based on the lattice Boltzmann method for the ternary fluid (Eulerian description) and a finite difference representation of the membrane (Lagrangian description). The ternary fluid and membrane solvers are coupled through the immersed boundary method. For validation purposes, we consider the relaxation dynamics of a two-dimensional elastic capsule placed at a fluid-fluid interface. The capsule shapes, resulting from the balance of surface tension and elastic forces, are compared with equilibrium numerical solutions obtained by surface evolver. Furthermore, the Galilean invariance of the proposed model is proven. The proposed approach is versatile, allowing for the simulation of a wide range of geometries. To demonstrate this, we address the problem of a capillary bridge formed between two deformable capsules.

Wetting of a liquid annulus in a capillary tube

In this paper, we systematically investigate the static wetting behavior of a liquid ring in a cylindrical capillary tube. We obtain analytical solutions of the axisymmetric Young-Laplace equation for arbitrary contact angles. We find that, for specific values of the contact angle and the volume of the liquid ring, two solutions of the Young-Laplace equation exist, but only the one with the lower value of the total interfacial energy corresponds to a stable configuration. Based on a numerical scheme determining configurations with a local minimum of the interfacial energy, we also discuss the stability limit between axisymmetric rings and non-axisymmetric configurations. Beyond the stable regime, a liquid plug or a sessile droplet exists instead of a liquid ring, depending on the values of the liquid volume and the contact angle. The stability limit is characterized by specific critical parameters such as the liquid volume, throat diameter, etc. The results are presented in terms of a map showing the different stable liquid morphologies that are obtained from an axisymmetric ring as base state.

Connecting particle clustering and rheology in attractive particle networks

The structural properties of suspensions and other multiphase systems are vital to overall processability, functionality and acceptance among consumers. Therefore, it is crucial to understand the intrinsic connection between the microstructure of a material and the resulting rheological properties. Here, we demonstrate how the transitions in the microstructural conformations can be quantified and correlated to rheological measurements. We find semi-local parameters from graph theory, the mathematical study of networks, to be useful in linking structure and rheology. Our results, using capillary suspensions as a model system, show that the use of the clustering coefficient, in combination with the coordination number, is able to capture not only the agglomeration of particles, but also measures the formation of groups. These phenomena are tightly connected to the rheological properties. The present sparse networks cannot be described by established techniques such as betweenness centrality.

Unstable, Super Critical CO2-Water Displacement in Fine Grained Porous Media under Geologic Carbon Sequestration Conditions

In this study we investigated fluid displacement water with supercritical (sc) CO₂ in chalk under conditions close to those used for geologic CO₂ sequestration (GCS), to answer two main questions: How much volume is available for scCO₂ injection? And what is the main mechanism of displacement over a range of temperatures? Characterization of immiscible scCO₂ displacement, at the pore scale in the complex microstructure in chalk reservoirs, offers a pathway to better understand the macroscopic processes at the continuum scale. Fluid behavior was simulated by solving the Navier-Stokes equations, using finite-volume methods within a pore network. The pore network was extracted from a high resolution 3D image of chalk, obtained using X-ray nanotomography. Viscous fingering dominates scCO₂ infiltration and pores remain only partially saturated. The unstable front, developed with high capillary number, causes filling of pores aligned with the flow direction, reaching a maximum of 70% scCO₂ saturation. The saturation rate increases with temperature but the final saturation state is the same for all investigated temperatures. The higher the saturation rate, the higher the dynamic capillary pressure coefficient. A higher dynamic capillary pressure coefficient indicates that scCO₂ needs more time to reach capillary equilibrium in the porous medium.

Effect of an interstitial fluid on the dynamics of three-dimensional granular media

The propagation of mechanical energy in granular materials has been intensively studied in recent years given the wide range of fields that have processes related to this phenomena, from geology to impact mitigation and protection of buildings and structures. In this paper, we experimentally explore the effect of an interstitial fluid on the dynamics of the propagation of a mechanical pulse in a granular packing under controlled confinement pressure. The experimental results reveal the occurrence of an elastohydrodynamic mechanism at the scale of the contacts between wet particles. We describe our results in terms of an effective medium theory, including the presence of the viscous fluid. Finally, we study the nonlinear weakening of the granular packing as a function of the amplitude of the pulses. Our observations demonstrate that the softening of the material can be impeded by adjusting the viscosity of the interstitial fluid above a threshold at which the elastohydrodynamic interaction overcomes the elastic repulsion due to the confinement.

Effect of geometry on the dewetting of granular chains by evaporation

Understanding evaporation or drying in granular media still remains complex despite recent advancements. Evaporation depends on liquid transport across a connected film network from the bulk to the surface. In this study, we investigate the stability of film networks as a function of the geometry of granular chains of spherical grains. Using a controlled experimental approach, we vary the grain arrangement or packing and measure the height of the liquid film network during evaporation as packing shifts from loose-packed to close-packed arrangement. This height can be calculated from an equilibrium between hydrostatic pressure and the capillary pressure difference in the vertical film network. Following a simulation approach using Surface Evolver, we evaluate the pressure variation due to dewetting of the meniscus volume in the grains in both the percolating front and evaporating front within the two-phase zone of air/water mixture. Results show good agreement between model and experiment. We find that above a "critical" packing angle, the liquid continuity is broken and films connections fragment into separate, isolated capillary bridges.