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

Forced capillary wetting of viscoelastic fluids

HYPOTHESIS

Achieving rapid capillary wetting is highly desirable in nature and industries. Previous endeavors have primarily concentrated on passive wetting strategies through surface engineering. However, these approaches are inadequate for high-viscosity fluids due to the significant viscous resistance, especially for non-Newtonian fluids. In contrast, forced wetting emerges as a promising method to address the challenges associated with achieving rapid wetting of non-Newtonian fluids in capillaries.

EXPERIMENTS

To investigate the forced wetting behavior of viscoelastic fluids in capillaries, we employ Xanthan Gum (XG) aqueous solutions as target fluids with the storage modulus significantly exceeding the loss modulus. We utilize smooth glass capillaries connected to a syringe pump to achieve high moving speeds of up to 1 m/s.

FINDINGS

Our experiments reveal a significant distinction in the power-law exponent that governs the scaling relationship between the dynamic contact angle and velocity for viscoelastic fluids compared to Newtonian fluids. This exponent is considerably smaller and varies based on the concentration of viscoelastic fluids and the diameter of the capillaries. We suggest that the viscosity dominates the wetting dynamics of viscoelastic fluids, manifested by the contact line morphology-dependent behavior. This insight has significant implications for microfluidics and drug injectability.

Profiles of Static Liquid-Gas Interfaces in Axisymmetric Containers with Different Accelerations

Second-order perturbation solutions of profiles of bubbles suspended in liquid and liquid-gas interfaces when liquid all sinks in the bottom with different accelerations are derived. Six procedures are developed based on these solutions, and they are divided into two types. One type takes the coordinates of end points of profiles as input, and the other type takes liquid volume or gas volume as input. Numerical simulations are performed with the Volume of Fluid method, and numerical results are in good agreement with the predictions of these procedures. The greater the acceleration, the flatter the bubble until all liquid sinks to the bottom. Effects of acceleration on bubble shape must be considered; otherwise, it will cause a volume prediction error of up to 10%. When all liquid sinks to the bottom, predictions of liquid volume with the same liquid meniscus height as inputs differ considerably for different accelerations. The most significant change in liquid volume occurs when the bond number Bo ≪ 1. Effects of acceleration and liquid contact angle on the liquid-gas interfaces must be considered when evaluating liquid residue. These findings should be quite helpful for liquid residue measurement and fine management in spacecraft.

Insights into mechanism and modelling of dynamic moisture sorption in dual-porous insulation materials with micro- and nano-scale pores

HYPOTHESIS

Understanding moisture sorption in porous insulation materials is challenging due to the influence of multiscale pore structures on phase behavior and transport properties. Dynamic moisture sorption in dual-porous materials is likely co-determined by interior micro- and nano-scale pores, and an accurate physical model for predicting moisture evolution can be developed by clarifying the sorption mechanisms.

EXPERIMENTS

Moisture behavior during the dynamic sorption of dual-porous insulation material is measured by low-field nuclear magnetic resonance (NMR) experiments. The contributions of micro- and nano-scale pores to the adsorbed moisture are differentiated using NMR relaxometry, and the evolution of moisture morphology is quantitatively analyzed.

FINDINGS

Analysis of T2 evolution reveals that the moisture in nano-scale pores alters from adsorption layers to liquid with increasing relative humidity (RH), while minimal sorption occurs in micro-scale pores. Moisture is mainly transferred as vapor molecules at low RH levels, with the dynamic sorption enhanced by molecular diffusion in micro-scale pores. Capillary flow in nano-scale pores dominates moisture transport when RH rises above a threshold, leading to a significant increase in apparent moisture diffusivity. According to the elucidated mechanism, a physical model is further developed to predict moisture sorption inside dual-porous insulation materials, and it may serve as a basis for evaluating and optimizing the performance of dual-porous systems in different environments.

Dynamic Pore Network Modeling of Imbibition in Real Porous Media with Corner Film Flow

Wetting films can develop in the corners of pore structures during imbibition in a strongly wetting porous medium, which may significantly influence the two-phase flow dynamics. Due to the large difference in scales between main meniscus and corner film, accurate and efficient modeling of the dynamics of corner film remains elusive. In this work, we develop a novel two-pressure dynamic pore network model incorporating the interacting capillary bundle model to analyze the competition between the main meniscus and corner film flow in real porous media. A pore network with four-point star-shaped pore bodies and throat bonds is extracted from the real porous medium based on the pore shape factor and pore cross-sectional area, which is then decomposed into several layers of sub-pore networks, where the first layer of sub-pore network simulates the main meniscus flow while the upper layers characterize the corner film flow. The two-phase flow conductance of throat bonds for different layers of sub-pore networks are determined by high-resolution two-phase lattice Boltzmann modeling, thus inherently considering the viscous coupling effect. In addition, two artificial neural network models are developed to predict the two phases' flow conductance based on the shape of the throat cross section and the fluid properties. The accuracy of the developed model is validated with a lattice Boltzmann simulation of imbibition in a strongly wetting square tube. Then the model is used to simulate imbibition in a strongly wetting sandstone porous medium, and the competition between the main meniscus and the corner film flow is analyzed. The results show that with decreasing capillary number and viscosity ratio between wetting and nonwetting fluids, the development of the wetting corner film becomes more significant.

Auto-ejection of liquid from a nozzle

Auto-ejection of liquid is an important process in engineering applications, and is also very complicated since it involves interface moving, deforming, and jet breaking up. In this work, a theoretical velocity of meniscus at nozzle exit is first derived, which can be used to analyze the critical condition for auto-ejection of liquid. Then a consistent and conservative axisymmetric lattice Boltzmann (LB) method is proposed to study the auto-ejection process of liquid jet from a nozzle. We test the LB model by conducting some simulations, and find that the numerical results agree well with the theoretical and experimental data. We further consider the effects of contraction ratio, length ratio, contact angle, and nozzle structure on the auto-ejection, and observe some distinct phenomena during the ejection process, including the deformation of meniscus, capillary necking, and droplet pinch off. Finally, the results reported in the present work may play an instructive role on the design of droplet ejectors and the understanding of jetting dynamics in microgravity environment.

Polymer Imbibition Through Paper Strips

Liquid wicking and imbibition through porous strips are fundamental to paper microfluidics. In this study, we outline these processes via capillary rise dynamics (CRD) experiments by employing deionized water as a reference fluid and comparing its dynamics with those of aqueous polymer solutions. Replacing the working fluid with polymer solutions led to the occurrence of an intermediate viscous-dominated regime, followed by the gravity-dominated regime at a long-time scale. This transition from viscous-dominated to gravity-dominated was found to be a function of the porous substrate pore diameter. The delay in CRD from the viscous-dominated to gravity-dominated regime is explained by the presence of the prewetting front (PWF). To address it, PWF dynamics has also been quantified, along with the characterization of its morphological differences.

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.

Spontaneous imbibition of a liquid film wetting a wall-mounted cylinder corner

Spontaneous imbibition flows within confined geometries are commonly encountered in both natural phenomena and industrial applications. A profound knowledge of the underlying flow dynamics benefits a broad spectrum of engineering practices. Nonetheless, within this area, especially concerning complex geometries, there exists a substantial research gap. This work centers on the cylinder-plane geometry, employing a combined theoretical and numerical approach to investigate the process of a wetting film wrapping a cylinder corner. It is found that the advance of the liquid front generally follows the Lucas-Washburn kinetics, i.e., t1/2 scaling, but it also depends on the dynamics of the liquid source. Furthermore, a theoretical estimation of the timescale associated with the imbibition process is also provided, especially the merging time as an important time length characterizing the duration of the wetting process. The timescale is highly dependent on the wettability conditions and the properties of the involved liquid. The conclusion of this work lays a theoretical foundation for comprehensively understanding the capillary phenomena in complex media and shedding light on various microfluidic applications.

Capillary Filling in Open Rectangular Microchannels with a Spatially Varying Contact Angle

Capillary flow in microchannels is important for many technologies, such as microfluidic devices, heat exchangers, and fabrication of printed electronics. Due to a readily accessible interior, open rectangular microchannels are particularly attractive for these applications. Here, we develop modifications of the Lucas-Washburn model to explore how a spatially varying contact angle influences capillary flow in open rectangular microchannels. Four cases are considered: (i) different uniform contact angles on channel sidewalls and channel bottom, (ii) contact angles varying along the channel cross section, (iii) contact angle varying monotonically along the channel length, and (iv) contact angle varying periodically along the channel length. For case (i), it is found that the maximum filling velocity is more sensitive to changes in the wall contact angle. For case (ii), the contact angles can be averaged to transform the problem into that of case (i). For case (iii), the time evolution of the meniscus position no longer follows the simple square-root law at short times. Finally, for case (iv), the problem is well described by using a uniform contact angle that is a suitable average. These results provide insights into how to design contact-angle variations to control capillary filling and into the influence of naturally occurring contact-angle variations on capillary flow.

Chromophoric cerium oxide nanoparticle-loaded sucking disk-type strip sensor for optical measurement of glucose in tear fluid

BACKGROUND

Noninvasive monitoring of tear glucose levels can be convenient for patients to manage their diabetes mellitus. However, there are issues with monitoring tear glucose levels, such as the invasiveness of some methods, the miniaturization, inaccuracy, or the high cost of wearable devices. To overcome the issues, we newly designed a sucking disk-type (SD) strip biosensor that can quickly suck tear fluid and contains cerium oxide nanoparticle (CNP) that causes a unique color change according to the glucose level of the tear without complicated electronic components.

METHODS

The SD strip biosensor composed of three distinct parts (tip, channel, and reaction chamber) was designed to contain the sensing paper, onto which tear fluid can be collected and delivered. The sensing paper treated with CNP/APTS (aminopropyltriethoxysilane) /GOx (glucose oxidase) was characterized. Then we carried out the reliability of the SD strip biosensor in the diabetic rabbit animals. We quantitatively analyzed the color values of the SD strip biosensor through the colorimetric analysis algorithm.

RESULTS

We contacted the inferior palpebral conjunctiva (IPC) of a diabetic rabbit eye using an SD strip biosensor to collect tears without eye irritation and successfully verified the performance and quantitative efficacy of the sensor. An image processing algorithm that can optimize measurement accuracy is developed for accurate color change measurement of SD strip biosensors. The validation tests show a good correlation between glucose concentrations measured in the tear and blood.

CONCLUSION

Our findings demonstrate that the CNP-embedded SD strip biosensor and the associated image processing can simply monitor tear glucose to manage diabetes mellitus.

Self-Driven Droplet Motions Below their Icing Points

Liquid fluidity is a most key prerequisite for a broad range of technologies, from energy, fluid machineries, microfluidic devices, water, and oil transportation to bio-deliveries. While from thermodynamics, the liquid fluidity gradually diminishes as temperature decreases until completely solidified below icing points. Here, self-driven droplet motions are discovered and demonstrated occurring in icing environments and accelerating with both moving distances and droplet volumes. The self-driven motions, including self-depinning and continuous wriggling, require no surface pre-preparation or energy input but are triggered by the overpressure spontaneously established during icing and then continuously accelerated by capillary pulling of frosts. Such self-driven motions are generic to a broad class of liquid types, volumes, and numbers on various micro-nanostructured surfaces and can be facilely manipulated by introducing pressure gradients spontaneously or externally. The discovery and control of self-driven motions below icing points can greatly broaden liquid-related applications in icing environments.

Experiments on the Capillary Force of a Clam-Shell Droplet on Fibers by 3-D Model Reconstruction

The capillary force is critical to the moving and breaking of droplets on fibers. This study brings forward a 3-D model reconstruction method for a clam-shell droplet on fibers and obtains the capillary force by the surface integral of Laplace pressure on the whole droplet. The capillary force results are verified by the droplet gravity and axial drag force, respectively. Moreover, the tensile tangential stresses are analyzed to illustrate the top limits of Laplace pressure against droplet breaking or sliding on the fiber. The experiment shows that the capillary force obtained by the 3-D model accurately describes the vertical and tangential forces of the clam-shell droplet on the fiber. Sharp shrinking of the cross-section on the droplet's upper part results in an exponential increase in tensile and tangential stresses, which makes the droplet break or move on the fiber.

Gelatin Methacryloyl-Based Sponge with Designed Conical Microchannels for Rapidly Controlling Hemorrhage and Theoretical Verification

It remains a challenge to develop effective hemostatic products in battlefield rescue for noncompressible massive hemorrhage. Some previous research had concentrated on the modification of different materials to improve the hemostasis ability of sponges. Herein, to investigate the relationship between the taper of microchannels and hemostatic performance of porous sponges, gelatin methacryloyl-based sponges with designed conical microchannels and a disordered porous structure were prepared using the 3D printing method and freeze-drying technology. Experiments and theoretical model analysis demonstrated that the taper and distribution of microchannels in the sponge affected the water and blood absorption properties, as well as the expansion ability. In treatment of SD rat liver defect and SD rat liver perforation wound, GS-1 sponge with the taper (1/15) microchannels exhibited an excellent hemostatic effect with blood loss of 0.866 ± 0.093 g and a hemostasis time of 280 ± 10 s. Results showed that the hemostatic capacities of GelMA sponges were increased with the bottom diameter (taper) of conical microchannels. This is a potential strategy to develop designed taper sponges with designed taper microchannels for rapidly controlling hemorrhage.

Influencing Factors and Application of Spontaneous Imbibition of Fracturing Fluids in Tight Sandstone Gas Reservoir

This work is based on high-precision fluid spontaneous imbibition experiments to quantitatively study the imbibition rate, imbibition capacity, and imbibition curve characteristics of fracturing fluids in tight sandstone reservoirs. The objective of the work is to explore the influence of tight sandstone physical characteristics, fracturing fluid composition, salinity, viscosity, surface tension on fracturing fluid imbibition, and further analyze its main controlling factors. To evaluate imbibition characteristics more deeply, the pore throat structure and micromorphology of tight sandstone before and after imbibition were described by mercury intrusion test and scanning electron microscope test, respectively. Furthermore, the mineral composition and dilatation characteristics of the tight sandstone samples were identified by XRD and a linear dilatometer, respectively. The results show that the drilled tight sandstone samples from the Shaximiao Formation reservoir have strong heterogeneity, high clay mineral content, more developed micro/nanopores, less developed fractures, and strong hydration expansion. Since the average pore throat radius of tight sandstone samples is between 0.1 and 0.2 μm, the imbibition driving force is strong. The imbibition rate is fast, and the imbibition basically reaches a steady state within 24 h, which makes the imbibition capacity basically greater than 50%. Based on the analysis of the main control factors of imbibition, the surface tension of the fluid properties has the greatest impact on the imbibition recovery factor. The result not only helps to understand the absorption mechanism of fracturing fluid in tight sandstone reservoirs and then evaluates the degree of interaction between fluid and tight sandstone but it is also crucial for the prediction of flowback rate.

Effect of TiO2 Nanoparticles on Capillary-Driven Flow in Water Nanofilters Based on Chitosan Cellulose and Polyvinylidene Fluoride Nanocomposites: A Theoretical Study

In this study, a novel concept of nanofiltration process of drinking water based on capillary-driven nanofiltration is demonstrated using a bio-based nanocomposites’ nanofilter as free power: a green and sustainable solution. Based on Lifshitz and Young–Laplace theories, we show that the chitosan (CS), cellulose acetate (CLA), and Polyvinylidene fluoride (PVDF) polymer matrixes demonstrate hydrophobic behavior, which leads to the draining of water from nanopores when negative capillary pressure is applied and consequently prevents the capillary-driven nanofiltration process. By incorporating 10%, 20%, and 30% volume fraction of titanium dioxide (TiO₂) nanoparticles (NPs) to the polymers’ matrixes, we demonstrate a wetting conversion from hydrophobic to hydrophilic behavior of these polymer nanocomposites. Subsequently, the threshold volume fraction of the TiO₂ NPs for the conversion from draining (hydrophobic) to filling (hydrophilic) by capillary pressure were found to be equal to 5.1%, 10.9%, and 13.9%, respectively, for CS/TiO₂, CLA/TiO₂, and PVDF/TiO₂ nanocomposites. Then, we demonstrated the negligible effect of the gravity force on capillary rise as well as the capillary-driven flow for nanoscale pore size. For nanofilters with the same effective nanopore radius, porosity, pore shape factor, and tortuosity, results from the modified Lucas–Washburn model show that the capillary rise as well as the capillary-driven water volume increase with increased volume fraction of the TiO₂ NPs for all nanocomposite nanofilter. Interestingly, the capillary-driven water volume was in range (5.26–6.39) L/h·m² with 30% volume fraction of TiO₂ NPs, which support our idea for capillary-driven nanofiltration as zero energy consumption nano-filtration process. Correspondingly, the biodegradable CS/TiO₂ and CLA/TiO₂ nanocomposites nanofilter demonstrate capillary-driven water volume higher, ~1.5 and ~1.2 times, respectively, more than the synthetic PVDF/TiO₂ nanocomposite.