Experimental measurement of forces and energies associated with capillary rise in a vertical tube

Energies Associated with a Meniscus along a Flat Vertical Wall

In this theoretical work, existing equations for the height and shape of a liquid meniscus along a vertical flat wall are used to estimate the volume and energies associated with its formation. A mechanism and an associated energy balance are proposed. Equations for the work of wetting, surface energy, gravitational energy, and dissipation are derived. This analysis shows that the energy spontaneously released during wetting is either stored in the air-liquid interface of the newly formed meniscus, stored in its bulk liquid as gravitational energy, or dissipated as heat. The absolute magnitude of these energies depends on the surface tension and density of the liquid as well as the wettability of the wall.

Modeling Approach to Determine Static Rivulet Height in Regular Polygonal Capillary Tubes

The rise of partially wetting liquids along the corners of noncircular capillary tubes is observed in many practical science and engineering applications such as wastewater treatment using membranes, remediation, oil recovery from petroleum reservoirs, and blood flow. In this paper, rivulet rise at the corners of polygonal capillary tubes is studied for partially wetting liquids with contact angles below the critical value. The presence of corners changes the distribution of a liquid in an incomplete wetting condition. In this study, geometrical models are proposed to better understand the capillary rise and flow behavior at the corners. A geometrical solution for the capillary rivulet height and profile is derived under gravity in triangular, square, and pentagonal capillary tubes. The effects of several factors including contact angle, number of polygon sides, and liquid properties on the capillary rivulet height are examined. It was found that the ratio of liquid surface tension to density directly affects the corner rise, while it has an inverse relationship with other factors. The maximum rivulet height of 91.6 mm is obtained in the triangular capillary tube with a side length of 1 mm and a contact angle of 30° for polydimethylsiloxane (PDMS-20)-air fluid pair. The minimum capillary rivulet height of 6.2 mm, on the other hand, is achieved in the pentagonal capillary tube, with a side length of 3 mm and a contact angle of 30°. To validate the developed analytical approach, comparisons are made between the model results, literature predictions, and experimental data. In addition, the geometrical model for a square capillary tube is compared with previous published studies, revealing a good agreement. This study provides quantitative results for the influence of capillary tube shape on the flow behavior of fluids in noncircular tubes that can be useful for control and optimization of transport phenomena in corresponding systems.

Meniscus Formation in a Vertical Capillary Tube

In this theoretical work, the energies associated with the formation of a meniscus in a small diameter capillary tube are analyzed. A mechanism for meniscus creation and an associated energy balance are proposed. Equations for work of wetting, surface energy, gravitational energy, and dissipation are derived. The relative magnitude of these quantities is compared, first to each other and then to energies from capillary rise. In capillary rise, the energy released as work of wetting is evenly split between gravitational energy stored in the liquid column and heat dissipated there. The analysis performed here suggests that meniscus formation is energetically distinct and more complex than capillary rise. In meniscus formation, most of the energy released as work of wetting is stored in the stretched air-liquid interface or dissipated in the bulk liquid; their relative distribution depends on the properties of the liquid and the tube.

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).

Reply to Comment on "Solid-Liquid Work of Adhesion"

Extrand's interpretation in his "Comment on "Solid-Liquid Work of Adhesion" by Tadmor and Coworkers" may lead to an important discussion and physical understanding of the problem. Below, we compare the two approaches and elucidate the differences to put them in the right perspective.

Comment on "Solid-Liquid Work of Adhesion"

In a recent article, Tadmor and co-workers (Tadmor, R., et al. Langmuir 2017, 33, 3594-3600) used a centrifugal adhesion balance (CAB) to detach liquid drops from solid surfaces. By orienting solid surfaces in their CAB such that normal and lateral surfaces were balanced, the debonding force acted perpendicularly to the surface and drops detached by the axisymmetric retraction of their contact line. The detachment force was used to estimate the work of adhesion. To match the work of adhesion values from CAB to those calculated from the Young-Dupré equation, relatively large contact angles were required. Here, an alternative interpretation of their results is offered. Receding contact angles were estimated from their data and then used to predict the work of adhesion. These alternative predictions of the work of adhesion agreed with their estimates from the CAB.

Origins of Wetting

This feature article provides an overview of wetting phenomena. Much of the analysis done on wetting in the last 100 years assumes that the phenomena are determined by molecular interactions within the interfacial area between the liquid and solid. However, there is now ample evidence that wetting is controlled by interactions in the vicinity of the contact line where the liquid and solid meet. Recent experiments and modeling that demonstrate this are reviewed.