Rise of the main meniscus in rectangular capillaries: Experiments and modeling (original) (raw)
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Meniscus formation in a capillary and the role of contact line friction
Soft Matter, 2014
Supplementary Material X-ray imaging of meniscus nucleation. Figure S1. Nucleation of meniscus of a) TBP and b) hexadecane in a D i = 400µm glass capillary. The frames are taken with the period of 1 ms. Contact angle determination. Using the image analysis, we analyzed the equilibrium contact angles by studying the maximum column height given by Jurin's formula. The meniscus position was defined through its lower point, see the red dot in Figure S2 b). To measure the height of the liquid column, two characteristic points were used. The zero-level of the liquid column was set at the free liquid surface far away from the capillary and the upper point was chosen at the meniscus sag. In parallel, we used the circular arc fit to obtain the contact angle. To extract the equilibrium contact angle from the image of the meniscus, we calculated the meniscus radius using a special Mallab based algorithm 1. An example of the meniscus arc determination is shown in Fig. S2 b). Table 2 collects the obtained contact angles. The error takes into account an uncertainly in the determination of the meniscus and wall contours.
Hydrodynamics of a Confined Meniscus in a Square Capillary Tube at Low Capillary Numbers
Frontiers in Heat Pipes, 2014
In microchannel fluid flow, understanding of the liquid-gas interface behavior is vital for developing a wide range of microfluidic devices. The dynamic contact angle of the liquid-air meniscus varies with its velocity and the ensuing meniscus shape has profound effect on the local transport characteristics in its vicinity. Depending on the application, dynamic menisci shapes eventually control the momentum, heat and mass transport coefficients in two-phase microchannel flow geometries, where such conditions are often encountered. To better understand the effect of dynamic contact angle on meniscus shape, high speed visualization of menisci of four different liquids (water, ethanol, glycerin and silicon oil) has been undertaken at different Capillary numbers. Quantitative information of the velocity field and its distribution near the moving liquid-air interface has been done using micro-PIV measurements in a 1 mm × 1 mm dry square capillary having deionized water as the working fluid. This provides vital information on the local flow transport characteristics (two-dimensional velocity fields on a longitudinal plane) in the wake of the meniscus. To augment and complement the study, three-dimensional simulation of the flow field near the liquid-air meniscus has also been performed on Comsol ® , applying the two-phase flow level-set method. The results clearly demonstrate that, while the u-velocity profile in the liquid domain is parabolic (Poiseuille-type flow) in nature away from the interface, it drastically changes (become flatter) as we approach the meniscus. Close to the meniscus the flow becomes three-dimensional with both v and w velocities showing a double-vortex, the strength of the latter being lower than the former. This observation is clearly noted both by PIV data as well as the simulations. The characteristic of the flow field in the meniscus wake is the most important parameter which affects the viscous stress generated due to the meniscus motion. The study reveals that controlling the wettability of the liquid can be an effective tool to control the overall transport behavior of the moving confined meniscus.
Capillary Rise between Planar Surfaces | NIST
2009
Minimization of free energy is used to calculate the equilibrium vertical rise and meniscus shape of a liquid column between two closely spaced, parallel planar surfaces that are inert and immobile. States of minimum free energy are found using standard variational principles, which lead not only to an Euler-Lagrange differential equation for the meniscus shape and elevation, but also to the boundary conditions at the three-phase junction where the liquid meniscus intersects the solid walls. The analysis shows that the classical Young-Dupré equation for the thermodynamic contact angle is valid at the three-phase junction, as already shown for sessile drops with or without the influence of a gravitational field. Integration of the Euler-Lagrange equation shows that a generalized Laplace-Young ͑LY͒ equation first proposed by O'Brien, Craig, and Peyton ͓J. Colloid Interface Sci. 26, 500 ͑1968͔͒ gives an exact prediction of the mean elevation of the meniscus at any wall separation, whereas the classical LY equation for the elevation of the midpoint of the meniscus is accurate only when the separation approaches zero or infinity. When both walls are identical, the meniscus is symmetric about the midpoint, and the midpoint elevation is a more traditional and convenient measure of capillary rise than the mean elevation. Therefore, for this symmetric system a different equation is fitted to numerical predictions of the midpoint elevation and is shown to give excellent agreement for contact angles between 15°a nd 160°and wall separations up to 30 mm. When the walls have dissimilar surface properties, the meniscus generally assumes an asymmetric shape, and significant elevation of the liquid column can occur even when one of the walls has a contact angle significantly greater than 90°. The height of the capillary rise depends on the spacing between the walls and also on the difference in contact angles at the two surfaces. When the contact angle at one wall is greater than 90°but the contact angle at the other wall is less than 90°, the meniscus can have an inflection point separating a region of positive curvature from a region of negative curvature, the inflection point being pinned at zero height. However, this condition arises only when the spacing between the walls exceeds a threshold value that depends on the difference in contact angles.
The steady movement of a liquid meniscus in a capillary tube
Journal of Fluid Mechanics, 1977
The steady movement of a liquid meniscus in a circular capillary tube has been examined theoretically for dynamic contact angles close to 90" with minute slippage of the liquid on the solid, thus relaxing the conventional no-slip boundary condition. The resulting flow field does not produce an unbounded force at the contact line, contrary to that with the no-slip condition. The interfacial velocity, wall stress, fluid pressure and the meniscus shape are calculated, and the significance of dynamic contact-angle measurements is discussed. A modified version of the classical Washburn equation which takes account of the meniscus also reveals the importance of slippage. $ Experimental values of the dynamic contact angle Od, the angle formed by the liquid interface and the solid surface at the moving contact line, are available in the literature (e.g. Elliott & Riddiford 1967) as a function of the contact-line velocity U for a number of spreading systems; however, efforts to predict Bd theoretically as a function of U , the static contact angle 0, and the properties of the liquid and solid have been generally unsuccessful.
Capillary Rise: Validity of the Dynamic Contact Angle Models
Langmuir, 2017
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 selflayering 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 selflayering. 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.
Capillary Rise in Porous Media
Journal of Colloid and Interface Science, 2001
Capillary rise experiments were performed in columns filled with glass beads and Berea sandstones, using visual methods to register the advance of the water front. For the glass bead filled columns, early time data are well fitted by the Washburn equation. However, in the experiments, the advancing front exceeded the predicted equilibrium height. For large times, an algebraic behavior of the velocity of the front is observed (T. Delker et al., Phys. Rev. Lett. 76, 2902 (1996)). A model for studying the capillary pressure evolution in a regular assembly of spheres is proposed and developed. It is based on a quasi-static advance of the meniscus with a piston-like motion and allows us to estimate the hydraulic equilibrium height, with values very close to those obtained by fitting early time data to a Washburn equation. The change of regime is explained as a transition in the mechanism of advance of the meniscus. On the other hand, only the Washburn regime was observed for the sandstones. The front velocity was fitted to an algebraical form with an exponent close to 0.5, a value expected from the asymptotic limit of the Washburn equation. C 2001 Academic Press
Modeling of Menisci and Capillary Forces from the Millimeter to the Micrometer Size Range
Journal of Physical Chemistry B, 2001
This paper examines lateral capillary interactions between millimeter-and sub-millimeter-sized objects floating at the interface between perfluorodecalin (PFD) and water. It describes methodssboth experimental and computationalsthat allow the shape of the interface to be described for various geometries of the interacting objects. From these shapes, it derives the energy profiles characterizing the lateral capillary interactions. This work also demonstrates a new experimental method of imaging and studying menisci, and of studying capillary interactions between objects.
Three-dimensional menisci in polygonal capillaries
Journal of Colloid and Interface Science, 1992
The shapes of gravity-free, three-dimensional menisci are computed from the augmented Young-Laplace equation. Incorporation of disjoining thin-film forces in the Young-Laplace relation eliminates the contact line, thereby eliminating the free boundary from the problem. To calculate a meniscus with finite contact angles, the conjoining/disjoining pressure isotherm must also contain an attractive, sharply varying, spike function. The width of this function, w, reflects the range of the thin-film forces. In the limit of w approaching zero, a solution of the Young-Laplace equation is recovered. The proposed calculation method is demonstrated for menisci in two different types of capillaries. In the first case, the capillary is regular-polygonal in cross section with either 3, 4, or 6 sides and with contact angles ,I~ ranging from 0 to 45 °. In the second case, the capillary is rectangular in section with aspect ratios ranging from 1.2 to 5 and with q~ = 0 °, 15 °, or 30 °. Gas-liquid menisci inside a square glass capillary of 0.5 mm inscribed radius are measured optically for air bubbles immersed in a solution of di-n-butyl phthalate and mineral oil. This liquid mixture exhibits a zero contact angle with the wall and matches the refractive index of the glass capillary, permitting precise visual location of the interface. Excellent agreement is found with the numerical results which further demonstrates that the limiting process of the proposed method is valid. Because it avoids the issue of locating the contact line, solution of the augmented Young-Laplace equation is a simple and powerful method for the calculation of three-dimensional menisci.
Langmuir : the ACS journal of surfaces and colloids, 2016
A theory of contact angle hysteresis of a meniscus inside thin capillaries with smooth, homogeneous solid walls is developed in terms of surface forces (disjoining/conjoining pressure isotherm) using a quasi-equilibrium approach. The disjoining/conjoining pressure isotherm includes electrostatic, intermolecular, and structural components. The values of the static receding θr, advancing θa, and equilibrium θe contact angles in thin capillaries were calculated on the basis of the shape of the disjoining/conjoining pressure isotherm. It was shown that both advancing and receding contact angles depend on the capillary radius. The suggested mechanism of the contact angle hysteresis has a direct experimental confirmation: the process of receding is accompanied by the formation of thick β-films on the capillary walls. The effect of the transition from partial to complete wetting in thin capillaries is predicted and analyzed. This effect takes place in very thin capillaries, when the recedi...