Different regimes in vertical capillary filling

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.

Capillary Wicking on Heliamphora minor-Mimicking Mesoscopic Trichomes Array

Liquid spontaneously spreads on rough lyophilic surfaces, and this is driven by capillarity and defined as capillary wicking. Extensive studies on microtextured surfaces have been applied to microfluidics and their corresponding manufacturing. However, the imbibition at mesoscale roughness has seldom been studied due to lacking fabrication techniques. Inspired by the South American pitcher plant Heliamphora minor, which wicks water on its pubescent inside wall for lubrication and drainage, we implemented 3D printing to fabricate a mimetic mesoscopic trichomes array and investigated the high-flux capillary wicking process. Unlike a uniformly thick climbing film on a microtextured surface, the interval filling of millimeter-long and submillimeter-pitched trichomes creates a film of non-uniform thickness. Different from the viscous dissipation that dominated the spreading on microtextured surfaces, we unveiled an inertia-dominated transition regime with mesoscopic wicking dynamics and constructed a scaling law such that the height grows to 2/3 the power of time for various conditions. Finally, we examined the mass transportation inside the non-uniformly thick film, mimicking a plant nutrition supply method, and realized an open system siphon in the film, with the flux saturation condition experimentally determined. This work explores capillary wicking in mesoscopic structures and has potential applications in the design of low-cost high-flux open fluidics.

Quantitative model for predicting the imbibition dynamics of viscoelastic fluids in nonuniform microfluidic assays

We develop a mathematical model to quantitatively describe the imbibition dynamics of an elastic non-Newtonian fluid in a conical (nonuniform cross section) microfluidic assay. We consider the simplified Phan-Thien-Tanner viscoelastic model to represent the rheology of the elastic non-Newtonian fluid. Our model accounts for the geometrical features of the fluidic assay, the key parameters affecting the rheological behavior of the fluid, and predicts the imbibition dynamics effectively. By demonstrating the temporal advancement of the filling length in the conical capillary graphically, obtained for pertinent parametric values belonging to their physically permissible range, we report an underlying balance between capillary and viscous forces during imbibition resulting in three distinct regimes of filling. Nonuniformity in the capillary cross section gives rise to an alteration in the viscous force being applied at the contact line (manifested through the alteration in shear rate) during the imbibition process, which upon maintaining a balance with the dominant capillary force results in three different regimes of filling. We believe that the present analysis has a twofold significance. First, this work will enhance the understanding of underlying imbibition dynamics of viscoelastic fluids (most of the biofluids exhibit viscoelastic rheology) in nonuniform fluidic pathways. Second, the developed model is of significant practical relevance for the optimum design of microfluidic assays, primarily used for sample diagnostics in biochemical and biomedical applications.

Dip-and-Fold Device: A Paper-Based Testing Platform for Rapid Assessment of Insecticides in Water Samples

The contamination of water and food in agricultural areas, where an enormous volume of pesticides is widely employed to enhance crop production, is a challenging reality. The rapid assessment of these contaminants is fundamental to assure water and food quality and safety, particularly for local community members. This work presents a nonexpensive and easy-operational paper-based testing device for the fast detection of insecticides (carbamates and organophosphates) in water samples. The structural design "dip-and-fold" allows us to carry out the analysis without introducing reagents or samples. The device is prepared using different high-quality papers to support the active acetylcholinesterase (AChE) and the customized chemical formulation for colorimetric detection. The chemical principle is based on the AChE inhibition reaction and Ellman's method. The experiments using standard solutions of carbofuran, propoxur, and chlorpyriphos indicated satisfactory detection at concentrations between 0.1 and 0.0001 mM, and the color results are revealed within 10 min. Therefore, this technique represents a promising alternative for implementing low-cost and efficient water monitoring and management solutions.

Capillary imbibition of non-Newtonian fluids in a microfluidic channel: analysis and experiments

We have presented an experimental analysis on the investigations of capillary filling dynamics of inelastic non-Newtonian fluids in the regime of surface tension dominated flows. We use the Ostwald–de Waele power-law model to describe the rheology of the non-Newtonian fluids. Our analysis primarily focuses on the experimental observations and revisits the theoretical understanding of the capillary dynamics from the perspective of filling kinematics at the interfacial scale. Notably, theoretical predictions of the filling length into the capillary largely endorse our experimental results. We study the effects of the shear-thinning nature of the fluid on the underlying filling phenomenon in the capillary-driven regime through a quantitative analysis. We further show that the dynamics of contact line motion in this regime plays an essential role in advancing the fluid front in the capillary. Our experimental results on the filling in a horizontal capillary re-establish the applicability of the Washburn analysis in predicting the filling characteristics of non-Newtonian fluids in a vertical capillary during early stage of filling (Digilov 2008 Langmuir 24 , 13 663–13 667 ( doi:10.1021/la801807j )). Finally, through a scaling analysis, we suggest that the late stage of filling by the shear-thinning fluids closely follows the variation x ~ t . Such a regime can be called the modified Washburn regime (Washburn 1921 Phys. Rev. 17 , 273–283 ( doi:10.1103/PhysRev.17.273 )).

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 t^0.7. 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.

Spontaneous rise in open rectangular channels under gravity

Fluid movement in microfluidic devices, porous media, and textured surfaces involves coupled flows over the faces and corners of the media. Spontaneous wetting of simple grooved surfaces provides a model system to probe these flows. This numerical study investigates the spontaneous rise of a liquid in an array of open rectangular channels under gravity, using the Volume-of-Fluid method with adaptive mesh refinement. The rise is characterized by the meniscus height at the channel center, outer face and the interior and exterior corners. At lower contact angles and higher channel aspect ratios, the statics and dynamics of the rise in the channel center show little deviation with the classical model for capillarity, which ignores the existence of corners. For contact angles smaller than 45°, rivulets are formed in the interior corners and a cusp at the exterior corner. The rivulets at long times obey the one-third power law in time, with a weak dependence on the geometry. The cusp behaviour at the exterior corner transforms into a smooth meniscus when the capillary force is higher in the channel, even for contact angles smaller than 45°. The width of the outer face does not influence the capillary rise inside the channel, and the channel size does not influence the rise on the outer face.

Invasion of gas into mica nanopores: a molecular dynamics study

The invasion of gas into liquid-filled nanopores is encountered in many engineering problems but is not yet well understood. We report molecular dynamics simulations of the invasion of methane gas into water-filled mica pores with widths of 2-6 nm. Gas invades into a pore only when the pressure exceeds a breakthrough pressure and a thin residual water film is left on the mica wall as the gas phase moves deeper into the pore. The gas breakthrough pressure of pores as narrow as 2 nm can be modeled reasonably well by the capillary pressure if the finite thickness of residual liquid water film and the liquid-gas interface are taken into account. The movement of the front of the liquid meniscus during gas invasion can be quantitatively described using the classical hydrodynamics when the negative slip length on the strongly hydrophilic mica walls is taken into account. Understanding the molecular mechanisms underlying the gas invasion in the system studied here will form the foundation for quantitative prediction of gas invasion in practical porous media.

Electrically modulated capillary filling imbibition of nematic liquid crystals

The flow of nematic liquid crystals (NLCs) in the presence of an electric field is typically characterized by the variation in its rheological properties due to transition in its molecular arrangements. Here, we bring out a nontrivial interplay of a consequent alteration in the resistive viscous effects and driving electrocapillary interactions, toward maneuvering the capillary filling dynamics over miniaturized scales. Considering a dynamic interplay of the relevant bulk and interfacial forces acting in tandem, our results converge nicely to previously reported experimental data. Finally, we attempt a scaling analysis to bring forth further insight to the reported observations. Our analysis paves the way for the development of microfluidic strategies with previously unexplored paradigms of interaction between electrical and fluidic phenomenon, providing with an augmented controllability on capillary filling as compared to tthose reported to be achievable by the existing strategies. This, in turn, holds utilitarian scopes in improved designs of functional capillarities in electro-optical systems, electrorheological utilities, electrokinetic flow control, as well as in interfacing and imaging systems for biomedical microdevices.

Sessile nanofluid droplet can act like a crane

Interactive droplet systems form the backbone for emerging avenues in droplet based technologies like cell sorting, inkjet printing and digital microfluidics, to name a few. These and their associated fields have gained significant importance in the recent times. Here, we report one such phenomenon wherein a naturally evaporating nanocolloidal sessile droplet interacts with a porous silica gel bead to mimic a macro scale mechanical crane assembly. Precisely, we show a sequence of events displayed by the particle laden aqueous droplet (nanoparticles of silica at different loading rates placed on a hydrophobic substrate) when brought in contact with a meso-porous silica gel bead. First, preferential self-assembly along droplet-bead interface is followed by formation of an adhesive bond. The phenomenon continues until the evaporating droplet naturally lifts the bead. The kinematics of the lift mechanism can be represented by a simple four bar linkage. This work provides insights into interactions between droplets and freely placed porous objects across multiple spatio-temporal scales. Present study should not just motivate researchers to design interactive droplet based systems but also use the same to perform engineering tasks like the crane action.

Alternating current electrothermal modulated moving contact line dynamics of immiscible binary fluids over patterned surfaces

In this paper, we report the results of our numerical study on incompressible flow of a binary system of two immiscible fluids in a parallel plate capillary using alternating current electrothermal kinetics as the actuation mechanism for flow. The surfaces of the capillary are wetted with two different alternating wettability patches. The dynamic motion of the interface of the two fluids is tracked using a phase-field order parameter-based approach. The results exhibit a stick-slip behavior involving acceleration and deceleration of the interface due to the interplay of electrothermal (Coulomb and dielectric) and surface tension forces. Controlling the interface motion through effective tuning of the chemical characteristics of the surfaces and forcing parameters was explored in detail. Finally, we were able to find a critical value of the dimensionless strength of the alternating current electrothermal force above which the interface "breaks", resulting in the formation of isolated droplets. These results have the potential to improve fundamental understanding and design optimization of various biomedical and physiological systems that involve flow of two or more immiscible fluids over chemically wetted surfaces.

DipTest: A litmus test for E. coli detection in water

We have developed a new litmus paper test (DipTest) for detecting Escherichia coli (E. coli) in water samples by performing enzymatic reactions directly on the porous paper substrate. The paper strip consists of a long narrow piece of cellulose blotting paper coated with chemoattractant (at bottom edge), wax hydrophobic barrier (at the top edge), and custom formulated chemical reagents (at reaction zone immediately below the wax hydrophobic barrier). When the paper strip is dipped in water, E. coli in the water sample is attracted toward the paper strip due to a chemotaxic mechanism followed by the ascent along the paper strip toward the reaction zone due to a capillary wicking mechanism, and finally the capillary motion is arrested at the top edge of the paper strip by the hydrophobic barrier. The E. coli concentrated at the reaction zone of the paper strip will react with custom formulated chemical reagents to produce a pinkish-red color. Such a color change on the paper strip when dipped into water samples indicates the presence of E. coli contamination in potable water. The performance of the DipTest device has been checked with different known concentrations of E. coli contaminated water samples using different dip and wait times. The DipTest device has also been tested with different interfering bacteria and chemical contaminants. It has been observed that the different interfering contaminants do not have any impact on the DipTest, and it can become a potential solution for screening water samples for E. coli contamination at the point of source.

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.

Surface hydration drives rapid water imbibition into strongly hydrophilic nanopores

Surface hydration-driven imbibition of water into strongly hydrophilic pores follows a diffusive scaling law and exhibits effective diffusion coefficients much higher than water molecules.

Diffusive dynamics on paper matrix

Writing with ink on a paper and the rapid diagnostics of diseases using paper cartridge, despite their remarkable diversities from application perspective, both involve the motion of a liquid from a source on a porous hydrophilic substrate. Here we bring out a generalization in the pertinent dynamics by appealing to the concerned ensemble-averaged transport with reference to the underlying molecular picture. Our results reveal that notwithstanding the associated complexities and diversities, the resultant liquid transport characteristics on a paper matrix, in a wide variety of applications, resemble universal diffusive dynamics. Agreement with experimental results from diversified applications is generic and validates our unified theory.

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.

Nanoscale Capillary Flows in Alumina: Testing the Limits of Classical Theory

Anodic aluminum oxide (AAO) membranes have well-formed cylindrical channels, as small as 10 nm in diameter, in a close packed hexagonal array. The channels in AAO membranes simulate very small leaks that may be present for example in an aluminum oxide device encapsulation. The 10 nm alumina channel is the smallest that has been studied to date for its moisture flow properties and provides a stringent test of classical capillary theory. We measure the rate at which moisture penetrates channels with diameters in the range of 10 to 120 nm with moist air present at 1 atm on one side and dry air at the same total pressure on the other. We extend classical theory for water leak rates at high humidities by allowing for variable meniscus curvature at the entrance and show that the extended theory explains why the flow increases greatly when capillary filling occurs and enables the contact angle to be determined. At low humidities our measurements for air-filled channels agree well with theory for the interdiffusive flow of water vapor in air. The flow rate of water-filled channels is one order of magnitude less than expected from classical capillary filling theory and is coincidentally equal to the helium flow rate, validating the use of helium leak testing for evaluating moisture flows in aluminum oxide leaks.

Capillary Penetration into Inclined Circular Glass Tubes

The spontaneous penetration of a wetting liquid into a vertical tube against the force of gravity and the imbibition of the same liquid into a horizontal tube (or channel) are both driven by capillary forces and described by the same fundamental equations. However, there have been few experimental studies of the transition from one orientation to the other. We report systematic measurements of capillary penetration of polydimethylsiloxane oils of viscosities 9.6, 19.2, and 48.0 mPa·s into glass capillary tubes. We first report the effect of tube radii R between 140 and 675 μm on the dynamics of spontaneous imbibition. We show that the data can be fitted using the exact numerical solution to the governing equations and that these are similar to fits using the analytical viscogravitational approximation. However, larger diameter tubes show a rate of penetration slower than expected using an equilibrium contact angle and the known value of liquid viscosity. To account for the slowness, an increase in viscosity by a factor (η/ρ)(scaling) is needed. We show full agreement with theory requires the ratio R/κ(-1) ∼ 0.1 or less, where κ(-1) is the capillary length. In addition, we propose an experimental method that enables the determination of the dynamic contact angle during imbibition, which gives values that agree with the literature values. We then report measurements of dynamic penetration into the tubes of R = 190 and 650 μm for a range of inclination angles to the horizontal, φ, from 5 to 90°. We show that capillary penetration can still be fitted using the viscogravitational solution, rather than the Bosanquet solution which describes imbibition without gravity, even for inclination angles as low as 10°. Moreover, at these low angles, the effect of the tube radius is found to diminish and this appears to relate to an effective capillary length, κ(-1)(φ) = (γ(LV)/ρg sin φ)(1/2).

Oscillatory regimes of capillary imbibition of viscoelastic fluids through concentric annulus

Here we report the capillary filling dynamics of a viscoelastic fluid through a concentric annulus, which offers a distinct disparity in the dynamical characteristics as compared to the classical cylindrical capillary based paradigm.

Electro-capillary effects in capillary filling dynamics of electrorheological fluids

The flow of electrorheological fluids is characterized by an apparent increase in viscosity manifested by the yield stress property of the fluid, which is a function of the applied electric field and the concentration of the suspended solute phase within the dielectric medium. This property of electrorheological fluids generally hinders flow through a capillary if the imposed shear stress is lower than the induced yield stress. This results in a plug-like zone in the flow profile, thus giving the fluid Bingham plastic properties. In the present work, we study such influences of the yield stress on the capillary filling dynamics of an electrorheological fluid by employing a rheologically consistent reduced order formalism. One important feature of the theoretical formalism is its ability to address the intricate interplay between the surface tension and viscous forces, both of which depend sensitively on the electric field. Our analysis reveals that the progress of the capillary front is hindered at an intermediate temporal regime, which is attributable to the increase of the span of the plug-zone across the channel width with time. With a preliminary understanding on the cessation of the capillary front advancement due to the yield stress property of the electrorheological fluids, we further strive to achieve a basic comparison with an experimental study made earlier. Reasonable agreements with the reported data support our theoretical framework. Comprehensive scaling analysis brings further insight to our reported observations over various temporal regimes.

Filling of charged cylindrical capillaries

We provide an analytical model to describe the filling dynamics of horizontal cylindrical capillaries having charged walls. The presence of surface charge leads to two distinct effects: It leads to a retarding electrical force on the liquid column and also causes a reduced viscous drag force because of decreased velocity gradients at the wall. Both these effects essentially stem from the spontaneous formation of an electric double layer (EDL) and the resulting streaming potential caused by the net capillary-flow-driven advection of ionic species within the EDL. Our results demonstrate that filling of charged capillaries also exhibits the well-known linear and Washburn regimes witnessed for uncharged capillaries, although the filling rate is always lower than that of the uncharged capillary. We attribute this to a competitive success of the lowering of the driving forces (because of electroviscous effects), in comparison to the effect of weaker drag forces. We further reveal that the time at which the transition between the linear and the Washburn regime occurs may become significantly altered with the introduction of surface charges, thereby altering the resultant capillary dynamics in a rather intricate manner.

Capillary filling under electro-osmotic effects in the presence of electromagneto-hydrodynamic effects

We report various regimes of capillary filling dynamics under electromagneto-hydrodynamic interactions, in the presence of electrical double layer effects. Our chosen configuration considers an axial electric field and transverse magnetic field acting on an electrolyte. We demonstrate that for positive interfacial potential, the movement of the capillary front resembles capillary rise in a vertical channel under the action of gravity. We also evaluate the time taken by the capillary front to reach the final equilibrium position for positive interfacial potential and show that the presence of a transverse magnetic field delays the time of travel of the liquid front, thereby sustaining the capillary motion for a longer time. Our scaling estimates reveal that the initial linear regime starts, as well as ends, much earlier in the presence of electrical and magnetic body forces, as compared to the corresponding transients observed under pure surface tension driven flow. We further obtain a long time solution for the capillary imbibition for positive interfacial potential, and derive a scaling estimate of the capillary stopping time as a function of the applied magnetic field and an intrinsic length scale delineating electromechanical influences of the electrical double layer. Our findings are likely to offer alternative strategies of controlling dynamical features of capillary imbibition, by modulating the interplay between electromagnetic interactions, electrical double layer phenomena, and hydrodynamics over interfacial scales.

Capillary filling dynamics of viscoelastic fluids

We consider the filling of a capillary by a viscoelastic fluid described by the Phan-Thien-Tanner (PTT) constitutive behavior. By considering both vertical capillary filling and horizontal capillary filling, we demarcate the role played by gravity and fluid rheology towards long-time oscillations in the capillary penetration depth. We also consider the isothermal filling of the capillary for a closed channel and thus bring out the fundamental differences in the nature of capillary filling for PTT and Newtonian fluids for closed channels in comparison to open channels. Through a scaling analysis, we highlight a distinct viscoelastic regime in the horizontal capillary filling which is in contrast to the Washburn scaling seen in the case of Newtonian fluids. Such an analysis with a very general constitutive behavior is therefore expected to shed light on many areas of microfluidics which focus on biofluids that are often well described by the PTT constitutive behavior.

Inverse problem of capillary filling

The inverse problem of capillary filling, as defined in this work, consists in determining the capillary radius profile from experimental data of the meniscus position l as a function of time t. This problem is central in diverse applications, such as the characterization of nanopore arrays or the design of passive transport in microfluidics; it is mathematically ill posed and has multiple solutions; i.e., capillaries with different geometries may produce the same imbibition kinematics. Here a suitable approach is proposed to solve this problem, which is based on measuring the imbibition kinematics in both tube directions. Capillary filling experiments to validate the calculation were made in a wide range of length scales: glass capillaries with a radius of around 150  μm and anodized alumina membranes with a pores radius of around 30  nm were used. The proposed method was successful in identifying the radius profile in both systems. Fundamental aspects also emerge in this study, notably the fact that the l(t)∝t1/2 kinematics (Lucas-Washburn relation) is not exclusive of uniform cross-sectional capillaries.

Temperature dependence of capillary dynamics: a multiphase and multicomponent adiabatic approach

We present an analysis of the effect of the temperature on the flow of multiphase systems made of multiple miscible components in uniform cylindrical capillaries in adiabatic conditions. The temperature was explicitly included in the dynamic contact angle, tension at the three-phase contact line, and densities and viscosities of the fluids. The mathematical framework accounted for conservative forces (gravity, inertial, and interfacial tensions), nonconservative forces (viscous dissipation), and fluid retardation effects in the reservoirs at the two capillary ends. Temperature-dependent flow regimes ranged from nonoscillatory to oscillatory in a two-phase binary liquid (water-ethanol) system and in a two-phase pure liquid (ether) system. The Ca-Bo orbits highlighted dynamic attractors that depended on specific system characteristics as well as temperature. We conclude that temperature alone expresses and important role in the dynamical characteristics of capillary rise flow around its equilibrium.