Contact-line singularities resolved exclusively by the Kelvin effect: volatile liquids in air

2018 ◽  
Vol 858 ◽  
pp. 881-916 ◽  
Author(s):  
A. Y. Rednikov ◽  
P. Colinet
Keyword(s):  
Contact Line ◽  
Contact Angles ◽  
Precursor Film ◽  
Navier Slip ◽  
Flat Substrate ◽  
Remarkable Result ◽  
Kelvin Effect ◽  
Volatile Liquids ◽  
Curvature Dependence ◽  
Line Singularities

The contact line of a volatile liquid on a flat substrate is studied theoretically. We show that a remarkable result obtained for a pure-vapour atmosphere (Phys. Rev. E, vol. 87, 2013, 010401) also holds for an isothermal diffusion-limited vapour exchange with air. Namely, for both zero and finite Young’s angles, the motion- and phase-change-related contact-line singularities can in principle be regularised solely by the Kelvin effect (curvature dependence of saturation conditions). The latter prevents the curvature from diverging and rather leads to its versatile self-adjustment. To illustrate the point, the problem is resolved for a distinguished vicinity of the contact line (‘microregion’) in a ‘minimalist’ way, i.e. without any disjoining pressure, precursor film, Navier slip or any other microphysics. This also leads to the determination of the ‘Kelvin-only’ evaporation- and motion-induced apparent contact angles. With the Kelvin-only microscales actually turning out to be quite nanoscopic, other microphysics effects may nonetheless interfere too in reality. The Kelvin-only results will then yield a limiting case within such a more general formulation.

Droplet spreading and absorption on rough, permeable substrates

2015 ◽  
Vol 784 ◽  
pp. 465-486 ◽  
Author(s):  
Leonardo Espín ◽  
Satish Kumar
Keyword(s):  
Surface Roughness ◽  
Contact Line ◽  
Nonlinear Evolution ◽  
Precursor Film ◽  
Radial Coordinate ◽  
Droplet Spreading ◽  
Liquid Spreading ◽  
Line Region ◽  
Influence Of Substrate ◽  
Contact Line Pinning

Wetting of permeable substrates by liquids is an important phenomenon in many natural and industrial processes. Substrate heterogeneities may significantly alter liquid spreading and interface shapes, which in turn may alter liquid imbibition. A new lubrication-theory-based model for droplet spreading on permeable substrates that incorporates surface roughness is developed in this work. The substrate is assumed to be saturated with liquid, and the contact-line region is described by including a precursor film and disjoining pressure. A novel boundary condition for liquid imbibition is applied that eliminates the need for a droplet-thickness-dependent substrate permeability that has been employed in previous models. A nonlinear evolution equation describing droplet height as a function of time and the radial coordinate is derived and then numerically solved to characterize the influence of substrate permeability and roughness on axisymmetric droplet spreading. Because it incorporates surface roughness, the new model is able to describe the contact-line pinning that has been observed in experiments but not captured by previous models.

Surface Topography Induced Ultrahydrophobic Behavior: Effect of Three-Phase Contact Line Topology

2006 ◽  
Author(s):  
Neeharika Anantharaju ◽  
Mahesh Panchagnula ◽  
Wayne Kimsey ◽  
Sudhakar Neti ◽  
Svetlana Tatic-Lucic
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Anomalous Behavior ◽  
Contact Angles ◽  
Wet Etching ◽  
Surface Geometry ◽  
Wetting Behavior ◽  
Void Fractions ◽  
Three Phase ◽  
Receding Contact

The wettability of silicon surface hydrophobized using silanization reagents was studied. The advancing and receding contact angles were measured with the captive needle approach. In this approach, a drop under study was held on the hydrophobized surface with a fine needle immersed in it. The asymptotic advancing and receding angles were obtained by incrementally increasing the volume added and removed, respectively, until no change in angles was observed. The values were compared with the previously published results. Further, the wetting behavior of water droplets on periodically structured hydrophobic surfaces was investigated. The surfaces were prepared with the wet etching process and contain posts and holes of different sizes and void fractions. The surface geometry brought up a scope to study the Wenzel (filling of surface grooves) and Cassie (non filling of the surface grooves) theories and effects of surface geometry and roughness on the contact angle. Experimental data point to an anomalous behavior where the data does not obey either Wenzel or Cassie type phenomenology. This behavior is explained by an understanding of the contact line topography. The effect of contact line topography on the contact angle was thus parametrically studied. It was also inferred that, the contact angle increased with the increase in void fraction. The observations may serve as guidelines in designing surfaces with the desired wetting behavior.

scholarly journals Morphological evolution of microscopic dewetting droplets with slip

2017 ◽  
Vol 828 ◽  
pp. 271-288 ◽  
Author(s):  
Tak Shing Chan ◽  
Joshua D. McGraw ◽  
Thomas Salez ◽  
Ralf Seemann ◽  
Martin Brinkmann
Keyword(s):  
Slip Length ◽  
Morphological Evolution ◽  
Early Time ◽  
Slip Boundary Condition ◽  
Similarity Solutions ◽  
Contact Angles ◽  
Equilibrium Contact Angle ◽  
Navier Slip ◽  
Slip Boundary ◽  
Quasistatic Regime

We investigate the dewetting of a droplet on a smooth horizontal solid surface for different slip lengths and equilibrium contact angles. Specifically, we solve for the axisymmetric Stokes flow using the boundary element method with (i) the Navier-slip boundary condition at the solid/liquid boundary and (ii) a time-independent equilibrium contact angle at the contact line. When decreasing the rescaled slip length $\tilde{b}$ with respect to the initial central height of the droplet, the typical non-sphericity of a droplet first increases, reaches a maximum at a characteristic rescaled slip length $\tilde{b}_{m}\approx O(0.1{-}1)$ and then decreases. Regarding different equilibrium contact angles, two universal rescalings are proposed to describe the behaviour of the non-sphericity for rescaled slip lengths larger or smaller than $\tilde{b}_{m}$. Around $\tilde{b}_{m}$, the early time evolution of the profiles at the rim can be described by similarity solutions. The results are explained in terms of the structure of the flow field governed by different dissipation channels: elongational flows for $\tilde{b}\gg \tilde{b}_{m}$, friction at the substrate for $\tilde{b}\approx \tilde{b}_{m}$ and shear flows for $\tilde{b}\ll \tilde{b}_{m}$. Following the changes between these dominant dissipation mechanisms, our study indicates a crossover to the quasistatic regime when $\tilde{b}$ is many orders of magnitude smaller than $\tilde{b}_{m}$.

scholarly journals Photo-Induced Super-hydrophilic Thin Films on Quartz Glass by UV Irradiation of Precursor Films Involving a Ti(IV) Complex at Room Temperature

Materials ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 348 ◽  
Author(s):  
Hsiang-Jung Wu ◽  
Kota Tanabe ◽  
Hiroki Nagai ◽  
Mitsunobu Sato
Keyword(s):  
Thin Films ◽  
Uv Irradiation ◽  
Quartz Glass ◽  
Room Temperature ◽  
Contact Angles ◽  
Chemical Components ◽  
Precursor Film ◽  
Dark Condition ◽  
Xps Spectra ◽  
Molecular Precursor

Photo-induced super-hydrophilic thin films were fabricated on a quartz glass substrate by ultraviolet (UV) irradiation of a molecular precursor film at room temperature. A molecular precursor film exhibiting high solubility to both ethanol and water was obtained by spin-coating a solution involving a Ti(IV) complex; this complex was prepared by the reaction of Ti(IV) alkoxide with butylammonium hydrogen oxalate and hydrogen peroxide in ethanol. Transparent and well-adhered amorphous thin films of 160–170 nm thickness were obtained by weak UV irradiation (4 mW·cm−2 at 254 nm) of the precursor films for over 4 h at room temperature. The resultant thin films exhibiting low refractive indices of 1.78–1.79 were mechanically robust and water-insoluble. The chemical components of the thin films were examined by means of Fourier transform-infrared (FT-IR) and X-ray photoelectron spectroscopy (XPS) spectra, focusing on the presence of the original ligands. The super-hydrophilic properties (evaluated based on the water contact angles on the surfaces) of the thin films after being kept in a dark condition overnight emerged when the aforementioned UV-light irradiation was performed for 10 min. It was additionally clarified that the super-hydrophilicity can be photo-induced repeatedly by UV irradiation for 10 min (indicated by a contact angle smaller than 4°) even after the hydrophilic level of the thin films had once been lowered by being in a dark condition for 4 h.

Detection of Advancing Edge and Existing Length of Precursor Film Ahead Macroscopic Contact Line of Droplet Spreading on Solid Substrate

2008 ◽  
Author(s):  
Ichiro Ueno
Keyword(s):  
Contact Line ◽  
High Speed ◽  
Thin Liquid Film ◽  
Experimental Studies ◽  
Laser Interferometry ◽  
Spreading Rate ◽  
Solid Substrate ◽  
Precursor Film ◽  
Boundary Line ◽  
Droplet Spreading

The author introduces a series of experimental studies on a simple but complex wetting process; a droplet spreads on a solid substrate. The spreading droplet on the solid substrate is accompanied with the movement of a visible boundary line so-called ‘macroscopic contact line.’ Existing studies have indicated there exits a thin liquid film known as ‘precursor film’ ahead the macroscopic contact line of the droplet. The present author’s group has dedicated their special effort to detect the advancing edge of the precursor film by applying a convectional laser interferometry and a high-speed camera, and to evaluate the spreading rate of the precursor film.

Dynamic wetting failure in surfactant solutions

2016 ◽  
Vol 789 ◽  
pp. 285-309 ◽  
Author(s):  
Chen-Yu Liu ◽  
Eric Vandre ◽  
Marcio S. Carvalho ◽  
Satish Kumar
Keyword(s):  
Contact Line ◽  
Rectangular Channel ◽  
Air Entrainment ◽  
Steady State Solution ◽  
Contact Angles ◽  
Pressure Gradients ◽  
Computationally Efficient ◽  
Dynamic Wetting ◽  
Surfactant Solutions ◽  
Limit Points

The influence of insoluble surfactants on dynamic wetting failure during displacement of Newtonian fluids in a rectangular channel is studied in this work. A hydrodynamic model for steady Stokes flows of dilute surfactant solutions is developed and evaluated using three approaches: (i) a one-dimensional (1D) lubrication-type approach, (ii) a novel hybrid of a 1D description of the receding phase and a 2D description of the advancing phase, and (iii) an asymptotic theory of Cox (J. Fluid Mech., vol. 168, 1986b, pp. 195–220). Steady-state solution families in the form of macroscopic contact angles as a function of the capillary number are determined and limit points are identified. When air is the receding fluid, Marangoni stresses are found to increase the receding-phase pressure gradients near the contact line by thinning the air film without significantly changing the capillary-pressure gradients there. As a consequence, the limit points shift to lower capillary numbers and the onset of wetting failure is promoted. The model predictions are then used to interpret decades-old experimental observations concerning the influence of surfactants on air entrainment (Burley & Kennedy, Chem. Engng Sci., vol. 31, 1976, pp. 901–911). In addition to being a computationally efficient alternative for the rectangular geometries considered here, the hybrid modelling approach developed in this paper could also be applied to more complicated geometries where a thin air layer is present near a contact line.

Direct Numerical Simulation of the Microscale Fluid Flow and Heat Transfer in the Three-Phase Contact Line Region During Evaporation

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Stefan Batzdorf ◽  
Tatiana Gambaryan-Roisman ◽  
Peter Stephan
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Contact Line ◽  
Thin Liquid Film ◽  
Contact Angles ◽  
Length Scale ◽  
Phase Contact ◽  
Flow And Heat Transfer ◽  
Three Phase

The heat and mass transfer close to the apparent three-phase contact line is of tremendous importance in many evaporation processes. Despite the extremely small dimensions of this region referred to as the microregion compared to the macroscopic length scale of a boiling process, a considerable fraction of heat can be transferred in this region. Due to its small characteristic length scale, physical phenomena are relevant in the microregion, which are completely negligible on the macroscopic scale, including the action of adhesion forces and the interfacial heat resistance. In the past, models have been developed taking these effects into account. However, so far these models are based on the assumption of one-dimensional (1D) heat conduction, and the flow within the thin liquid film forming the microregion near the apparent three-phase contact line is modeled utilizing the lubrication approximation. Hence, the application of existing models is restricted to small apparent contact angles. Moreover, the effects of surface structures or roughness are not included in these lubrication models. To overcome these limitations, a direct numerical simulation (DNS) of the liquid flow and heat transfer within the microregion is presented in this paper. The DNS is employed for validation of the existing lubrication model and for investigation of the influence of surface nanostructures on the apparent contact angle and in particular on the heat transfer within the microregion.

scholarly journals Contact lines over random topographical substrates. Part 1. Statics

2011 ◽  
Vol 672 ◽  
pp. 358-383 ◽  
Author(s):  
NIKOS SAVVA ◽  
GRIGORIOS A. PAVLIOTIS ◽  
SERAFIM KALLIADASIS
Keyword(s):  
Numerical Experiments ◽  
Random Variable ◽  
Contact Angles ◽  
Contact Lines ◽  
Substrate Roughness ◽  
Random Functions ◽  
Flat Substrate ◽  
The Subject ◽  
Influence Of Substrate ◽  
Theoretical Results

We investigate theoretically the statistics of the equilibria of two-dimensional droplets over random topographical substrates. The substrates are appropriately represented as families of certain stationary random functions parametrized by a characteristic amplitude and wavenumber. In the limit of shallow topographies and small contact angles, a linearization about the flat-substrate equilibrium reveals that the droplet footprint is adequately approximated by a zero-mean, normally distributed random variable. The theoretical analysis of the statistics of droplet shift along the substrate is highly non-trivial. However, for weakly asymmetric substrates it can be shown analytically that the droplet shift approaches a Cauchy random variable; for fully asymmetric substrates its probability density is obtained via Padé approximants. Generalization to arbitrary stationary random functions does not change qualitatively the behaviour of the statistics with respect to the characteristic amplitude and wavenumber of the substrate. Our theoretical results are verified by numerical experiments, which also suggest that on average a random substrate neither enhances nor reduces droplet wetting. To address the question of the influence of substrate roughness on wetting, a stability analysis of the equilibria must be performed so that we can distinguish between stable and unstable equilibria, which in turn requires modelling the dynamics. This is the subject of Part 2 of this study.

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