Mechanisms of dynamic wetting failure in the presence of soluble surfactants

2017 ◽  
Vol 825 ◽  
pp. 677-703 ◽  
Author(s):  
Chen-Yu Liu ◽  
Marcio S. Carvalho ◽  
Satish Kumar
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Rectangular Channel ◽  
Dynamic Contact ◽  
Slip Boundary Condition ◽  
Dynamic Wetting ◽  
Navier Slip ◽  
Static Contact ◽  
Soluble Surfactants ◽  
Dynamic Contact Line

A hydrodynamic model and flow visualization experiments are used to understand the mechanisms through which soluble surfactants can influence the onset of dynamic wetting failure. In the model, a Newtonian liquid displaces air in a rectangular channel in the absence of inertia. A Navier-slip boundary condition and constant contact angle are used to describe the dynamic contact line, and surfactants are allowed to adsorb to the interface and moving channel wall (substrate). The Galerkin finite element method is used to calculate steady states and identify the critical capillary number $Ca^{crit}$ at which wetting failure occurs. It is found that surfactant solubility weakens the influence of Marangoni stresses, which tend to promote the onset of wetting failure. Adsorption of surfactants to the substrate can delay the onset of wetting failure due to the emergence of Marangoni stresses that thicken the air film near the dynamic contact line. The experiments indicate that $Ca^{crit}$ increases with surfactant concentration. For the more viscous solutions used, this behaviour can largely be explained by accounting for changes to the mean surface tension and static contact angle produced by surfactants. For the lowest-viscosity solution used, comparison between the model predictions and experimental observations suggests that other surfactant-induced phenomena such as Marangoni stresses may play a more important role.

Dynamics of sessile drops. Part 1. Inviscid theory

2014 ◽  
Vol 760 ◽  
pp. 5-38 ◽  
Author(s):  
J. B. Bostwick ◽  
P. H. Steen
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Dynamic Contact ◽  
Linear Operators ◽  
Sessile Droplet ◽  
Physical Reason ◽  
Spherical Cap ◽  
Static Contact ◽  
Dynamic Contact Line ◽  
Line Condition

AbstractA sessile droplet partially wets a planar solid support. We study the linear stability of this spherical-cap base state to disturbances whose three-phase contact line is (i) pinned, (ii) moves with fixed contact angle and (iii) moves with a contact angle that is a smooth function of the contact-line speed. The governing hydrodynamic equations for inviscid motions are reduced to a functional eigenvalue problem on linear operators, which are parameterized by the base-state volume through the static contact angle and contact-line mobility via a spreading parameter. A solution is facilitated using inverse operators for disturbances (i) and (ii) to report frequencies and modal shapes identified by a polar $k$ and azimuthal $l$ wavenumber. For the dynamic contact-line condition (iii), we show that the disturbance energy balance takes the form of a damped-harmonic oscillator with ‘Davis dissipation’ that encompasses the dynamic effects associated with (iii). The effect of the contact-line motion on the dissipation mechanism is illustrated. We report an instability of the super-hemispherical base states with mobile contact lines (ii) that correlates with horizontal motion of the centre-of-mass, called the ‘walking’ instability. Davis dissipation from the dynamic contact-line condition (iii) can suppress the instability. The remainder of the spectrum exhibits oscillatory behaviour. For the hemispherical base state with mobile contact line (ii), the spectrum is degenerate with respect to the azimuthal wavenumber. We show that varying either the base-state volume or contact-line mobility lifts this degeneracy. For most values of these symmetry-breaking parameters, a certain spectral ordering of frequencies is maintained. However, because certain modes are more strongly influenced by the support than others, there are instances of additional modal degeneracies. We explain the physical reason for these and show how to locate them.

scholarly journals Moving contact lines and dynamic contact angles: a ‘litmus test’ for mathematical models, accomplishments and new challenges

2020 ◽  
Vol 229 (10) ◽  
pp. 1945-1977 ◽  
Author(s):  
Yulii D. Shikhmurzaev
Keyword(s):  
Contact Angle ◽  
Mathematical Models ◽  
Contact Line ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Dynamic Wetting ◽  
Line Speed ◽  
Moving Contact ◽  
New Challenges ◽  
Litmus Test

Abstract After a brief overview of the ‘moving contact-line problem’ as it emerged and evolved as a research topic, a ‘litmus test’ allowing one to assess adequacy of the mathematical models proposed as solutions to the problem is described. Its essence is in comparing the contact angle, an element inherent in every model, with what follows from a qualitative analysis of some simple flows. It is shown that, contrary to a widely held view, the dynamic contact angle is not a function of the contact-line speed as for different spontaneous spreading flows one has different paths in the contact angle-versus-speed plane. In particular, the dynamic contact angle can decrease as the contact-line speed increases. This completely undermines the search for the ‘right’ velocity-dependence of the dynamic contact angle, actual or apparent, as a direction of research. With a reference to an earlier publication, it is shown that, to date, the only mathematical model passing the ‘litmus test’ is the model of dynamic wetting as an interface formation process. The model, which was originated back in 1993, inscribes dynamic wetting into the general physical context as a particular case in a wide class of flows, which also includes coalescence, capillary breakup, free-surface cusping and some other flows, all sharing the same underlying physics. New challenges in the field of dynamic wetting are discussed.

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.

The Pressure Drop and Dynamic Contact Angle of Motion of Triple-Lines in Hydrophobic Microchannels

2010 ◽  
Author(s):  
Dongin Yu ◽  
Chiwoong Choi ◽  
Moohwan Kim
Keyword(s):  
Contact Angle ◽  
Pressure Drop ◽  
Liquid Film ◽  
Dynamic Contact Angle ◽  
Triple Line ◽  
Dynamic Contact ◽  
Superficial Velocity ◽  
Channel Diameter ◽  
Fluid Property ◽  
Static Contact

At two-phase flow in microchannels, slug flow regime is different for wettability of surface. A slug in a hydrophilic microchannel has liquid film. However, a slug in a hydrophobic microchannel has no liquid film instead, the slug has triple-lines and makes higher pressure drop due to the motion of the triple-line. In previous researches, pressure drop of triple-line is depended of dynamic contact angle, channel diameter and fluid property. And, dynamic contact angle is depended of static contact angle, superficial velocity and fluid property. In order to understand the pressure drop of motion of triple-lines, pressure drop of slug with triple-lines in case of various diameters (0.546, 0.763, 1.018, 1.555, 2.075 mm), various fluids (D.I.water, D.I.water-1, 5, 10% ethanol mixture) and various superficial velocity (j = 0.01∼0.4 m/s) was measured. Dynamic contact angle was calculated from relation of the pressure drop of slug with triple-lines. Comparing with previous dynamic contact angle correlations, previous correlation underestimated dynamic contact angle in the region of this study. (10−4≤Ca≤10−3, 10−2≤We≤10−1, 68°≤θS≤110°)

Marangoni-enhanced capillary wetting in surfactant-driven superspreading

2018 ◽  
Vol 855 ◽  
pp. 181-209 ◽  
Author(s):  
Hsien-Hung Wei
Keyword(s):  
Contact Line ◽  
Stress Singularity ◽  
Marangoni Effect ◽  
Dynamic Contact ◽  
Sorption Kinetics ◽  
Colloid Interface ◽  
Hydrodynamic Approach ◽  
Interfacial Surfactant ◽  
Dynamic Contact Line ◽  
Air Liquid Interface

Superspreading is a phenomenon such that a drop of a certain class of surfactant on a substrate can spread with a radius that grows linearly with time much faster than the usual capillary wetting. Its origin, in spite of many efforts, is still not fully understood. Previous modelling and simulation studies (Karapetsas et al. J. Fluid Mech., vol. 670, 2011, pp. 5–37; Theodorakis et al. Langmuir, vol. 31, 2015, pp. 2304–2309) suggest that the transfer of the interfacial surfactant molecules onto the substrate in the vicinity of the contact line plays a crucial role in superspreading. Here, we construct a detailed theory to elaborate on this idea, showing that a rational account for superspreading can be made using a purely hydrodynamic approach without involving a specific surfactant structure or sorption kinetics. Using this theory it can be shown analytically, for both insoluble and soluble surfactants, that the curious linear spreading law can be derived from a new dynamic contact line structure due to a tiny surfactant leakage from the air–liquid interface to the substrate. Such a leak not only establishes a concentrated Marangoni shearing toward the contact line at a rate much faster than the usual viscous stress singularity, but also results in a microscopic surfactant-devoid zone in the vicinity of the contact line. The strong Marangoni shearing then turns into a local capillary force in the zone, making the contact line in effect advance in a surfactant-free manner. This local Marangoni-driven capillary wetting in turn renders a constant wetting speed governed by the de Gennes–Cox–Voinov law and hence the linear spreading law. We also determine the range of surfactant concentration within which superspreading can be sustained by local surfactant leakage without being mitigated by the contact line sweeping, explaining why only limited classes of surfactants can serve as superspreaders. We further show that spreading of surfactant spreaders can exhibit either the $1/6$ or $1/2$ power law, depending on the ability of interfacial surfactant to transfer/leak to the bulk/substrate. All these findings can account for a variety of results seen in experiments (Rafai et al. Langmuir, vol. 18, 2002, pp. 10486–10488; Nikolov & Wasan, Adv. Colloid Interface Sci., vol. 222, 2015, pp. 517–529) and simulations (Karapetsas et al. 2011). Analogy to thermocapillary spreading is also made, reverberating the ubiquitous role of the Marangoni effect in enhancing dynamic wetting driven by non-uniform surface tension.

scholarly journals Numerical Bifurcation Analysis of a Film Flowing over a Patterned Surface through Enhanced Lubrication Theory

Fluids ◽  
2021 ◽  
Vol 6 (11) ◽  
pp. 405
Author(s):  
Nicola Suzzi ◽  
Giulio Croce
Keyword(s):  
Contact Angle ◽  
Bifurcation Analysis ◽  
Dynamic Contact Angle ◽  
Flow Characteristics ◽  
Dynamic Contact ◽  
Contact Angles ◽  
Inclined Plate ◽  
Lubrication Equation ◽  
Static Contact ◽  
Numerical Bifurcation

The bifurcation analysis of a film falling down an hybrid surface is conducted via the numerical solution of the governing lubrication equation. Instability phenomena, that lead to film breakage and growth of fingers, are induced by multiple contamination spots. Contact angles up to 75∘ are investigated due to the full implementation of the free surface curvature, which replaces the small slope approximation, accurate for film slope lower than 30∘. The dynamic contact angle is first verified with the Hoffman–Voinov–Tanner law in case of a stable film down an inclined plate with uniform surface wettability. Then, contamination spots, characterized by an increased value of the static contact angle, are considered in order to induce film instability and several parametric computations are run, with different film patterns observed. The effects of the flow characteristics and of the hybrid pattern geometry are investigated and the corresponding bifurcation diagram with the number of observed rivulets is built. The long term evolution of induced film instabilities shows a complex behavior: different flow regimes can be observed at the same flow characteristics under slightly different hybrid configurations. This suggest the possibility of controlling the rivulet/film transition via a proper design of the surfaces, thus opening the way for relevant practical application.

scholarly journals Numerical Study of Formation of a Series of Bubbles from an Orifice by Applying Dynamic Contact Angle Model

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Nan Chen ◽  
Xiyu Chen ◽  
Antonio Delgado
Keyword(s):  
Contact Angle ◽  
Gas Flow ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Static Contact Angle ◽  
Bubble Shape ◽  
Flow Rates ◽  
Bubble Detachment ◽  
Static Contact ◽  
Detachment Time

The dynamic contact angle model is applied in the formation process of a series of bubbles from Period-I regime to Period-II regime by using the VOF method on a 2D axisymmetric domain. In the first process of the current research, the dynamic contact angle model is validated by comparing the numerical results to the experimental data. Good agreement in terms of bubble shape and bubble detachment time is observed from a lower flow rate Q = 150.8 cm3/min (Re = 54.77, Period-I regime) to a higher flow rate Q = 603.2 cm3/min (Re = 219.07, Period-III regime). The comparison between the dynamic contact angle model and the static contact angle model is also performed. It is observed that the static contact angle model can obtain similar results as the dynamic contact angle model only for smaller gas flow rates (Q ≤ 150.8 cm3/min and Re ≤ 54.77)). For higher gas flow rates, the static contact angle model cannot produce good results as the dynamic contact angle model and has larger relative errors in terms of bubble detachment time and bubble shape.

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