scholarly journals Air entrainment in dynamic wetting: Knudsen effects and the influence of ambient air pressure

2015 ◽  
Vol 769 ◽  
pp. 444-481 ◽  
Author(s):  
James E. Sprittles
Keyword(s):  
Air Entrainment ◽  
Ambient Air ◽  
Drop Impact ◽  
Viscosity Data ◽  
Dynamic Wetting ◽  
Reduced Pressure ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Reduced Pressures ◽  
Non Equilibrium

Recent experiments on coating flows and liquid drop impact both demonstrate that wetting failures caused by air entrainment can be suppressed by reducing the ambient gas pressure. Here, it is shown that non-equilibrium effects in the gas can account for this behaviour, with ambient pressure reductions increasing the mean free path of the gas and hence the Knudsen number $\mathit{Kn}$. These effects first manifest themselves through Maxwell slip at the boundaries of the gas, so that for sufficiently small $\mathit{Kn}$ they can be incorporated into a continuum model for dynamic wetting flows. The resulting mathematical model contains flow structures on the nano-, micro- and millimetre scales and is implemented into a computational platform developed specifically for such multiscale phenomena. The coating flow geometry is used to show that for a fixed gas–liquid–solid system (a) the increased Maxwell slip at reduced pressures can substantially delay air entrainment, i.e. increase the ‘maximum speed of wetting’, (b) unbounded maximum speeds are obtained, as the pressure is reduced only when slip at the gas–liquid interface is allowed for, and (c) the observed behaviour can be rationalised by studying the dynamics of the gas film in front of the moving contact line. A direct comparison with experimental results obtained from a dip-coating process shows that the model recovers most trends but does not accurately predict some of the high viscosity data at reduced pressures. This discrepancy occurs because the gas flow enters the ‘transition regime’, so that more complex descriptions of its non-equilibrium nature are required. Finally, by collapsing onto a master curve experimental data obtained for drop impact in a reduced pressure gas, it is shown that the same physical mechanisms are also likely to govern splash suppression phenomena.

scholarly journals Dynamic drying transition via free-surface cusps

2018 ◽  
Vol 858 ◽  
pp. 760-786 ◽  
Author(s):  
Catherine Kamal ◽  
James E. Sprittles ◽  
Jacco H. Snoeijer ◽  
Jens Eggers
Keyword(s):  
Gas Phase ◽  
Slip Length ◽  
Air Entrainment ◽  
Cusp Forms ◽  
Radius Of Curvature ◽  
Order Unity ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Solid Plate ◽  
Critical Capillary Number

We study air entrainment by a solid plate plunging into a viscous liquid, theoretically and numerically. At dimensionless speeds $Ca=U\unicode[STIX]{x1D702}/\unicode[STIX]{x1D6FE}$ of order unity, a near-cusp forms due to the presence of a moving contact line. The radius of curvature of the cusp’s tip scales with the slip length multiplied by an exponential of $-Ca$. The pressure from the air flow drawn inside the cusp leads to a bifurcation, at which air is entrained, i.e. there is ‘wetting failure’. We develop an analytical theory of the threshold to air entrainment, which predicts the critical capillary number to depend logarithmically on the viscosity ratio, with corrections coming from the slip in the gas phase.

scholarly journals Boundary conditions for dynamic wetting - A mathematical analysis

2020 ◽  
Vol 229 (10) ◽  
pp. 1849-1865 ◽  
Author(s):  
Mathis Fricke ◽  
Dieter Bothe
Keyword(s):  
Boundary Conditions ◽  
Contact Line ◽  
Stokes Equations ◽  
Mathematical Tool ◽  
Regular Solutions ◽  
Dynamic Wetting ◽  
Two Phase ◽  
Completely Regular ◽  
Moving Contact Line ◽  
Moving Contact

Abstract The moving contact line paradox discussed in the famous paper by Huh and Scriven has lead to an extensive scientific discussion about singularities in continuum mechanical models of dynamic wetting in the framework of the two-phase Navier–Stokes equations. Since the no-slip condition introduces a non-integrable and therefore unphysical singularity into the model, various models to relax the singularity have been proposed. Many of the relaxation mechanisms still retain a weak (integrable) singularity, while other approaches look for completely regular solutions with finite curvature and pressure at the moving contact line. In particular, the model introduced recently in [A.V. Lukyanov, T. Pryer, Langmuir 33, 8582 (2017)] aims for regular solutions through modified boundary conditions. The present work applies the mathematical tool of compatibility analysis to continuum models of dynamic wetting. The basic idea is that the boundary conditions have to be compatible at the contact line in order to allow for regular solutions. Remarkably, the method allows to compute explicit expressions for the pressure and the curvature locally at the moving contact line for regular solutions to the model of Lukyanov and Pryer. It is found that solutions may still be singular for the latter model.

Slipping moving contact lines: critical roles of de Gennes’s ‘foot’ in dynamic wetting

2019 ◽  
Vol 873 ◽  
pp. 110-150
Author(s):  
Hsien-Hung Wei ◽  
Heng-Kwong Tsao ◽  
Kang-Ching Chu
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Capillary Number ◽  
Dynamic Contact Angle ◽  
Wall Slip ◽  
Dynamic Contact ◽  
Colloid Interface ◽  
Dynamic Wetting ◽  
Moving Contact Line ◽  
Moving Contact

In the context of dynamic wetting, wall slip is often treated as a microscopic effect for removing viscous stress singularity at a moving contact line. In most drop spreading experiments, however, a considerable amount of slip may occur due to the use of polymer liquids such as silicone oils, which may cause significant deviations from the classical Tanner–de Gennes theory. Here we show that many classical results for complete wetting fluids may no longer hold due to wall slip, depending crucially on the extent of de Gennes’s slipping ‘foot’ to the relevant length scales at both the macroscopic and microscopic levels. At the macroscopic level, we find that for given liquid height $h$ and slip length $\unicode[STIX]{x1D706}$, the apparent dynamic contact angle $\unicode[STIX]{x1D703}_{d}$ can change from Tanner’s law $\unicode[STIX]{x1D703}_{d}\sim Ca^{1/3}$ for $h\gg \unicode[STIX]{x1D706}$ to the strong-slip law $\unicode[STIX]{x1D703}_{d}\sim Ca^{1/2}\,(L/\unicode[STIX]{x1D706})^{1/2}$ for $h\ll \unicode[STIX]{x1D706}$, where $Ca$ is the capillary number and $L$ is the macroscopic length scale. Such a no-slip-to-slip transition occurs at the critical capillary number $Ca^{\ast }\sim (\unicode[STIX]{x1D706}/L)^{3}$, accompanied by the switch of the ‘foot’ of size $\ell _{F}\sim \unicode[STIX]{x1D706}Ca^{-1/3}$ from the inner scale to the outer scale with respect to $L$. A more generalized dynamic contact angle relationship is also derived, capable of unifying Tanner’s law and the strong-slip law under $\unicode[STIX]{x1D706}\ll L/\unicode[STIX]{x1D703}_{d}$. We not only confirm the two distinct wetting laws using many-body dissipative particle dynamics simulations, but also provide a rational account for anomalous departures from Tanner’s law seen in experiments (Chen, J. Colloid Interface Sci., vol. 122, 1988, pp. 60–72; Albrecht et al., Phys. Rev. Lett., vol. 68, 1992, pp. 3192–3195). We also show that even for a common spreading drop with small macroscopic slip, slip effects can still be microscopically strong enough to change the microstructure of the contact line. The structure is identified to consist of a strongly slipping precursor film of length $\ell \sim (a\unicode[STIX]{x1D706})^{1/2}Ca^{-1/2}$ followed by a mesoscopic ‘foot’ of width $\ell _{F}\sim \unicode[STIX]{x1D706}Ca^{-1/3}$ ahead of the macroscopic wedge, where $a$ is the molecular length. It thus turns out that it is the ‘foot’, rather than the film, contributing to the microscopic length in Tanner’s law, in accordance with the experimental data reported by Kavehpour et al. (Phys. Rev. Lett., vol. 91, 2003, 196104) and Ueno et al. (Trans. ASME J. Heat Transfer, vol. 134, 2012, 051008). The advancement of the microscopic contact line is still led by the film whose length can grow as the $1/3$ power of time due to $\ell$, as supported by the experiments of Ueno et al. and Mate (Langmuir, vol. 28, 2012, pp. 16821–16827). The present work demonstrates that the behaviour of a moving contact line can be strongly influenced by wall slip. Such slip-mediated dynamic wetting might also provide an alternative means for probing slippery surfaces.

scholarly journals Multiscale dynamic wetting of a droplet on a lyophilic pillar-arrayed surface

2013 ◽  
Vol 716 ◽  
pp. 171-188 ◽  
Author(s):  
Quanzi Yuan ◽  
Ya-Pu Zhao
Keyword(s):  
Scaling Laws ◽  
Dynamic Balance ◽  
Combination Method ◽  
Scaling Analysis ◽  
Dynamic Wetting ◽  
Practical Applications ◽  
Molecular Kinetic Theory ◽  
Future Design ◽  
Moving Contact Line ◽  
Moving Contact

AbstractDynamic wetting of a droplet on lyophilic pillars was explored using a multiscale combination method of experiments and molecular dynamics simulations. The excess lyophilic area not only provided excess driving force, but also pinned the liquid around the pillars, which kept the moving contact line in a dynamic balance state every period of the pillars. The flow pattern and the flow field of the droplet on the pillar-arrayed surface, influenced by the concerted effect of the liquid–solid interactions and the surface roughness, were revealed from the continuum to the atomic level. Then, the scaling analysis was carried out employing molecular kinetic theory. Controlled by the droplet size, the density of roughness and the pillar height, two extreme regimes were distinguished, i.e. $R\sim {t}^{1/ 3} $ for the rough surface and $R\sim {t}^{1/ 7} $ for the smooth surface. The scaling laws were validated by both the experiments and the simulations. Our results may help in understanding the dynamic wetting of a droplet on a pillar-arrayed lyophilic substrate and assisting the future design of pillar-arrayed lyophilic surfaces in practical applications.

scholarly journals Convex Nanobending at a Moving Contact Line: The Missing Mesoscopic Link in Dynamic Wetting

ACS Nano ◽  
2014 ◽  
Vol 8 (11) ◽  
pp. 11493-11498 ◽  
Author(s):  
Lei Chen ◽  
Jiapeng Yu ◽  
Hao Wang
Keyword(s):  
Contact Line ◽  
Dynamic Wetting ◽  
Moving Contact Line ◽  
Moving Contact

Moving contact line

2001 ◽  
Vol 11 (PR6) ◽  
pp. Pr6-199-Pr6-212 ◽  
Author(s):  
Y. Pomeau
Keyword(s):  
Contact Line ◽  
Moving Contact Line ◽  
Moving Contact

Influence of Non-Equilibrium Fluid Properties During Fogging on Intake Duct and Compressor Characteristics

2017 ◽  
Author(s):  
Christoph Günther ◽  
Franz Joos
Keyword(s):  
Relative Humidity ◽  
Gas Turbine ◽  
Thermophysical Properties ◽  
Ambient Air ◽  
Compressor Stage ◽  
Compression Process ◽  
Fluid Properties ◽  
Temperature And Pressure ◽  
Gas Turbine Compressor ◽  
Non Equilibrium

This study reports on numerically calculated thermophysical properties of air passing through a gas turbine compressor after passage through an intake duct affected by wet compression. Case of reference is unaffected ambient air (referenced to as dry scenario) passing through intake duct and compressor. Furthermore, ambient air cooled down by (overspray) fogging (referenced to as wet scenarios) was considered. Acceleration at the end of intake duct causing reduction of static temperature and pressure results in supersaturated fluid properties at inlet to gas turbine compressor. These supersaturated fluid properties are non-equilibrium with saturation level above relative humidity of φ = 1. Entrance of supersaturated fluid into gas turbine compressor can result in condensation within first compressor stage. At the same time delayed impact of evaporative cooling influences compression process.

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