Washburn Model Research Articles

Two-Step Wetting of Nanoporous Carbons: Small-Angle Scattering Analysis of Capillary Rise.

Numerous applications of nanoporous materials require their pores to be filled with liquids. In spite of its huge technological importance, the conditions for the wetting of nanometer-sized pores and its phenomenology are still poorly understood. We report on capillary rise experiments with water in carbon xerogels, with synchrotron small-angle scattering used to follow the process in situ at the nanometer scale. The data reveal a two-step wetting process whereby water permeates first into molecular-sized micropores, which is followed by the imbibition of larger mesopores. A Cassie-Baxter analysis shows that the presence of water in the micropores is central, as it turns the mesopores from being hydrophobic to hydrophilic. Based on the so-calculated contact angles, the mesopore wetting kinetics are found to be quantitatively described by a classical Washburn model. Modeling of the experimental water profile ahead of the Washburn front reveals strong surface barriers opposing water transfer from the mesopores to the micropores.

Gradient-Pattern Micro-Grooved Wicks Fabricated by the Ultraviolet Nanosecond Laser Method and Their Enhanced Capillary Performance.

Capillary-gradient wicks can achieve fast or directional liquid transport, but they face fabrication challenges by traditional methods in terms of precise patterns. Laser processing is a potential solution due to its high pattern accuracy, but there are a few studies on laser-processed capillary-gradient wicks. In this paper, capillary step-gradient micro-grooved wicks (CSMWs) were fabricated by an ultraviolet nanosecond pulsed laser, and their capillary performance was studied experimentally. The CSMWs could be divided into three regions with a decreasing capillary radius. The equilibrium rising height of the CSMWs was enhanced by 124% compared to the non-gradient parallel wick. Different from the classical Lucas-Washburn model describing a uniform non-gradient wick, secondary capillary acceleration was observed in the negative gradient direction of the CSMWs. With the increase in laser power and the decrease in scanning speed, the capillary performance was promoted, and the optimal laser processing parameters were 4 W-10 mm/s. The laser-enhanced capillary performance was attributed to the improved hydrophilicity and reduced capillary radius, which resulted from the increased surface roughness, protrusion morphology, and deep-narrow V-shaped grooves induced by the high energy density of the laser. Our study demonstrates that ultraviolet pulsed laser processing is a highly efficient and low-cost method for fabricating high-performance capillary gradient wicks.

Mechanisms of the imbibition behavior in shales: A critical review

Despite the success of hydraulic fracturing in yielding large production increases from shale gas reservoirs, uncertainties associated with basic transport processes require understanding in order to improve the efficiency and minimize environmental impacts. The hydraulic fracturing process brings in large volumes of water into shale reservoir formations, most of which remains unrecoverable and interferes with shale gas production. The imbibition behavior in shales is commonly observed during the hydraulic fracturing process, and the mechanism greatly influences the hydrocarbon recovery in shale gas reservoirs. In this review, the imbibition models in shales are briefly summarized using the Lucas–Washburn model, piston repulsion model, capillary bundle model, and scalar model. Then the experimental study and numerical simulation of shale imbibition are discussed. Moreover, the influencing factors of the imbibition behavior in shales are analyzed, such as shale and fluid properties. Finally, the main conclusions and the future research direction prospects of the imbibition behavior in shale gas reservoirs are summarized. An accurate description of the imbibition behavior in shale is crucial for optimizing the hydraulic fracturing design and enhancing shale gas production in the development of shale gas reservoirs. It is proposed that the research on the individual influencing factors of shale percolation and the geological mechanism under coupling should be strengthened and that the research on the experimental aspects of shale powder percolation should be emphasized.

Liquid Permeability Determination from Vacuum Imbibition in Tight/Shale Core Plugs

Liquid permeability is a key petrophysical parameter that quantifies the ability of a liquid to flow through porous rock/soil and can be used in determining the efficiency of many subsurface processes, including enhanced hydrocarbon recovery, groundwater transport, carbon dioxide geostorage, underground hydrogen storage, etc. However, it is time-consuming (usually >16–240 h) and challenging to measure the liquid permeability for tight/shale rocks, particularly when the permeability is 100 nD or lower. The objective of this study is to develop a rapid and simple approach to determine liquid (brine or oil) permeability in tight siltstones/shales. Specifically, the developed method is based on the combination of one-dimensional (1D) vacuum imbibition experiments in tight/shale core plugs and a modified Lucas–Washburn model. For our proof-of-concept study, the results have demonstrated that (1) only 44–116 h are required to determine the liquid permeability (98–608 nD) for the analyzed samples from the Montney and Yanchang Formations; and (2) the acquired brine permeability was 28.3–28.5% lower than the slip-corrected nitrogen (N2) permeability derived from the pulse-decay permeability tests. This is the first attempt to determine the absolute permeability of a liquid according to a 1D vacuum imbibition experiment and theory. This study provides a promising technique for the fast characterization of ultratight formation permeability of around 100 nD.

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.

Mathematical model and field application of aqueous phase trapping release

ABSTRACT Aqueous phase trapping (APT) is a kind of mechanical formation damage, which occurs in tight sandstone gas reservoirs. The occurrence of APT has a dramatically adverse effect on the productivity of gas wells due to the decrease of water saturation and gas permeability near wellbore. In this research, a spontaneous imbibition experiment was carried out. The Lucas–Washburn model was used to describe the imbibition behavior. Then, a mathematical model of release judgment conditions was established based on the imbibition model, taking the threshold pressure gradient into consideration. Finally, combined with the two-phase flow mechanism of gas and water, the release time of APT was deduced. This model was used to calculate the releasing time of APT in actual producing wells, and the difference between the actual release time and predicted release time is only 0.1%, which indicates that the model established in this paper can be applied to predicting release judgment condition and release time in tight sandstone gas reservoirs precisely. The proposed model along with the findings of this research can pave the way for the continuous development of water breakthrough wells in tight sandstone gas reservoirs.

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.

Enhanced Liquid Transport on a Highly Scalable, Cost‐Effective, and Flexible 3D Topological Liquid Capillary Diode

AbstractDirectional liquid‐transport surfaces have various applications, such as, open microfluidic devices, fog collection, oil–water separation, and surface lubrication. However, current liquid‐transport surfaces are expensive, complicated to manufacture, and lack scalability. Moreover, they exhibit low transport speeds and distances. In this study, a laser cutter is used to fabricate scalable, low‐cost unidirectional liquid‐transporting surfaces with enhanced transport speed and distance using polymeric materials. Cutting and engraving methods are used to create a liquid capillary diode comprising 3D wedge shapes, thereby obtaining an appropriate pressure gradient and liquid pinning. The developed liquid capillary diode exhibits the fastest transport speed (3–17.7 mm s−1) reported so far, and a large normalized distance (L/R: transport distance/radius of dispensed droplet). The transport distance increases with the square root of time under various contact angles and liquid viscosities, which agree well with the theoretical scaling results obtained using the modified Washburn model. Additionally, the flexible liquid capillary diode operates adequately even when bent with the maximum curvature of 0.1 mm−1. The results provide better design guidelines for 3D topological liquid‐transport surfaces for various applications.

Capillary-flow dynamics in open rectangular microchannels

Abstract

Influence of droplet velocity, spacing, and inter-arrival time on line formation and saturation in binder jet additive manufacturing

Binder Jetting (BJ) is a low-cost Additive Manufacturing (AM) process that uses inkjet technology to selectively bind particles in a powder bed. BJ relies on the ability to control, not only the placement of binder on the surface but also its imbibition into the powder bed. This is a complex process in which picoliter-sized droplets impact powder beds at velocities of 1–10 m/s. However, the effects of printing parameters such as droplet velocity, size, spacing, and inter-arrival time on saturation level (fraction of pore space filled with binder) and line formation (merging of droplets to form a line) are unknown. Prior attempts to predict saturation levels with simple measurements of droplet primitives and capillary pressure assume that droplet/powder interactions are dominated by static equilibrium and neglect the impact of printing parameters. This study analyzes the influence of these parameters on the effective saturation level and conditions for line formation when printing single lines into powder beds of varied materials (316 stainless steel, 420 stainless steel, and alumina) and varied particle size (d50=10–47 µm). Results show that increasing droplet velocity or droplet spacing decreases effective saturation while droplet spacing, velocity, and inter-arrival time affect line formation. At constant printing velocity, the conditions for successful line printing are shown to be a function of droplet spacing and square root of the droplet inter-arrival time analogous to the Washburn model for infiltration into a porous media. The results have implications to maximizing build rates and improving quality of small features in BJ.

Liquid Wicking in a Paper Strip: An Experimental and Numerical Study.

In this decade, paper-based microfluidics has gained more interest in the research due to the vast applications in medical diagnosis, environmental monitoring, food safety analysis, etc. In this work, we presented a set of experiments to understand the physics of the capillary flow phenomenon through paper strips. Here, using the wicking phenomenon of the liquid in porous media, experimentally, we find out the capillary height of the liquid in filter paper at different time intervals. It was found that the Lucas–Washburn (L–W) model, as well as the evaporation model, fails to predict the capillary rise accurately. However, the detailed numerical solution shows a better similarity with the experimental results. We have also shown the different regimes of the wicking phenomenon using scaling analysis of the modified L–W model. The capillary rise method was applied to detect the added water content in milk. We used milk as a liquid food and found the added water content from the change in the capillary height at different concentrations of milk. Finally, results obtained from the paper-based device were verified with the commercially available lactometer data.

Wicking in Paper Strips under Consideration of Liquid Absorption Capacity

Paper-based microfluidic devices have the potential of being a low-cost platform for diagnostic devices. Electrical circuit analogy (ECA) model has been used to model the wicking process in paper-based microfluidic devices. However, material characteristics such as absorption capacity cannot be included in the previous ECA models. This paper proposes a new model to describe the wicking process with liquid absorption in a paper strip. We observed that the fluid continues to flow in a paper strip, even after the fluid reservoir has been removed. This phenomenon is caused by the ability of the paper to store liquid in its matrix. The model presented in this paper is derived from the analogy to the current response of an electric circuit with a capacitance. All coefficients in the model are fitted with data of capillary rise experiments and compared with direct measurement of the absorption capacity. The theoretical data of the model agrees well with experimental data and the conventional Washburn model. Considering liquid absorption capacity as a capacitance helps to explain the relationship between material characteristics and the wicking mechanism.

Microfluidic Behavior of Alumina Nanotube-Based Pathways within Hydrophobic CNT Barriers.

The use of porous micro-and nanostructured materials within microfluidic devices results in unique fluid transport characteristics. In this paper, we investigate the microfluidic behavior of hybrid alumina nanotube-based pathways within the hydrophobic carbon nanotube (CNT) barriers. These hybrid systems provide unique benefits for potential liquid transport control in porous structures with real-time sensing of fluids. In particular, we examine how the alignment of the alumina nanostructures with high internal porosity enables increased capillary action and sensitivity of detection. Based on the Lucas and Washburn model (LW) and the modified LW models, the microfluidic behavior of these systems is detailed. The time exponent prediction from the models for capillary transport in porous media is determined to be ≤0.5. The experimental results demonstrate that the average capillary rise in the nanostructured media driven by a capillary force follows t0.7. The hydrophilic/electrically insulating and hydrophobic/electrically conductive patterned structures of the device are used for electronic measurements within the microfluidic channels. The device structure enables the detection of fluid samples of very low analyte concentrations (1 μM) that can be achieved due to the very high surface area of the hybrid structure combined with the electrical conductivity of the CNT support structure.

Investigation of Capillary Filling Dynamics of Multicomponent Fluids in Straight and Periodically Constricted Microchannels.

An extensive study of capillary flow of fluids with various viscosities in straight and periodically constricted microchannels with different surface wettability is presented. Capillary filling speed in hydrophilic, less hydrophilic, and hydrophobic microchannels were experimentally monitored and compared with the Washburn theoretical model. For all liquids, a linear relationship was found between the square of propagation distance and time, which is expected for Newtonian fluids. Experimental results indicated slower velocity compared to the theoretical prediction due to simplifications of the Washburn model. Capillary filling speed of fluids into long-fluororinated chain silane modified channels confirmed the expected lyophobic nature of the coating (i.e., not favorable for either hydrophilic or hydrophobic liquids). Presence of the precursor film ahead of the three-phase contact line in the microscopic level was demonstrated. White light and fluorescent images confirmed the presence of precursor film and capillary evaporation at the interface. Evaporation enhanced the deviation between experimental and theoretical results due to continuous wettability alteration of penetrating fluid.

Polycaprolactone solution–based ink for designing microfluidic channels on paper via 3D printing platform for biosensing application

This work reports a novel fabrication technique for development of channels on paper‐based microfluidic devices using the syringe module of a 3D printing syringe–based system. In this study, printing using polycaprolactone (PCL)‐based ink (Mw 70 000‐90 000) was employed for the generation of functional hydrophobic barriers on Whatman qualitative filter paper grade 1 (approximate thickness of 180 μm and pore diameter of 11 μm), which would effectively channelize fluid flow to multiple assay zones dedicated for different analyte detection on a microfluidic paper‐based analytical device (μPAD). The standardization studies reveal that a functional hydrophilic channel for sample conduction fabricated using the reported technique can be as narrow as 460.7 ± 20 μm and a functional hydrophobic barrier can be of any width with a lower limit of about 982.2 ± 142.75 μm when a minimum number of two layers of the ink is extruded onto paper. A comparison with the hydrodynamic model established for writing with ink is used to explain the width of the line printed by this system. A fluid flow analysis through a single channel system was also carried out to establish its conformity with the Washburn model, which governs the fluid flow in two‐dimensional μPAD. The presented fabrication technique proves to be a robust strategy that effectively taps the advantages of this 3D printing technique in the production of μPADs with enhanced speed and reproducibility.

Antibody consumption reduction in lateral flow immunoassays within porous media

In this study, the effect of the geometrical parameters of the Lateral Flow Immunoassay (LFI) membrane on the performance of the pregnancy kits is investigated. Consequently, a new geometry for LFI membrane is proposed based on some theoretical, numerical and experimental observations in order to improve the performance of the related kits. A pregnancy kit (for the detection of hCG in urine samples) is developed and the effect of the relocation of the test and the control lines over the membrane was studied based on the variation of the sample fluid velocity. Using Lattice-Boltzmann simulation of the lateral flow within the porous media and the experimental results, the fluid flow within the kit membrane was fully analyzed. Finally, by focusing on the Washburn model, a modified geometry for the kit’s membrane was suggested while the flow characteristics were studied by using numerical and experimental methods. It is concluded from the observations that in our proposed geometry, the color intensity in the reaction zone of the kit is improved by 9.4 percent that can result in the reduction of antibody consumption in the kit’s membrane that could be a considerable saving during the production process of LFI.

Assessing the rapid flow in multilayer paper-based microfluidic devices

A hot topic in paper-based microfluidics is the achievement of capillary-driven flows much faster than the ones theoretically allowed by the hydrodynamic permeability of common filter papers. Recent works have experimentally shown that the flow rates can be substantially improved by using multilayer paper systems instead of single-layer papers. The present work discusses a theoretical assessment of fluid transport in multilayer paper-based microfluidic devices. The proposed model effectively predicts a series of experimental observations, namely: the occurrence of fluid velocities 2 orders of magnitude larger than those measured in single-layer paper; the variation of fluid velocity as a function of the gap thickness, which presents a particular maximum; the effects of gravity on the filling dynamics, which is unexpected for single-layer paper; and the effect of the sample volume size, which leads to non-trivial filling dynamics. It is worth mentioning that these effects cannot be described by Lucas–Washburn model for single layers, because they arise from the interplay among the coupled flow domains in the multilayer system, together with the action of the gravitational force. The proposed model provides clues to understand the fundamentals behind the capillary-driven flow in multilayer systems, and hence to better design paper-based microfluidics devices for specified flow rates and time-stepped functions.

3D inkjet printing of biomaterials with strength reliability and cytocompatibility: Quantitative process strategy for Ti-6Al-4V

Among additive manufacturing (AM) techniques, laser or electron beam based processes have been widely investigated for metallic implants. Despite the potential in manufacturing of patient-specific biomedical implants, 3D inkjet powder printing (3DIJPP, a variant of AM) of biomaterials is still in its infancy, as little is known quantitatively about the transient process physics and dynamics. An equally important challenge has been the ink formulation to manufacture biomaterials with reliable mechanical properties and desired biocompatibility. We have developed, for the very first time, the theoretical foundation and experimental formulation of a unique process strategy involving the ‘on-demand’ delivery of a novel in situ polymerisable acrylic ink system to print a model biomaterial, Ti-6Al-4V. The post-ejection in-flight dynamics of ink droplets have been captured in situ by employing high speed stroboscopic shadowgraphy, to quantitatively estimate the dimensionless numbers of fluid physics for ‘printability’ assessment. Washburn model was adapted extensively to quantify the capillary ink infiltration time in porous powder bed of finite thickness. On the other hand, particle tracking mode in diffusing wave spectroscopy (DWS) was exploited to analyse the timescale for effective binding of powder particles during in situ polymerisation. The clinically relevant combination of 3D porous architecture with 98.4% interconnectivity among 10–40 μm pores together with modest combination of elastic modulus (4 GPa) and strength reliability (Weibull modulus ∼8.1) establish the potential of inkjet printed Ti-6Al-4V as cortical bone analogue. A better cell attachment, viability, cytoskeletal spreading with pronounced proliferation of murine fibroblasts and pre-osteoblasts on 3DIJPP Ti-6Al-4V, when benchmarked against the metallurgically processed (commercial) or selective laser melted (SLM) Ti-6Al-4V, has been demonstrated, in vitro. The enhanced cellular activities on the 3DIJPP Ti-6Al-4V was explained in terms of an interplay among the elastic stiffness, surface roughness and wettability against the same benchmarking. It is conceived that the quantitative understanding of the integrated process physics and dynamics to print Ti-6Al-4V with reliable mechanical properties together with better cytocompatibility can lead to a paradigm shift in adapting the scalable 3DIJPP for manufacturing of metallic biomaterials.

A functionalized nano-structured cellulosic sorbent aerogel for oil spill cleanup: Synthesis and characterization.

A new synthesis strategy was adopted to convert cellulose to a biodegradable sorbent with properties of very high oil absorption and retention capacities, excellent oil-water selectivity, good mechanical strength and recycling ability. The sorbent in form of a hydrophobic/oleophilic nano-structured aerogel was prepared through functionalizing cotton cellulose with low surface energy moieties followed by dissolving and chemically cross-linking the product in an organic medium (DMSO), and freeze-drying. High absorption capacities of 40.7, 57.1, and 47.3 g/g were achieved for three different light crude oils at 25 °C which is comparable with most synthetic oil sorbents. Washburn's model was utilized to describe the wicking dynamics and fluid flow through the pores and to evaluate the effects of all important factors on the sorption process. Via comparing the experimental data with the predictions made by the model, it was revealed that unlike other cellulose-based oil sorbents reported in the literature, the swelling of fibrous network in the synthesized aerogel plays an important role in the absorption process besides the capillary pressure, resulting in a very good oil retention capacity and at the same time lowering the absorption rate, especially for viscose organic liquids.

Topographical effects of laser surface texturing on various time-dependent wetting regimes in Ti6Al4V

Laser surface texturing (LST) processes have great potential to alter surface wetting properties of widely known bioactive Ti–6Al–4V alloy. Micro-pillars arrays of different topography are produced by Nd:YAG laser of 1064 nm wavelength to investigate the influence of its physical and geometrical parameter on wettability. Micro-textures named as: THS (high density, square pillars of 30 × 30 μm), TMS (medium density, square pillars of 60 × 60 μm), TLS (low density, square pillars of 170 × 170 μm), TLL (low density, landscape pillars of 300 × 100 μm) and TLP (low density, portrait pillars of 100 × 300 μm) are produced to analyze the effect of texture areal density, aspect ratio and shape over surface wetting phenomenon. It is observed that on the flat textured surface shows hydrophilic and spontaneous wetting behavior up to 24 h after machining. Percentage increment in water contact angle (CA) value varies with time, maximum increase in CA was found to be in THS (215%) followed by TMS (197%), TLS (166%), TLP (144%) and TLL (122%) after 20 days of machining (as compared with the untextured surface). The response of the textured surface to spontaneous wetting behavior with respect to varying viscosity is also studied and validated through Washburn's model. It is found that early viscous regime of capillary rise in the textured surface can be altered by regulating the geometrical parameters of the micro-textures array. Time taken to rise up to 40 mm by low, medium and high viscosity fluids are 200 s, 600 s and 9334 s respectively. The texture (THS) with highest areal density micro-pillars of 60 μm width exhibits maximum capillary action.