Forces, pressures and energies associated with liquid rising in nonuniform capillary tubes

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.

The effect of surface roughness on capillary rise in micro-grooves

The capillary action is a unique feature of micro-grooves with numerous applications. This spontaneous flow eliminates the need for an extra pumping device to deliver a liquid. Capillary action depends on physical properties and features of the solid surface, as well as on thermophysical properties of the liquid. In this study, our previously proposed unifying capillary rise model is extended to include the effect of surface roughness. A new characteristic length scale is proposed that includes salient geometrical parameters, such as micro-grooves height, width, and surface roughness. Furthermore, it is shown that by using the proposed characteristic length scale, it can be determined whether the capillary action would occur in a given micro-groove and liquid. Various metallic and polymeric surfaces with a wide range of surface roughness are fabricated from aluminum, stainless-steel, natural graphite sheet, and 3D-printed stainless-steel and a polymer. A profilometer and sessile drop method are used to measure surface roughness and the contact angles, respectively. The present unifying model is compared against our measured data, and it is shown that it can predict the capillary rise in rough micro-grooves with less than a 10% relative difference. It is observed that the capillary height can be increased for a wetting surface by introducing surface roughness and by using optimal micro-groove cross-sections that are triangular as opposed to rectangular. The proposed compact, unifying model can be used to predict the capillary rise for any given micro-groove cross-section, and as a design tool for numerous industrial and biomedical applications, such as heat pipes, power electronic cooling solutions, sorption systems, medicine delivery devices, and microfluidics that utilize capillary micro-grooves.

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.

Capillary force-induced superlattice variation atop a nanometer-wide graphene flake and its moiré origin studied by STM

We present strong experimental evidence for the moiré origin of superlattices on graphite by imaging a live transition from one superlattice to another with concurrent and direct measurement of the orientation angle before and after rotation using scanning tunneling microscopy (STM). This has been possible due to a fortuitous observation of a superlattice on a nanometer-sized graphene flake wherein we have induced a further rotation of the flake utilizing the capillary forces at play at a solid-liquid interface using STM tip motion. We propose a more "realistic" tip-surface meniscus relevant to STM at solid-liquid interfaces and show that the capillary force is sufficient to account for the total expenditure of energy involved in the process.

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.

Is a Knowledge of Surface Topology and Contact Angles Enough to Define the Drop Impact Outcome?

It is well known that a superhydrophobic surface may not be able to repel impacting droplets because of the so-called Cassie-to-Wenzel transition. It has been proven that a critical value of the receding contact angle (θR) exists for the complete rebound of water, recently experimentally measured to be 100° for a large range of impact velocities. On the contrary, in the present work, no rebound was observed when low-surface-tension liquids such as hexadecane (σ = 27.5 mN/m at 25 °C) are concerned, even for very low impact velocities and very high values of θR and low contact angle hysteresis. Therefore, the critical threshold of θR ≈ 100° does not sound acceptable for all liquids and for all hydrophobic surfaces. For the same Weber numbers, a Cassie-to-Wenzel state transition occurs after the impact as a result of the easier penetration of low-surface-tension fluids in the surface structure. Hence, a criterion for the drop rebound of low-surface-tension liquids must consider not only the contact angle values with surfaces but also their surface tension and viscosity. This suggests that, even if it is possible to produce surfaces with enhanced static repellence against oils and organics, generally the realization of synthetic materials with self-cleaning and antisticking abilities in dynamic phenomena, such as spray impact, remains an unsolved task. Moreover, it is demonstrated that the chemistry of the surface, the physicochemical interactions with the liquid drops, and the possible wettability gradient of the surface asperity also play important roles in determining the critical Weber number above which impalement occurs. Therefore, the classical numerical simulations of drop impact on dry surfaces are definitively not able to capture the final outcomes of the impact for all possible fluids if the surface topology and chemistry and/or the wettability gradient in the surface structure are not properly reflected.