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

Early-Stage Liquid Infiltration in Nanoconfinements

Liquid infiltration is one of the commonly adapted flow mechanisms in microscale/nanoscale heat-transfer applications. The theoretical modeling of dynamic infiltration profile in the microscale/nanoscale requires a deep study, because the acting forces are entirely different from those of a large-scale system. Herein, a model equation is developed from the fundamental force balance at the microscale/nanoscale level, to capture the dynamic infiltration flow profile. Molecular kinetic theory (MKT) is used to predict the dynamic contact angle. Molecular dynamics (MD) simulations are performed to study the capillary infiltration in two different geometries. The infiltration length is computed from the simulation results. The model is also evaluated over surfaces having different surface wettability. The generated model provides a better estimation of the infiltration length, compared to the well-established models. The developed model is expected to aid in the designing of microscale/nanoscale devices where liquid infiltration plays a key role.

Dynamic wetting of various liquids: Theoretical models, experiments, simulations and applications

Dynamic wetting is a ubiquitous phenomenon and frequently observed in our daily life, as exemplified by the famous lotus effect. It is also an interfacial process of upmost importance involving many cutting-edge applications and has hence received significantly increasing academic and industrial attention for several decades. However, we are still far away to completely understand and predict wetting dynamics for a given system due to the complexity of this dynamic process. The physics of moving contact lines is mainly ascribed to the full coupling with the solid surface on which the liquids contact, the atmosphere surrounding the liquids, and the physico-chemical characteristics of the liquids involved (small-molecule liquids, metal liquids, polymer liquids, and simulated liquids). Therefore, to deepen the understanding and efficiently harness wetting dynamics, we propose to review the major advances in the available literature. After an introduction providing a concise and general background on dynamic wetting, the main theories are presented and critically compared. Next, the dynamic wetting of various liquids ranging from small-molecule liquids to simulated liquids are systematically summarized, in which the new physical concepts (such as surface segregation, contact line fluctuations, etc.) are particularly highlighted. Subsequently, the related emerging applications are briefly presented in this review. Finally, some tentative suggestions and challenges are proposed with the aim to guide future developments.

Capillary Flow Dynamics in Composite Rectangular Microchannels with Rough Walls

In this article, we consider rectangular microchannels composed of glass and thin polymeric walls with different roughness in which opposed walls are of the same material but adjacent walls are not. We propose a model for fluid capillary transport into these rectangular microchannels when horizontally positioned and focus our research on how the microchannel aspect ratio modifies the motion during the initial viscous regimes. The model relies on an effective static contact angle and an effective friction coefficient that averages local magnitudes in the cross section. An extensive experimental investigation with different microchannels enabled us to obtain these coefficients for different aspect ratios. While for low aspect ratios, the effective contact angle presents the smallest values, the effective friction coefficient shows the larger ones. With rough surfaces, the spontaneous occurrence of pinning and depinning events associated with sharp wall defects notably reduces the effective static contact angle even when high aspect ratios are used. The obtained values of the effective friction coefficient show good agreement with previous literature investigations for rough and smooth lateral wall surfaces. Finally, we propose a nondimensional time to establish when contact angle effects dominate the dynamics. We found that for the materials and fluid properties used in this work, these effects become negligible for times larger than t ∼ 1 s.

Effects of Tube Radius and Surface Tension on Capillary Rise Dynamics of Water/Butanol Mixtures

Capillary-driven action is an important phenomenon which aids the development of high-performance heat transfer devices, such as microscale heat pipes. This study examines the capillary rise dynamics of n-butanol/water mixture in a single vertical capillary tube with different radii (0.4, 0.6, and 0.85 mm). For liquids, distilled water, n-butanol, and their blends with varying concentrations of butanol (0.3, 0.5, and 0.7 wt.%) were used. The results show that the height and velocity of the capillary rise were dependent on the tube radius and liquid surface tension. The larger the radius and the higher the surface tension, the lower was the equilibrium height (he) and the velocity of rise. The process of capillary rise was segregated into three characteristic regions: purely inertial, inertial + viscous, and purely viscous regions. The early stages (purely inertial and inertial + viscous) represented the characteristic heights h1 and h2, which were dominant in the capillary rise process. There were linear correlations between the characteristic heights (h1, h2, and he), tube radius, and surface tension. Based on these correlations, a linear function was established between each of the three characteristic heights and the consolidated value of tube radius and surface tension (σL/2πr2).

Spreading and Drying Dynamics of Water Drop on Hot Surface of Superwicking Ti-6Al-4V Alloy Material Fabricated by Femtosecond Laser

A superwicking Ti-6Al-4V alloy material with a hierarchical capillary surface structure was fabricated using femtosecond laser. The basic capillary surface structure is an array of micropillars/microholes. For enhancing its capillary action, the surface of the micropillars/microholes is additionally structured by regular fine microgrooves using a technique of laser-induced periodic surface structures (LIPSS), providing an extremely strong capillary action in a temperature range between 23 °C and 80 °C. Due to strong capillary action, a water drop quickly spreads in the wicking surface structure and forms a thin film over a large surface area, resulting in fast evaporation. The maximum water flow velocity after the acceleration stage is found to be 225–250 mm/s. In contrast to other metallic materials with surface capillarity produced by laser processing, the wicking performance of which quickly degrades with time, the wicking functionality of the material created here is long-lasting. Strong and long-lasting wicking properties make the created material suitable for a large variety of practical applications based on liquid-vapor phase change. Potential significant energy savings in air-conditioning and cooling data centers due to application of the material created here can contribute to mitigation of global warming.

Direct Measurement of Contact Angle Change in Capillary Rise

Capillary rise is important in many aspects of physical phenomena from transport in porous media to biotechnology. It is typically described by the Lucas-Washburn-Rideal equation (LWRE), but discrepancy between some experiments and the model still remains elusive. In this paper, we show that the discrepancy is simply from the contact angle change during the capillary rise with no help of any specific models, such as dynamic contact angle (DCA) models. To demonstrate this, we directly measure the contact angle change in the capillary rise for glycerol and carboxymethyl cellulose solutions as examples of Newtonian and non-Newtonian liquids. Unlike previous studies that used DCA models to explain the discrepancy, when the contact angle change is directly applied to the LWRE for all four tested fluids, the model agrees well with experimental data. The estimated contact angle from the capillary rise as a function of time is in good agreement with the directly measured contact angle within a narrow margin of error. To pinpoint the conditions for the discrepancy, we propose a new time scale when contact angle dynamics dominates. The contact angle dynamics that can be obtained from the macroscopic capillary rise may provide useful information for capillary flow in a more complicated geometry such as porous media.

Capillary Imbibition of Binary Fluid Mixtures in Nanochannels

Many-body Dissipative Particle Dynamics (MDPD) simulations of binary fluid mixtures imbibing cylindrical nanochannels reveal a strong segregation of fluids differing in their affinities to the pore walls. Surprisingly, the imbibition front furthest into the channel is highly enriched in the fluid with the lower affinity for the walls, i.e., the fluid less prone to enter the pore. This effect is caused by the more-wetting fluid forming a monolayer covering the walls of the pore, while the lesser-wetting fluid is expelled from the walls to the interior of the pore where the higher axial flow velocity carries it to the front. The fluids remix after cessation of the flow. Nonwetting fluids can be made to enter a pore by mixing with a small amount of wetting fluid. The imbibition depth of the mixtures scales with the square root of time, in agreement with Bell-Cameron-Lucas-Washburn theory for pure fluids.

Inertial capillary uptake of drops

Uptake of liquid drops into capillary tubes has been experimentally studied and quantitatively analyzed. In experiments, drops of water and aqueous glycerol (≤50 wt %) were drawn into cylindrical borosilicate glass and quartz tubes with an inner diameter of 0.50-0.75 mm. The meniscus height rise was measured using high-speed images captured at 4000 frames per second, and results within a conservatively defined inertial regime indicate constant uptake velocity. An increase in the inertial velocity with drop curvature was observed due to increasing Laplace pressure in the drop, as drop sizes were comparable to the width of the capillary tubes. Measured velocities were slower than predicted by a purely inertial-capillary model and best described by introducing a contact line friction, consistent with the observed variability and viscosity dependence of the results. Mean friction coefficients in borosilicate capillaries ranged from 169±1 for 50 wt % glycerol drops to 218±1 for water drops. Peaks in the instantaneous Laplace pressure caused by surface oscillations were also measured. Correlations with uptake velocity were qualitatively apparent, with a delay between peaks of similar magnitude to the inertial-capillary oscillation time.

Capillary Nylon 6 polymer material produced by femtosecond laser processing

A wicking Nylon 6 polymer material was produced through surface structuring by a direct femtosecond laser nano/microstructuring approach. The produced wicking structure is an array of parallel microgrooves, the surface of which is textured with irregular nanostructures and fine microstructures. High-speed imaging of water spreading vertically uphill against the gravity discloses a series of capillary flow regimes with h ∝ t, h ∝ t1/2, and h ∝ t1/3 scaling laws, where h is the height of capillary rise and t is the time. In the initial stage, the capillary flow occurs with a single front, from which at a certain time a precursor front forms and advances ahead of the main one. Our study shows that the onset of the precursor front occurs in h ∝ t flow regime. The created material exhibits excellent wicking properties and may find applications in various technologically important areas.

The effect of viscosity and surface tension on inkjet printed picoliter dots

In this study, we investigated the effect of liquid viscosity and surface tension for inkjet printing on porous cellulose sheets. We used five model liquids, representing the operational field of an industrial high speed inkjet printer, as specified by Ohnesorge- and Reynolds number. Drops with 30 pl and 120 pl drop size were jetted with a commercial HSI printhead. We printed on four uncoated papers representing the most relevant grades on the market in terms of hydrophobisation and surface treatment. We are presenting a quantitative analysis of viscosity and surface tension on the print outcome, evaluating dot size, liquid penetration (print through) and surface coverage of the printed dots. The most important finding is that for liquids within the jetting window the variation of the liquid viscosity typically has a 2–3 times higher impact on the print outcome than variation of the liquid surface tension. Increased viscosity in all cases reduces dot area, liquid penetration and liquid surface coverage. Surface tension plays a smaller role for liquid spreading and penetration, except for hydrophobised substrates, where both are reduced for higher surface tension. Interestingly, higher surface tension consistently increases liquid surface coverage for all papers and drop sizes. A detailed analysis on the competing effect of dot spreading and liquid penetration is presented, in terms of viscosity, surface tension and surface coverage of the liquid.

In this study, we investigated the effect of liquid viscosity and surface tension for inkjet printing on porous cellulose sheets.

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.

Principles around Accurate Blood Volume Collection Using Capillary Action

Capillary action is one mechanism microfluidics uses to draw liquid autonomously in a substrate without the need of external energy. This behavior can be exploited to collect accurate volumes of liquids such as blood in narrow columns known as capillary tubes and help the development of inexpensive, user-friendly personalized biomedical tools. Precision bore glass capillaries demonstrate the "state of the art" for volume accuracy and precision, but height and radius must be carefully chosen in order to exploit the capillary action behavior efficiently. This Article investigates the influence of surface glass aging, due to prolonged exposure to humid air, and hematocrit level on the blood capillary rise. It provides also the tools to correctly define the optimum capillary dimensions to collect an accurate volume of blood in a glass capillary tube.

Capillary Rise: Validity of the Dynamic Contact Angle Models

The classical Lucas-Washburn-Rideal (LWR) equation, using the equilibrium contact angle, predicts a faster capillary rise process than experiments in many cases. The major contributor to the faster prediction is believed to be the velocity dependent dynamic contact angle. In this work, we investigated the dynamic contact angle models for their ability to correct the dynamic contact angle effect in the capillary rise process. We conducted capillary rise experiments of various wetting liquids in borosilicate glass capillaries and compared the model predictions with our experimental data. The results show that the LWR equations modified by the molecular kinetic theory and hydrodynamic model provide good predictions on the capillary rise of all the testing liquids with fitting parameters, while the one modified by Joos' empirical equation works for specific liquids, such as silicone oils. The LWR equation modified by molecular self-layering model predicts well the capillary rise of carbon tetrachloride, octamethylcyclotetrasiloxane, and n-alkanes with the molecular diameter or measured solvation force data. The molecular self-layering model modified LWR equation also has good predictions on the capillary rise of silicone oils covering a wide range of bulk viscosities with the same key parameter W(0), which results from the molecular self-layering. The advantage of the molecular self-layering model over the other models reveals the importance of the layered molecularly thin wetting film ahead of the main meniscus in the energy dissipation associated with dynamic contact angle. The analysis of the capillary rise of silicone oils with a wide range of bulk viscosities provides new insights into the capillary dynamics of polymer melts.

Dynamics of capillary transport in semi-solid channels

Capillary action has been described by Lucas and Washburn and extensively studied experimentally in hard materials, but few studies have examined capillary action in soft materials such as hydrogels. In tissue engineering, cells or dispersions must be often distributed within a hydrogel via microporous paths. Capillary action is one way to disperse such substances. Here, we examine the dynamics of capillary action in a model system of straight capillaries in two hydrogels. The channels had a circular cross-section in the micrometer size range (180-630 μm). The distance travelled over time was recorded and compared with the predictions of Lucas and Washburn. Besides water, we used a sucrose solution and a hydroxyethyl cellulose solution, both with viscosities slightly higher than that of water. The results showed that the distance travelled is proportional to the square root of time, , and that larger capillaries and lower viscosities result, as expected, in faster speeds. However, the absolute experimental values display large discrepancies from the predictions. We demonstrate that several possible reasons for these discrepancies can be ruled out and we describe a novel hypothesis for the cause of the retarded meniscus movement.

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).

Rise of the main meniscus in rectangular capillaries: Experiments and modeling

The rise of the main meniscus in rectangular capillaries is important in interpreting the phenomenon of fluid flow in porous media. Despite many experimental studies reported in the literature, there is no universal model for the rise of the main meniscus in either rectangular or square capillaries. In this work, we present an extensive experimental study and modeling of the rise of the main meniscus in both square and rectangular capillaries. Experimental work was carried out using three different liquids (water, ethanol, and hexadecane) in borosilicate glass and plastic (polystyrene) capillaries to investigate the effect of the contact angle and capillary size on the equilibrium main meniscus height. A universal model (an extended two-wall model) based on the Laplace equation was developed to predict the equilibrium height of the main meniscus in rectangular capillaries. Results have shown that, in a wide range of capillary sizes and contact angles, the predicted equilibrium heights of the main meniscus are in good agreement with the experimentally measured values.