Effect of dynamic contact angle in a volume of fluid (VOF) model for a microfluidic capillary flow

Gravity-driven flow control in a fully integrated microfluidic cartridge for molecular point-of-care testing

Molecular point-of-care testing (POCT) system is crucial for the timely prevention and control of infectious diseases. We recently proposed a gravity-driven microfluidic cartridge for molecular POCT detection, without the need for external sources or actuators, demonstrating the advantages in terms of the reduced cartridge size and low development costs. How to achieve precise control of liquid flow behavior is challenging for the gravity-driven cartridge. In this work, we explored the underlying mechanism of flow control in the cartridge and offered optimized solutions for our cartridge design to achieve precise control of dynamic flow rates and enhance pumping efficiency significantly. Through the computational fluid dynamics simulations, we demonstrated that adopting an asymptotic contraction chamber geometry design and a closed-loop air flow channel design with the cartridge inlet can facilitate stable laminar flow of the liquid in our microfluidic cartridge, enabling precise control of flow velocity. We further optimized the microchannel diameter and the contact angle of the liquid with the microchannel wall. The effectiveness of the optimized cartridge for POCT detection was well validated by the accurate detection of the human papillomavirus type 16 virus in the 120 clinical swab samples.

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-driven horseshoe vortex forming around a micro-pillar

HYPOTHESIS

Horseshoe vortices are known to emerge around large-scale obstacles, such as bridge pillars, due to an inertia-driven adverse pressure gradient forming on the upstream-side of the obstacle. We contend that a similar flow structure can arise in thin-film Stokes flow around micro-obstacles, such as used in textured surfaces to improve wettability. This could be exploited to enhance mixing in microfluidic devices, typically limited to creeping-flow regimes.

EXPERIMENTS

Numerical simulations based on the Navier-Stokes equations are carried out to elucidate the flow structure associated with the wetting dynamics of a liquid film spreading around a 50 μm diameter micro-pillar. The employed multiphase solver, which is based on the volume of fluid method, accurately reproduces the wetting dynamics observed in current and previous (Mu et al., Langmuir, 2019) experiments.

FINDINGS

The flow structure within the liquid meniscus forming at the foot of the micro-pillar evinces a horseshoe vortex wrapping around the obstacle, notwithstanding that the Reynolds number in our system is extremely low. Here, the adverse pressure gradient driving flow reversal near the bounding wall is caused by capillarity instead of inertia. The horseshoe vortex is entangled with other vortical structures, leading to an intricate flow system with high-potential mixing capabilities.

Numerical Study of the Coalescence and Mixing of Drops of Different Polymeric Materials

In this study, we employ direct numerical simulation (DNS) to investigate the solutal hydrodynamics dictating the three-dimensional coalescence of microscopic, identical-sized sessile drops of different but miscible shear-thinning polymeric liquids (namely, PVAc or polyvinyl acetate and PMMA or polymethylmethacrylate), with the drops being in partially wetted configuration. Despite the ubiquitousness of the interaction of different dissimilar droplets in a variety of engineering problems ranging from additive manufacturing to understanding the behavior of photonic crystals, coalescence of drops composed of different polymeric and non-Newtonian materials has not been significantly explored. Interaction of such dissimilar droplets often involves simultaneous drop spreading, coalescence, and mixing. The mixing dynamics of the dissimilar drops are governed by interphase diffusion, the residual kinetic energy of the drops stemming from the fact that coalescence starts before the spreading of the drops have been completed, and the solutal Marangoni convection. We provide the three-dimensional velocity fields and velocity vectors inside the completely miscible, dissimilar coalescing droplets. Our simulations explicate the relative influence of these different effects in determining the flow field at different locations and at different time instances and the consequent mixing behavior inside the interacting drops. We also show the non-monotonic (in terms of the direction of migration) propagation of the mixing front of the miscible coalescing drops over time. We also establish that the overall mixing (on either side of the mixing front) speeds up as the Marangoni effects dictate the mixing. We anticipate that our study will provide an important foundation for studying miscible multi-material liquid systems, which will be crucial for applications such as inkjet or aerosol jet printing, lab-on-a-chip, polymer processing, etc.

Investigation of the Different Regimes Associated with the Growth of an Interface at the Exit of a Capillary Tube into a Reservoir: Analytical Solutions and CFD Validation

The emergence of a droplet from a capillary tube opening into a reservoir is an important phenomenon in several applications. In this work, we are particularly interested in this phenomenon in an attempt to highlight the physics behind droplet appearance. The emergence of a droplet from a tube opening into a reservoir under quasi-static conditions passes through three stages. The first stage starts when the meniscus in the tube reaches the exit. At this moment, the meniscus intersects the wall of the tube at the equilibrium contact angle. The interface then develops until its radius of curvature becomes equal to the tube radius. During this stage, the capillary pressure increases. In the second stage, the interface continues to evolve with its radius of curvature increasing until the static contact angle with respect to the surface of the reservoir is achieved. This marks the end of the second stage and the start of the third in which the contact line (CL) starts to depart the tube opening along the reservoir surface and the contact angle remains constant. Analytical models for the three stages have been derived based on the law of conservation of linear momentum. The models account for pressure, gravitational, capillary, and viscous forces, while inertia force is ignored. The model can predict the profiles of the mean velocity in the tube, the capillary pressure, and the evolution of the contact angle. In addition, a computational fluid dynamics (CFD) simulation has been conducted to provide a framework for validation and verification of the developed model. The CFD simulation shows qualitative behavior in terms of snapshots of the emerging droplet with time similar to that speculated by the analytical model. In addition, quantitative comparisons with respect to velocity, pressure, and volume profiles of the droplet show very good agreement, which builds confidence in the modeling approach.

An Ultra-Micro-Volume Adhesive Transfer Method and Its Application in fL-pL-Level Adhesive Distribution

This study is aimed at addressing the urgent demand for ultra-micro-precision dispensing technology in high-performance micro- and nanometer encapsulation, connection, and assembly manufacturing, considering the great influence of colloid viscosity and surface tension on the dispensing process in micro- and nanometer scale. According to the principle of liquid transfer, a method of adhesive transfer that can realize fL-pL levels is studied in this paper. A mathematical model describing the initial droplet volume and the transfer droplet volume was established, and the factors affecting the transfer process of adhesive were analyzed by the model. The theoretical model of the transfer droplet volume was verified by a 3D scanning method. The relationships between the transfer droplet volume and the initial droplet volume, stay time, initial distance, and stretching speed were systematically analyzed by a single-factor experiment, and the adhesive transfer rate was calculated. Combined with trajectory planning, continuous automatic dispensing experiments with different patterns were developed, and the problems of the transfer droplet size, appearance quality, and position accuracy were analyzed comprehensively. The results show that the average relative deviation of the transfer droplet lattice position obtained by the dispensing method in this paper was 6.2%. The minimum radius of the transfer droplet was 11.7 μm, and the minimum volume of the transfer droplet was 573.3 fL. Furthermore, microporous encapsulation was realized using the method of ultra-micro-dispensing.

Capillary-Driven Ejection of a Droplet from a Micropore into a Channel: A Theoretical Model and a Computational Fluid Dynamics Verification

In this work, the problem of re-ejection of a permeating droplet through a membrane pore back to the feed channel when the transmembrane pressure (TMP) becomes zero is investigated. This problem is important in the context of oily water filtration using membranes. In particular, in the novel periodic feed pressure technique (PFPT), which has been proposed to combat membrane fouling, the TMP alternates between the operating value and zero in a periodic manner. During the period in which TMP is high, filtration occurs, and when it is zero, cleaning commences. We are particularly interested in what happens to a droplet, initially undergoing permeation, when the TMP becomes zero. It is evident that when the TMP is zero the meniscus inside the pore reverses its motion toward the feed channel rather than toward the permeate side by the action of interfacial tension force. A theoretical model is built to determine the rate at which the meniscus inside the pore advances when the TMP is zero. The conservation of momentum equation is used to establish a one-dimensional model that updates the location of the meniscus with time. The derived model considers both quasi-static and dynamic scenarios. In addition, the model accounts for both the viscosity contrast between the two fluids, as well as the gravity. A computational fluid dynamics (CFD) simulation has been built to provide a framework for model verification and validation. The model, based on quasi-static conditions, provides an overall similar trend to that obtained via CFD analysis. Nevertheless, the quasi-static model predicts a more rapid meniscus advancement inside the pore than the CFD simulation. When the dynamic contact angle is incorporated, very good matching is observed.

Is contact-line mobility a material parameter?

Dynamic wetting phenomena are typically described by a constitutive law relating the dynamic contact angle θ to contact-line velocity UCL. The so-called Davis–Hocking model is noteworthy for its simplicity and relates θ to UCL through a contact-line mobility parameter M, which has historically been used as a fitting parameter for the particular solid–liquid–gas system. The recent experimental discovery of Xia & Steen (2018) has led to the first direct measurement of M for inertial-capillary motions. This opens up exciting possibilities for anticipating rapid wetting and dewetting behaviors, as M is believed to be a material parameter that can be measured in one context and successfully applied in another. Here, we investigate the extent to which M is a material parameter through a combined experimental and numerical study of binary sessile drop coalescence. Experiments are performed using water droplets on multiple surfaces with varying wetting properties (static contact angle and hysteresis) and compared with numerical simulations that employ the Davis–Hocking condition with the mobility M a fixed parameter, as measured by the cyclically dynamic contact angle goniometer, i.e. no fitting parameter. Side-view coalescence dynamics and time traces of the projected swept areas are used as metrics to compare experiments with numerical simulation. Our results show that the Davis–Hocking model with measured mobility parameter captures the essential coalescence dynamics and outperforms the widely used Kistler dynamic contact angle model in many cases. These observations provide insights in that the mobility is indeed a material parameter.

Coalescence of Microscopic Polymeric Drops: Effect of Drop Impact Velocities

In this paper, we employ the direct numerical simulation (DNS) method for probing three-dimensional, axisymmetric coalescence of microscale, power-law-obeying, and shear-thinning polymeric liquid drops of identical sizes impacting a solid, solvophilic substrate with a finite velocity. Unlike the cases of drop coalescence of Newtonian liquid drops, coalescence of non-Newtonian polymeric drops has received very little attention. Our study bridges this gap by providing (1) the time-dependent, three-dimensional (3D) velocity field and 3D velocity vectors inside two coalescing polymeric drops in the presence of a solid substrate and (2) the effect of the drop impact velocity (on the solid substrate), quantified by the Weber number (We), on the coalescence dynamics. Our simulations reveal that the drop coalescence is qualitatively similar for different We values, although the velocity magnitudes involved, the time required to attain different stages of coalescence, and the time needed to attain equilibrium vary drastically for finitely large We values. Finally, we provide detailed simulation-based, as well as physics-based, scaling laws describing the growth of the height and the width of the bridge (formed due to coalescence) dictating the 3D coalescence event. Our analyses reveal distinct scaling laws for the growth of bridge height and width for early and late stages of coalescence as a function of We. We also provide simulation-based coalescence results for the case of two unequal sized drops impacting on a substrate (nonaxisymmetric coalescence) as well as results for axisymmetric coalescence for drops of different rheology. We anticipate that our findings will be critical in better understanding events such as inkjet or aerosol jet polymer printing, dynamics of polymer blends, and many more.

Phase-Field Simulation of Imbibition for the Matrix-Fracture of Tight Oil Reservoirs Considering Temperature Change

Injection water temperature is often different from that of the reservoir during water injection development in the tight reservoir. Temperature change causes different fluid properties and oil-water interface properties, which further affects the imbibition process. In this paper, a matrix-fracture non-isothermal oil-water imbibition flow model in tight reservoirs is established and solved by the finite element method based on the phase-field method. The ideal inhomogeneous rock structure model was used to study the influence of a single factor on the imbibition. The actual rock structure model was used to study the influence of temperature. The mechanism of temperature influence in the process of imbibition is studied from the micro-level. It is found that the imbibition of matrix-fracture is a process in which the water enters the matrix along with the small pores, and the oil is driven into the macropores and then into the fractures. Temperature affects the imbibition process by changing the oil-water contact angle, oil-water interfacial tension, and oil-water viscosity ratio. Reducing oil-water contact angle and oil-water viscosity ratio and increasing oil-water interfacial tension are conducive to the imbibition process. The increase in injection water temperature is usually beneficial to the occurrence of the imbibition. Moreover, the actual core structure imbibition degree is often lower than that of the ideal core structure. The inhomogeneous distribution of rock particles has a significant influence on imbibition. This study provides microscale theoretical support for seeking reasonable injection velocity, pressure gradient, injection temperature, and well-shutting time in the field process. It provides a reference for the formulation of field process parameters.

Grayscale Nanopixel Printing at Sub-10-nanometer Vertical Resolution via Light-Controlled Nanocapillarity

Nanotextures play increasingly important roles in nanotechnology. Recent studies revealed that their functionalities can be further enhanced by spatially modulating the height of their nanoscale pixels. Realizing the concept, however, is very challenging as it requires "grayscale" printing of the nanopixels in which their height is controlled within a few nanometers as a micrometric function of position. This work demonstrates such a high vertical and lateral resolution grayscale printing of polymeric nanopixels. We realize the height modulation by exploiting the discovery that the capillary rise of certain photopolymers can be optically controlled to stop at a predetermined height with sub-10-nm accuracy. Microscale spatial patterning of the control light directly extends the height modulation into a two-dimensionally patterned, grayscale nanopixel printing. Its utility is verified through readily reconfigurable, maskless printing of grayscale nanopixel arrays in dielectric and metallo-dielectric forms. This work also reveals the highly nonlinear and unstable nature of the polymeric nanocapillary effect, expanding its understanding and application scope.

Comparison of Surface Tension Models for the Volume of Fluid Method

With the increasing use of Computational Fluid Dynamics to investigate multiphase flow scenarios, modelling surface tension effects has been a topic of active research. A well known associated problem is the generation of spurious velocities (or currents), arising due to inaccuracies in calculations of the surface tension force. These spurious currents cause nonphysical flows which can adversely affect the predictive capability of these simulations. In this paper, we implement the Continuum Surface Force (CSF), Smoothed CSF and Sharp Surface Force (SSF) models in OpenFOAM. The models were validated for various multiphase flow scenarios for Capillary numbers of 10 − 3 –10. All the surface tension models provide reasonable agreement with benchmarking data for rising bubble simulations. Both CSF and SSF models successfully predicted the capillary rise between two parallel plates, but Smoothed CSF could not provide reliable results. The evolution of spurious current were studied for millimetre-sized stationary bubbles. The results shows that SSF and CSF models generate the least and most spurious currents, respectively. We also show that maximum time step, mesh resolution and the under-relaxation factor used in the simulations affect the magnitude of spurious currents.

An energy-based equilibrium contact angle boundary condition on jagged surfaces for phase-field methods

We consider an energy-based boundary condition to impose an equilibrium wetting angle for the Cahn-Hilliard-Navier-Stokes phase-field model on voxel-set-type computational domains. These domains typically stem from μCT (micro computed tomography) imaging of porous rock and approximate a (on μm scale) smooth domain with a certain resolution. Planar surfaces that are perpendicular to the main axes are naturally approximated by a layer of voxels. However, planar surfaces in any other directions and curved surfaces yield a jagged/topologically rough surface approximation by voxels. For the standard Cahn-Hilliard formulation, where the contact angle between the diffuse interface and the domain boundary (fluid-solid interface/wall) is 90°, jagged surfaces have no impact on the contact angle. However, a prescribed contact angle smaller or larger than 90° on jagged voxel surfaces is amplified. As a remedy, we propose the introduction of surface energy correction factors for each fluid-solid voxel face that counterbalance the difference of the voxel-set surface area with the underlying smooth one. The discretization of the model equations is performed with the discontinuous Galerkin method. However, the presented semi-analytical approach of correcting the surface energy is equally applicable to other direct numerical methods such as finite elements, finite volumes, or finite differences, since the correction factors appear in the strong formulation of the model.

Passive Mixing inside Microdroplets

Droplet-based micromixers are essential units in many microfluidic devices for widespread applications, such as diagnostics and synthesis. The mixers can be either passive or active. When compared to active methods, the passive mixer is widely used because it does not require extra energy input apart from the pump drive. In recent years, several passive droplet-based mixers were developed, where mixing was characterized by both experiments and simulation. A unified physical understanding of both experimental processes and simulation models is beneficial for effectively developing new and efficient mixing techniques. This review covers the state-of-the-art passive droplet-based micromixers in microfluidics, which mainly focuses on three aspects: (1) Mixing parameters and analysis method; (2) Typical mixing element designs and the mixing characters in experiments; and, (3) Comprehensive introduction of numerical models used in microfluidic flow and diffusion.

Investigation of the Dynamic Contact Angle Using a Direct Numerical Simulation Method

A large amount of residual oil, which exists as isolated oil slugs, remains trapped in reservoirs after water flooding. Numerous numerical studies are performed to investigate the fundamental flow mechanism of oil slugs to improve flooding efficiency. Dynamic contact angle models are usually introduced to simulate an accurate contact angle and meniscus displacement of oil slugs under a high capillary number. Nevertheless, in the oil slug flow simulation process, it is unnecessary to introduce the dynamic contact angle model because of a negligible change in the meniscus displacement after using the dynamic contact angle model when the capillary number is small. Therefore, a critical capillary number should be introduced to judge whether the dynamic contact model should be incorporated into simulations. In this study, a direct numerical simulation method is employed to simulate the oil slug flow in a capillary tube at the pore scale. The position of the interface between water and the oil slug is determined using the phase-field method. The capacity and accuracy of the model are validated using a classical benchmark: a dynamic capillary filling process. Then, different dynamic contact angle models and the factors that affect the dynamic contact angle are analyzed. The meniscus displacements of oil slugs with a dynamic contact angle and a static contact angle (SCA) are obtained during simulations, and the relative error between them is calculated automatically. The relative error limit has been defined to be 5%, beyond which the dynamic contact angle model needs to be incorporated into the simulation to approach the realistic displacement. Thus, the desired critical capillary number can be determined. A three-dimensional universal chart of critical capillary number, which functions as static contact angle and viscosity ratio, is given to provide a guideline for oil slug simulation. Also, a fitting formula is presented for ease of use.

Pulsating electric field modulated contact line dynamics of immiscible binary systems in narrow confinements under an electrical double layer phenomenon

We investigate the interfacial electro-chemical-hydrodynamics of an incompressible immiscible binary fluid system that moves in a narrow fluidic channel under time-periodic electroosmotic effects. We apply an alternating electrical voltage that sets the binary fluids in motion along the channel, whereas the channel walls are lined with chemical patch to alter the wetting characteristics of the surface. We demonstrate that the pulsating nature of the externally applied electric field in conjunction with the wetting characteristics of the surface may lead to some fascinating behavior of the contact line motion; which, in turn, may affect the capillary filling dynamics in an intriguing manner. Our results also unveil the profound influence of two important governing factors actuating the flow, namely, the frequency and amplitude of the time periodic electric field, on the tunability of the capillary filling rate and power requirement for filling the fluids into the channel.

VOF simulations of the contact angle dynamics during the drop spreading: standard models and a new wetting force model

INTRODUCTION

In this study,a novel numerical implementation for the adhesion of liquid droplets impacting normally on solid dry surfaces is presented. The advantage of this new approach, compared to the majority of existing models, is that the dynamic contact angle forming during the surface wetting process is not inserted as a boundary condition, but is derived implicitly by the induced fluid flow characteristics (interface shape) and the adhesion physics of the gas-liquid-surface interface (triple line), starting only from the advancing and receding equilibrium contact angles. These angles are required in order to define the wetting properties of liquid phases when interacting with a solid surface.

METHODOLOGY

The physical model is implemented as a source term in the momentum equation of a Navier-Stokes CFD flow solver as an "adhesion-like" force which acts at the triple-phase contact line as a result of capillary interactions between the liquid drop and the solid substrate. The numerical simulations capture the liquid-air interface movement by considering the volume of fluid (VOF) method and utilizing an automatic local grid refinement technique in order to increase the accuracy of the predictions at the area of interest, and simultaneously minimize numerical diffusion of the interface.

RESULTS

The proposed model is validated against previously reported experimental data of normal impingement of water droplets on dry surfaces at room temperature. A wide range of impact velocities, i.e. Weber numbers from as low as 0.2 up to 117, both for hydrophilic (θadv=10°-70°) and hydrophobic (θadv=105°-120°) surfaces, has been examined. Predictions include in addition to droplet spreading dynamics, the estimation of the dynamic contact angle; the latter is found in reasonable agreement against available experimental measurements.

CONCLUSION

It is thus concluded that theimplementation of this model is an effective approach for overcoming the need of a pre-defined dynamic contact angle law, frequently adopted as an approximate boundary condition for such simulations. Clearly, this model is mostly influential during the spreading phase for the cases of low We number impacts (We<˜80) since for high impact velocities, inertia dominates significantly over capillary forces in the initial phase of spreading.

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.

The effect of contact angles and capillary dimensions on the burst frequency of super hydrophilic and hydrophilic centrifugal microfluidic platforms, a CFD study

This paper employs the volume of fluid (VOF) method to numerically investigate the effect of the width, height, and contact angles on burst frequencies of super hydrophilic and hydrophilic capillary valves in centrifugal microfluidic systems. Existing experimental results in the literature have been used to validate the implementation of the numerical method. The performance of capillary valves in the rectangular and the circular microfluidic structures on super hydrophilic centrifugal microfluidic platforms is studied. The numerical results are also compared with the existing theoretical models and the differences are discussed. Our experimental and computed results show a minimum burst frequency occurring at square capillaries and this result is useful for designing and developing more sophisticated networks of capillary valves. It also predicts that in super hydrophilic microfluidics, the fluid leaks consistently from the capillary valve at low pressures which can disrupt the biomedical procedures in centrifugal microfluidic platforms.

Capillary rise dynamics of aqueous glycerol solutions in glass capillaries: a critical examination of the Washburn equation

The classic description of capillary rise given by the Washburn equation was recently questioned in the light of experimental evidence for a velocity dependent dynamic contact angle at a moving contact line. We present a systematic investigation of the capillary rise dynamics of glycerol and aqueous glycerol solutions in vertical glass capillaries of various radii. For pure glycerol, the results of our experiments are in almost perfect agreement with the predictions of the Washburn equation using independently measured values for the liquid and capillary parameters. For aqueous glycerol solutions we observe discrepancies between the theoretical expectations and the experimental results, which are increasing with the water content of the solution. A thorough analysis, combined with scaling arguments, allows us to conclude that dynamic contact angle effects alone cannot provide a consistent explanation for these discrepancies. Rather, they can be perfectly accounted for if the mixture flowing in the capillary would have an effective, increased viscosity (in respect to the nominal value). We suggest and briefly discuss various mechanisms that could contribute to this observed behavior.

Different regimes in vertical capillary filling

In this paper, we identify that the different regimes encountered in a vertical capillary filling or a capillary-rise problem are determined entirely by two dimensionless parameters: Ohnesorge number (Oh) and Bond number (Bo). The initial universal inertial regime, which has been analyzed in our recent paper [Das et al., Phys. Rev. E 86, 067301 (2012)], is followed by any one of three possible regimes, dictated by the ratio Oh/Bo. For Oh/Bo>>1, the viscous effects dominate the gravitational effects, and one encounters the classical Washburn regime. For the other limit, i.e., Oh/Bo<<1, the viscous effects are insignificant and there is no Washburn regime. On the contrary, the inertial regime transits to the oscillatory regime with the filling length ℓ oscillating about the Jurin height (~1/Bo), which is the maximum height attained by a liquid column in vertical capillary filling, with the viscous effects (~Oh) dictating the nature of the oscillations. For Oh/Bo~1, we get a behavior intermediate of these two extreme regimes. Finally, we identify the correct force picture that drives the oscillatory regime and in the process achieve quantitative match with the experimental results, that was precluded in the previous studies.

Early regimes of capillary filling

In this paper we analyze the inviscid regime (for which viscosity is unimportant and the flow occurs due to the balance between the capillary and the inertial effects) that invariably precedes the classical century-old Washburn regime during capillary filling. We demonstrate that a new nondimensional number, namely, the product of the Ohnesorge number and the ratio between the filling length (ℓ) and the radius of the capillary (R), dictates the occurrence of this regime and the other well-known regimes in a capillary filling problem. We also identify that this inviscid regime occurs for the time that is of the order of the capillary time scale and, as has been quantified before [Quere, Eur. Phys. Lett. 39, 533 (1997); Joly, J. Chem. Phys. 135, 214705 (2011)], is characterized by the filling length being linearly proportional to the filling time. We establish the universality of this regime by pinpointing the existence of this regime (showing appropriate dependencies of the capillary radii and density) from existing experimental and Molecular Dynamics Simulation results that signify disparate ranges of length and time scales.

Nanoscale surface modifications to control capillary flow characteristics in PMMA microfluidic devices

Polymethylmethacrylate (PMMA) microfluidic devices have been fabricated using a hot embossing technique to incorporate micro-pillar features on the bottom wall of the device which when combined with either a plasma treatment or the coating of a diamond-like carbon (DLC) film presents a range of surface modification profiles. Experimental results presented in detail the surface modifications in the form of distinct changes in the static water contact angle across a range from 44.3 to 81.2 when compared to pristine PMMA surfaces. Additionally, capillary flow of water (dyed to aid visualization) through the microfluidic devices was recorded and analyzed to provide comparison data between filling time of a microfluidic chamber and surface modification characteristics, including the effects of surface energy and surface roughness on the microfluidic flow. We have experimentally demonstrated that fluid flow and thus filling time for the microfluidic device was significantly faster for the device with surface modifications that resulted in a lower static contact angle, and also that the incorporation of micro-pillars into a fluidic device increases the filling time when compared to comparative devices.

Flux characteristics of cell culture medium in rectangular microchannels

Rectangular microchannels 50 μm high and 30, 40, 50, 60, or 70 μm wide were fabricated by adjusting the width of a gap cut in a polyethylene sheet 50 μm thick and sandwiching the sheet between an acrylic plate and a glass plate. Flux in the microchannels was measured under three different inner surface conditions: uncoated, albumin-coated, and confluent growth of rat fibroblasts on the bottom of the microchannels. The normalized flux in microchannels with cultured fibroblasts or albumin coating was significantly larger than that in the uncoated channels. The experimental data for all microchannels deviated from that predicted by classical hydrodynamic theory. At small aspect ratio the flux in the microchannels was larger than that predicted theoretically, whereas it became smaller at large aspect ratio. The aspect ratio rather than Reynolds number is the correct property for predicting the variation of the normalized friction factor. We postulate that two counteracting effects, rotation of large molecules and slip velocity at the corners of the microchannels, are responsible for the deviation. From these results we conclude that albumin coating should be carried out in the same way as when fabricating our integrating cell-culture system. The outcomes of this study are not only important for the design of our culture system, but also quite informative for general microfluidics.