Geometry-induced asymmetric capillary flow

The Fastest Capillary Flow in Root-like Networks under Gravity

Capillary flow has garnered significant attention due to its unique dynamic characteristics that require no external force. Creating a quantitative analytical model to evaluate capillary flow behaviors in root-like networks is essential for enhancing fluid control properties in functional textiles. In this study, we explore the capillary dynamics within root-like networks under the influence of gravity and derive the most rapid capillary flow via structural optimization. The flow time in a capillary is dominated by the capillary pressure, viscous pressure loss, and gravity, each of which exhibits diverse sensitivities to the structures of root-like networks. We scrutinize various structural parameters to understand their impact on capillary flow in root-like networks. Subsequently, optimal structural parameters (namely, the mother tube diameter and diameter ratio) are identified to minimize capillary flow time. Moreover, we discovered that the correlation between flow time and distance for capillary flow in root-like networks does not obey the classical Lucas-Washburn equation. These results affirm that root-like networks can enhance capillary flow, providing critical insights for numerous capillary-flow-dependent engineering applications.

Effects of Relative Humidity and Paper Geometry on the Imbibition Dynamics and Reactions in Lateral Flow Assays

Lateral flow assays and paper microfluidics have the potential to replace benchtop instrumented medical diagnostic systems with instrument-free systems that rely on passive transport of liquid through micro-porous paper substrates. Predicting the imbibition dynamics of liquid through dry paper substrates is mostly modeled through the Lucas-Washburn (LW) equations. However, the LW framework assumes that the fluid front exhibits a sharp boundary between the dry and wet phases across the liquid imbibition interface. Additionally, the relative humidity in the environment results in moisture trapped within the pores of the paper substrates as the paper attains an equilibrium with the ambient air. Here, we apply a two-phase transport framework based on Brooks and Corey's model to capture imbibition dynamics on partially saturated paper substrates. The model is experimentally validated and is then used to predict the liquid-paper imbibition dynamics in simulated environments with 1-70% relative humidity. The model was also used to determine the saturation gradient of liquid along the imbibition interface of the paper substrate. Insights from these studies enabled us to determine the mechanism of the liquid transport in partially saturated porous paper substrates. The model also enabled us to evaluate the optimal paper shapes and relative humidity of the environment that maximize imbibition rates and minimize imbibition front broadening. Finally, we evaluate the effect of moisture content of paper on the rate of paper-based biochemical reaction by amplifying a sequence of the SARS-CoV-2 RNA target via reverse transcriptase loop-mediated isothermal amplification. Taken together, this study provides some important guidelines to academic and applied researchers working in point-of-care diagnostics to develop paper-based testing platforms that are capable of functioning in a robust manner across multiple environmental conditions.

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.

Rational Design of Li-Wicking Hosts for Ultrafast Fabrication of Flexible and Stable Lithium Metal Anodes

The ever-increasing development of flexible and wearable electronics has imposed unprecedented demand on flexible batteries of high energy density and excellent mechanical stability. Rechargeable lithium (Li) metal battery shows great advantages in terms of its high theoretical energy density. However, the use of Li metal anode for flexible batteries faces huge challenges in terms of its undesirable dendrite growth, poor mechanical flexibility, and slow fabrication speed. Here, a highly scalable Li-wicking strategy is reported that allows ultrafast fabrication of mechanically flexible and electrochemically stable Li metal anodes. Through the rational design of the interface and structure of the wicking host, the mean speed of Li-wicking reaches 10 m² min^-1 , which is 1000 to 100 000 fold faster than the reported electrochemical deposition or thermal infusion methods and meets the industrial fabrication speed. Importantly, the Li-wicking process results in a unique 3D Li metal structure, which not only offers remarkable flexibility but also suppresses the dendrite formation. Paring the Li metal anode with lithium-iron phosphate or sulfur cathode yields flexible full cells that possess a high charging rate (8.0 mA cm^-2 ), high energy density (300-380 Wh kg^-1 ), long cycling stability (over 550 cycles), and excellent mechanical robustness (500 bending cycles).

Imbibition of Newtonian Fluids in Paper-like Materials with the Infinitesimal Control Volume Method

Paper-based microfluidic devices are widely used in point-of-care testing applications. Imbibition study of paper porous media is important for fluid controlling, and then significant to the applications of paper-based microfluidic devices. Here we propose an analytical approach based on the infinitesimal control volume method to study the imbibition of Newtonian fluids in commonly used paper-like materials. Three common paper shapes (rectangular paper strips, fan-shaped and circular paper sheets) are investigated with three modeling methods (corresponding to equivalent tiny pores with circle, square and regular triangle cross section respectively). A model is derived for liquid imbibition in rectangular paper strips, and the control equations for liquid imbibition in fan-shaped and circular paper sheets are also derived. The model is verified by imbibition experiments done using the mixed cellulose ester filter paper and pure water. The relation of imbibition distance and time is similar to that of the Lucas−Washburn (L−W) model. In addition, a new porosity measurement method based on the imbibition in circular paper sheets is proposed and verified. Finally, the flow rates are investigated. This study can provide guidance for the design of different shapes of paper, and for better applications of paper-based microfluidic devices.

Marangoni effect inspired robotic self-propulsion over a water surface using a flow-imbibition-powered microfluidic pump

Certain aquatic insects rapidly traverse water by secreting surfactants that exploit the Marangoni effect, inspiring the development of many self-propulsion systems. In this research, to demonstrate a new way of delivering liquid fuel to a water surface for Marangoni propulsion, a microfluidic pump driven by the flow-imbibition by a porous medium was integrated to create a novel self-propelling robot. After triggered by a small magnet, the liquid fuel stored in a microchannel is autonomously transported to an outlet in a mechanically tunable manner. We also comprehensively analyzed the effects of various design parameters on the robot's locomotory behavior. It was shown that the traveled distance, energy density of fuel, operation time, and motion directionality were tunable by adjusting porous media, nozzle diameter, keel-extrusion, and the distance between the nozzle and water surface. The utilization of a microfluidic device in bioinspired robot is expected to bring out new possibilities in future development of self-propulsion system.

Equilibrium structures of water molecules confined within a multiply connected carbon nanotube: a molecular dynamics study

Water confinement inside a carbon nanotube (CNT) has been one of the most exciting subjects of both experimental and theoretical interest. Most of the previous studies, however, considered CNT structures with simple cylindrical shapes. In this paper, we report a classical molecular dynamics study of the equilibrium structural arrangement of water molecules confined in a multiply connected carbon nanotube (MCCNT) containing two Y-junctions. We investigate the structural arrangement of the water molecules in the MCCNT in terms of the density of water molecules and the average number of hydrogen bonds per water molecule. Our results show that the structural rearrangement of the H2O molecules takes place several angstroms ahead of the Y-junction, rather than only at the CNT junction itself. This phenomenon arises because it is difficult to match the boundary condition for hydrogen bonding in the region where two different hydrogen-bonded structures are interconnected with each other.

Tailoring porous media for controllable capillary flow

HYPOTHESIS

Control of capillary flow through porous media has broad practical implications. However, achieving accurate and reliable control of such processes by tuning the pore size or by modification of interface wettability remains challenging. Here we propose that the liquid flow by capillary penetration can be accurately adjusted by tuning the geometry of porous media.

METHODOLOGIES

On the basis of Darcy's law, a general framework is proposed to facilitate the control of capillary flow in porous systems by tailoring the geometric shape of porous structures. A numerical simulation approach based on finite element method is also employed to validate the theoretical prediction.

FINDINGS

A basic capillary component with a tunable velocity gradient is designed according to the proposed framework. By using the basic component, two functional capillary elements, namely, (i) flow accelerator and (ii) flow resistor, are demonstrated. Then, multi-functional fluidic devices with controllable capillary flow are realized by assembling the designed capillary elements. All the theoretical designs are validated by numerical simulations. Finally, it is shown that the proposed concept can be extended to three-dimensional design of porous media.

Nanojunction Effects on Water Flow in Carbon Nanotubes

We report on the results of extensive molecular dynamics simulation of water imbibition in carbon nanotubes (CNTs), connected together by converging or diverging nanojunctions in various configurations. The goal of the study is to understand the effect of the nanojunctions on the interface motion, as well as the differences between what we study and water imbibition in microchannels. While the dynamics of water uptake in the entrance CNT is the same as that of imbibition in straight CNTs, with the main source of energy dissipation being the friction at the entrance, water uptake in the exit CNT is more complex due to significant energy loss in the nanojunctions. We derive an approximate but accurate expression for the pressure drop in the nanojunction. A remarkable difference between dynamic wetting of nano- and microjunctions is that, whereas water absorption time in the latter depends only on the ratios of the radii and of the lengths of the channels, the same is not true about the former, which is shown to be strongly dependent upon the size of each segment of the nanojunction. Interface pinning-depinning also occurs at the convex edges.

Spontaneous imbibition in fractal tortuous micro-nano pores considering dynamic contact angle and slip effect: phase portrait analysis and analytical solutions

Shales have abundant micro-nano pores. Meanwhile, a considerable amount of fracturing liquid is imbibed spontaneously in the hydraulic fracturing process. The spontaneous imbibition in tortuous micro-nano pores is special to shale, and dynamic contact angle and slippage are two important characteristics. In this work, we mainly investigate spontaneous imbibition considering dynamic contact angle and slip effect in fractal tortuous capillaries. We introduce phase portrait analysis to analyse the dynamic state and stability of imbibition. Moreover, analytical solutions to the imbibition equation are derived under special situations, and the solutions are verified by published data. Finally, we discuss the influences of slip length, dynamic contact angle and gravity on spontaneous imbibition. The analysis shows that phase portrait is an ideal tool for analysing spontaneous imbibition because it can evaluate the process without solving the complex governing ordinary differential equations. Moreover, dynamic contact angle and slip effect play an important role in fluid imbibition in fractal tortuous capillaries. Neglecting slip effect in micro-nano pores apparently underestimates imbibition capability, and ignoring variations in contact angle causes inaccuracy in predicting imbibition speed at the initial stage of the process. Finally, gravity is one of the factors that control the stabilisation of the imbibition process.

Design of Nanofibrous and Microfibrous Channels for Fast Capillary Flow

The speed of capillary flow is a key bottleneck in improving the performance of nanofluidic and microfluidic devices for various applications including microfluidic diagnostics, thermal management heat pipes, micromolding devices, functional fabrics, and oil-water separators. Here, we present a novel nanofibrous or microfibrous hollow-wedged channel (named as W-Channel), which can significantly speed up the capillary flow. The capillary flow in the initial 100 s in the nanofibrous W-Channel was shown to be 8 times faster than that in the single-layer strip of the same material when placed vertically and over 20 times faster when placed horizontally. The enhanced flow under gravity is attributed to the adaptive interplay of capillary pressure and flow resistance within the triangular hollow wedge between the fibrous layers. The W-Channel can be fabricated following a simple procedure using inexpensive materials such as electrospun nanofibers or microfibrous filter papers.

A review on wax printed microfluidic paper-based devices for international health

Paper-based microfluidics has attracted attention for the last ten years due to its advantages such as low sample volume requirement, ease of use, portability, high sensitivity, and no necessity to well-equipped laboratory equipment and well-trained manpower. These characteristics have made paper platforms a promising alternative for a variety of applications such as clinical diagnosis and quantitative analysis of chemical and biological substances. Among the wide range of fabrication methods for microfluidic paper-based analytical devices (μPADs), the wax printing method is suitable for high throughput production and requires only a commercial printer and a heating source to fabricate complex two or three-dimensional structures for multipurpose systems. μPADs can be used by anyone for in situ diagnosis and analysis; therefore, wax printed μPADs are promising especially in resource limited environments where people cannot get sensitive and fast diagnosis of their serious health problems and where food, water, and related products are not able to be screened for toxic elements. This review paper is focused on the applications of paper-based microfluidic devices fabricated by the wax printing technique and used for international health. Besides presenting the current limitations and advantages, the future directions of this technology including the commercial aspects are discussed. As a conclusion, the wax printing technology continues to overcome the current limitations and to be one of the promising fabrication techniques. In the near future, with the increase of the current interest of the industrial companies on the paper-based technology, the wax-printed paper-based platforms are expected to take place especially in the healthcare industry.

Capillary Displacement of Viscous Liquids in Geometries with Axial Variations

Axial variations in geometry and presence of viscous displaced fluid are known to alter the diffusive-dynamics of capillary imbibition of a wetting liquid. We here show that the coupled effect of axially varying capillary geometry and finite viscosity of the displaced fluid can lead to significant variations in both short and long time dynamics of imbibition. Based on a theoretical model and lattice Boltzmann simulations, we analyze capillary displacement of a viscous liquid in straight and diverging capillaries. At short times, the imbibition length scales proportionally with time as opposed to the diffusive-dynamics of imbibition of a single wetting liquid. Whereas, at long times, geometry-dependent power-law behavior occurs which qualitatively resembles single liquid imbibition. The distance at which the crossover between these two regimes occurs depends strongly on the viscosities of the imbibing and the displaced liquid. Additionally, our simulations show that the early time imbibition dynamics are also affected by the dynamic contact angle of the meniscus.

Evaporation Limited Radial Capillary Penetration in Porous Media

The capillary penetration of fluids in thin porous layers is of fundamental interest in nature and various industrial applications. When capillary flows occur in porous media, the extent of penetration is known to increase with the square root of time following the Lucas-Washburn law. In practice, volatile liquid evaporates at the surface of porous media, which restricts penetration to a limited region. In this work, on the basis of Darcy's law and mass conservation, a general theoretical model is developed for the evaporation-limited radial capillary penetration in porous media. The presented model predicts that evaporation decreases the rate of fluid penetration and limits it to a critical radius. Furthermore, we construct a unified phase diagram that describes the limited penetration in an annular porous medium, in which the boundaries of outward and inward liquid are predicted quantitatively. It is expected that the proposed theoretical model will advance the understanding of penetration dynamics in porous media and facilitate the design of engineered porous architectures.

Intrusion of a Liquid Droplet into a Powder under Gravity

Intrusion of a liquid droplet into a hexagonal close-packed array of spheres under gravity is investigated using analytical methods and volume-of-fluid simulations. Four regimes of ultimate fluid behavior are identified: (A) no liquid imbibition into the bed, (B) trapping of liquid high in the bed, (C) liquid descending to the bottom of the bed, and (D) liquid spreading around the surface of all particles. These regimes are mapped based on the contact angle and Bond number of the system. Many aspects of the dynamics and ultimate liquid behavior are captured using a simplified model of a mass of liquid moving under gravity in a vertical capillary of undulating cross-sectional area. This simplified model is used to form momentum transport equations with four forms of nondimensional time, which are shown to collapse the simulation data with different fluid parameters in different regimes.

Rational design of capillary-driven flows for paper-based microfluidics

The design of paper-based assays that integrate passive pumping requires a precise programming of the fluid transport, which has to be encoded in the geometrical shape of the substrate. This requirement becomes critical in multiple-step processes, where fluid handling must be accurate and reproducible for each operation. The present work theoretically investigates the capillary imbibition in paper-like substrates to better understand fluid transport in terms of the macroscopic geometry of the flow domain. A fluid dynamic model was derived for homogeneous porous substrates with arbitrary cross-sectional shapes, which allows one to determine the cross-sectional profile required for a prescribed fluid velocity or mass transport rate. An extension of the model to slit microchannels is also demonstrated. Calculations were validated by experiments with prototypes fabricated in our lab. The proposed method constitutes a valuable tool for the rational design of paper-based assays.

Structural optimization of porous media for fast and controlled capillary flows

A general quantitative model of capillary flow in homogeneous porous media with varying cross-sectional sizes is presented. We optimize the porous structure for the minimization of the penetration time under global constraints. Programmable capillary flows with constant volumetric flow rate and linear evolution of flow distance to time are also obtained. The controlled innovative flow behaviors are derived based on a dynamic competition between capillary force and viscous resistance. A comparison of dynamic transport on the basis of the present design with Washburn's equation is presented. The regulation and maximization of flow velocity in porous materials is significant for a variety of applications including biomedical diagnostics, oil recovery, microfluidic transport, and water management of fabrics.

Biofunctionalized ceramic with self-assembled networks of nanochannels

Nature designs circulatory systems with hierarchically organized networks of gradually tapered channels ranging from micrometer to nanometer in diameter. In most hard tissues in biological systems, fluid, gases, nutrients and wastes are constantly exchanged through such networks. Here, we developed a biologically inspired, hierarchically organized structure in ceramic to achieve effective permeation with minimum void region, using fabrication methods that create a long-range, highly interconnected nanochannel system in a ceramic biomaterial. This design of a synthetic model-material was implemented through a novel pressurized sintering process formulated to induce a gradual tapering in channel diameter based on pressure-dependent polymer agglomeration. The resulting system allows long-range, efficient transport of fluid and nutrients into sites and interfaces that conventional fluid conduction cannot reach without external force. We demonstrate the ability of mammalian bone-forming cells placed at the distal transport termination of the nanochannel system to proliferate in a manner dependent solely upon the supply of media by the self-powering nanochannels. This approach mimics the significant contribution that nanochannel transport plays in maintaining living hard tissues by providing nutrient supply that facilitates cell growth and differentiation, and thereby makes the ceramic composite "alive".

Structural design of a double-layered porous hydrogel for effective mass transport

Mass transport in porous materials is universal in nature, and its worth attracts great attention in many engineering applications. Plant leaves, which work as natural hydraulic pumps for water uptake, have evolved to have the morphological structure for fast water transport to compensate large water loss by leaf transpiration. In this study, we tried to deduce the advantageous structural features of plant leaves for practical applications. Inspired by the tissue organization of the hydraulic pathways in plant leaves, analogous double-layered porous models were fabricated using agarose hydrogel. Solute transport through the hydrogel models with different thickness ratios of the two layers was experimentally observed. In addition, numerical simulation and theoretical analysis were carried out with varying porosity and thickness ratio to investigate the effect of structural factors on mass transport ability. A simple parametric study was also conducted to examine unveiled relations between structural factors. As a result, the porosity and thickness ratio of the two layers are found to govern the mass transport ability in double-layered porous materials. The hydrogel models with widely dispersed pores at a fixed porosity, i.e., close to a homogeneously porous structure, are mostly turned out to exhibit fast mass transport. The present results would provide a new framework for fundamental design of various porous structures for effective mass transport.