Capillary Displacement of Viscous Liquids in Geometries with Axial Variations

Capillary imbibition of confined monodisperse emulsions in microfluidic channels

We study imbibition of a monodisperse emulsion into high-aspect ratio microfluidic channels with the height h comparable to the droplet diameter d. Two distinct regimes are identified in the imbibition dynamics. In a strongly confined system (the confinement ratio d/h = 1.2 in our experiments), the droplets are flattened between the channel walls and move more slowly compared to the average suspension velocity. As a result, a droplet-free region forms behind the meniscus (separated from the suspension region by a sharp concentration front) and the suspension exhibits strong droplet-density and velocity fluctuations. In a weaker confinement, d/h = 0.65, approximately spherical droplets move faster than the average suspension flow, causing development of a dynamically unstable high-concentration region near the meniscus. This instability results in the formation of dense droplet clusters, which migrate downstream relative to the average suspension flow, thus affecting the entire suspension dynamics. We explain the observed phenomena using linear transport equations for the particle-phase and suspension fluxes driven by the local pressure gradient. We also use a dipolar particle interaction model to numerically simulate the imbibition dynamics. The observed large velocity fluctuations in strongly confined systems are elucidated in terms of migration of self-assembled particle chains with highly anisotropic mobility.

Capillary imbibition and flow of wetting liquid in irregular capillaries: A 100-year review

Capillary imbibition, such as plant roots taking up water, reservoir rocks absorbing brine and a tissue paper wiping stains, is pervasive occurred in nature, engineering and industrial fields, as well as in our daily life. This phenomenon is earliest modeled through the process that wetting liquid is spontaneously propelled by capillary pressure into regular geometry models. Recent studies have attracted more attention on capillary-driven flow models within more complex geometries of the channel, since a detailed understanding of capillary imbibition dynamics within irregular geometry models necessitates the fundamentals to fluid transport mechanisms in porous media with complex pore topologies. Herein, the fundamentals and concepts of different capillary imbibition models in terms of geometries over the past 100 years are reviewed critically, such as circular and non-circular capillaries, open and closed capillaries with triangular/rectangular cross-sections, and heterogeneous geometries with axial variations. The applications of these models with appropriate conditions are discussed in depth accordingly, with a particular emphasize on the capillary flow pattern as a consequence of capillary geometry. In addition, a universal model is proposed based on the dynamic wetting condition and equivalent cylindrical geometry to describe the capillary imbibition process in terms of various solid topologies. Finally, future research is suggested to focus on analyzing the dynamics during corner flow, the snap-off of wetting fluid, the capillary rise of non-Newtonian fluids and applying accurate physical simulation methods on capillary-driven flow processes. Generally, this review provides a comprehensive understanding of the capillary-driven flow models inside various capillary geometries and affords an overview of potential advanced developments to enhance the current understanding of fluid transport mechanisms in porous media.

Capillary Replacement in a Tube Prefilled with a Viscous Fluid

Capillary invasion of a liquid into an empty tube, which is called capillary rise when the tube axis is in the vertical direction, is one of the fundamental phenomena representing capillary effects. Usually, the tube is filled with another pre-existing fluid, air, whose viscosity and inertia can be practically neglected. In this study, we considered the effect of the pre-existing fluid, when its viscosity is non-negligible, in a horizontal geometry. We observed the dynamics when a capillary tube that is submerged horizontally in a liquid gets in contact with a second liquid. An appropriate combination of liquids allowed us to observe that the second liquid replaces the first without any prewetting process, thanks to a careful cleaning of capillary tubes. As a result, we experimentally observed three distinct viscous dynamics: (i) the conventional slowing-down dynamics, (ii) an unusual accelerating dynamics, and (iii) another unusual dynamics, which is linear in time. We derived a simple unified expression describing the three distinct dynamics, which accounts well for the observations. We also demonstrated a thorough experimental confirmation on the initial velocity of the replacement and the replacement time, the time required for the invading fluid to completely replace the pre-existing fluid in the horizontal geometry.

Inertia Controlled Capillary Pressure at the Juncture between Converging and Uniform Channels

In this research, we reveal the transient behavior of capillary pressure as the fluid-fluid interface travels across the juncture between a converging and uniform capillary, via high-resolution CFD (Computational Fluid Dynamics) simulations. Simulations were performed at different wetting conditions (strong-wet and intermediate-wet) and capillary wall convergence angles. Our results demonstrate that as the angle of convergence increases, capillary pressure at the junction decreases commensurately. Moreover, in contrast to strong-wet conditions, the profile of capillary pressure at the converging-uniform capillary juncture under intermediate-wet conditions is highly non-monotonic, being characterized by a parabola-like form. This non-monotonic behavior is a manifestation of strong inertial forces governing dynamic fluid-fluid interface morphology. This yields conditions that promote the advancement of the fluid-fluid interface, as inertial forces partially nullify the capillary pressure required for the immiscible interface to enter the uniform capillary. In addition to numerical analysis detailed above, a novel theoretical stability criteria that is capable of distinguishing between stable (capillary dominated) and unstable (inertia dominated) interfacial regimes at the converging-uniform capillary juncture is also proposed. In summary, this fundamental study offers new insights into the interface invasion protocol, and paves the way for the re-evaluation of capillary junction controlled interfacial dynamics.

Capillary displacement of viscous liquids in a multi-layered porous medium

Capillary driven displacement of viscous liquids into a porous matrix plays a significant role in several porous media applications such as fractured oil reservoirs and paper micro-fluidic devices. The inherent heterogeneity in porous media is known to cause the invading fluid front to lead in narrow pores followed by large pores during spontaneous imbibition. Here, we use experiments in a layered porous medium to show that the leading front is not always in the narrow pores. We observe in a two layered porous medium that the fluid front always advances faster in the narrow pores. However, in a multi-layered porous medium, the front displacement is strongly dependent on the arrangement of the layers, the relative difference between the capillary pressure, the permeability of the layers, and the viscosity ratio of the wetting and the non-wetting fluids. We also develop a one-dimensional lubrication approximation model based on the experimental observations, which predicts the imbibition dynamics in the layers seen in the experiments. Additionally, from our model, we present a scaling law governing the leading front in the porous layers. We also predict using our model that the volume imbibed in the layered porous medium cannot be determined by using the effective porous medium properties and a detailed knowledge of the characteristics of the layers is required to accurately predict the overall imbibition of the layered porous medium.

Help from a Hindrance: Using Astigmatism in Round Capillaries To Study Contact Angles and Wetting Layers

Round glass capillaries are a basic tool in soft-matter science, but often are shunned due to the astigmatism they introduce in micrographs. Here, we show how refraction in a capillary can be a help instead of a hindrance to obtain precise and sensitive information on two important interfacial properties: the contact angle of two immiscible fluids and the presence of thin films on the capillary wall. Understanding optical cusps due to refraction allows direct mesurement of the inner diameter of a capillary at the meniscus, which, with the height of the meniscus cap, determines the contact angle. The meniscus can thus be measured without intrusive additives to enhance visibility, such as dyes or calibrated particles, in uniform, curved, or even tapered capillaries or under demanding conditions not accessible by conventional methods, such as small volumes (μL), high temperatures, or high pressures. We further elicit the conditions for strong internal reflection on the inner capillary wall, involving the wall and fluid refractive indices and the wall thickness, and show how to choose the capillary section to detect thin (submicron) layers on the wall, by the contribution of total internal reflection to the cusps. As examples, we report the following: (i) CO₂-water or -brine contact angles at glass interfaces, measured at temperatures and pressures up to 200 °C and 600 bar, revealing an effect apparently so far unreported-the decrease in the water-wet character of glass, due to dissolved salts in brine, is strongly reduced at high temperatures, where contact angles converge toward the values in pure water; (ii) A tenuous gas hydrate layer growing from the water-guest contact line on glass, invisible in transmission microscopy but prominent in the cusps due to total internal reflection.

Spontaneous imbibition in parallel layers of packed beads

The imbibition of a wetting fluid in a homogeneous porous medium follows the diffusion-like behavior described by Washburn. The impregnation of a two-layered porous medium by a wetting fluid due to capillary action has been previously described to have two fronts, one saturating the medium and the other, leading front, which propagates in finer pores. Here, we report that the leading front is governed by the porous structure and is not always in the finer pores. Based on the experiments in a layered porous medium of permeability varying perpendicular to the direction of flow, we show that the permeability of the adjacent layers plays a significant role in determining the leading front amongst the layers. We have also developed an analytical model which describes the flow dynamics in the layered porous medium. The model predicts the condition for which the leading front in the larger pores is followed by the front in the finer pores. This condition is also verified experimentally.