scholarly journals Stokes flow near the contact line of an evaporating drop

2012 ◽  
Vol 709 ◽  
pp. 69-84 ◽  
Author(s):  
Hanneke Gelderblom ◽  
Oscar Bloemen ◽  
Jacco H. Snoeijer
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Stokes Equations ◽  
Similarity Solutions ◽  
Contact Angles ◽  
Singular Boundary ◽  
Air Interface ◽  
Evaporative Flux ◽  
Singular Boundary Condition ◽  
Critical Contact

AbstractThe evaporation of sessile drops in quiescent air is usually governed by vapour diffusion. For contact angles below $9{0}^{\ensuremath{\circ} } $, the evaporative flux from the droplet tends to diverge in the vicinity of the contact line. Therefore, the description of the flow inside an evaporating drop has remained a challenge. Here, we focus on the asymptotic behaviour near the pinned contact line, by analytically solving the Stokes equations in a wedge geometry of arbitrary contact angle. The flow field is described by similarity solutions, with exponents that match the singular boundary condition due to evaporation. We demonstrate that there are three contributions to the flow in a wedge: the evaporative flux, the downward motion of the liquid–air interface and the eigenmode solution which fulfils the homogeneous boundary conditions. Below a critical contact angle of $133. {4}^{\ensuremath{\circ} } $, the evaporative flux solution will dominate, while above this angle the eigenmode solution dominates. We demonstrate that for small contact angles, the velocity field is very accurately described by the lubrication approximation. For larger contact angles, the flow separates into regions where the flow is reversing towards the drop centre.

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.

Inertial effects in time-dependent motion of thin films and drops

2002 ◽  
Vol 467 ◽  
pp. 1-17 ◽  
Author(s):  
L. M. HOCKING ◽  
S. H. DAVIS
Keyword(s):  
Thin Films ◽  
Contact Angle ◽  
Contact Line ◽  
Evolution Equations ◽  
Liquid Films ◽  
Contact Angles ◽  
Terminal State ◽  
Lubrication Theory ◽  
Plate Motion ◽  
Special Cases

Capillarity is an important feature in controlling the spreading of liquid drops and in the coating of substrates by liquid films. For thin films and small contact angles, lubrication theory enables the analysis of the motion to be reduced to single evolution equations for the heights of the drops or films, provided the inertia of the liquid can be neglected. In general, the presence of inertia destroys the major simplification provided by lubrication theory, but two special cases that can be treated are identified here. In the first example, the approach of a drop to its equilibrium position is studied. For sufficiently low Reynolds numbers, the rate of approach to the terminal state and the contact angle are slightly reduced by inertia, but, above a critical Reynolds number, the approach becomes oscillatory. In the latter case there is no simple relation connecting the dynamic contact angle and contact-line speed. In the second example, the spreading drop is supported by a plate that is forced to oscillate in its own plane. For the parameter range considered, the mean spreading is unaffected by inertia, but the oscillatory motion of the contact line is reduced in magnitude as inertia increases, and the drop lags behind the plate motion. The oscillatory contact angle increases with inertia, but is not in phase with the plate oscillation.

Effect of Contact Angle on the Heat Transfer to an Evaporating Meniscus on a Moving Heated Surface

2005 ◽  
Author(s):  
A. Mukherjee ◽  
S. G. Kandlikar
Keyword(s):  
Heat Transfer ◽  
Contact Angle ◽  
Stokes Equations ◽  
Contact Region ◽  
Heated Surface ◽  
Contact Angles ◽  
Navier Stokes ◽  
Wall Heat Transfer ◽  
Moving Wall ◽  
Liquid Circulation

Numerical simulation is carried out to study a 2D evaporating meniscus formed on a moving wall. The complete Navier-Stokes equations along with continuity and energy equations are solved. The liquid vapor interface is captured using the level set technique. The meniscus is fed with saturated water from the top whereas the bottom wall is maintained at a higher temperature and is also imparted with a velocity. The meniscus attains a steady shape when all the incoming liquid gets evaporated due to heat transfer from the wall. The advancing and receding contact region of the meniscus are provided with different contact angles. Results indicate that the average heat flux at the meniscus base increases with increase in contact angle. The primary reason for heat transfer from the wall is attributed to the liquid circulation inside the meniscus and the corresponding transient conduction from the wall. As the meniscus contact angle increases the liquid circulation is found to disturb the thermal boundary layer more effectively thereby resulting in increased wall heat transfer. The effect of contact angle on wall heat transfer to the moving and evaporating meniscus is compared to partial nucleate pool boiling.

Metrics for Quantifying Surface Wetting Effects on Vaporization Processes at Nanostructured Hydrophilic Surfaces

2016 ◽  
Author(s):  
Claire M. Kunkle ◽  
Van P. Carey
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Contact Angles ◽  
Apparent Contact Angle ◽  
Static Contact Angle ◽  
Sensitive Indicator ◽  
Nanostructured Surfaces ◽  
Hydrophilic Surfaces ◽  
Static Contact ◽  
Spread Area

A static contact angle is most often used as a means of quantifying the wetting characteristics of the liquid phase in vaporization processes at a solid surface. This metric is often convenient to measure and intuitive in its interpretation, but when a surface is superhydrophilic, the resulting low contact angles are difficult to measure accurately from photographs of sessile droplet profiles or contact line regions. For droplets at ultra low contact angles, small changes of contact angle can produce very large changes in wetted surface area, which makes small uncertainties in contact angle result in large uncertainties in wetted area. For hydrophilic nanostructured surfaces, another disadvantage is that the relationship of the macroscopic (apparent) contact angle to the nanoscale interaction of the liquid and vapor contact line with the nanostructured surface is not always clear. In this study, a new wetting metric based on spreading characteristics of sessile droplets is proposed that can be easily measured for hydrophilic surfaces. This metric also has the advantage that it is a more direct and sensitive indicator of how a droplet spreads on the surface. The spread area directly impacts heat transfer interactions between the droplet and the surface, therefore affecting evaporation time. Consequently, a metric that more directly illustrates the spread area provides an indication of how the wetting will affect these mechanisms. Use of the proposed new metric is explored in the context of evaporation and boiling applications with superhydrophilic surfaces. Characteristics of this metric are also compared to static contact angle and other choices of wetting metrics suggested in earlier studies, such as dynamic advancing and receding contact angles, and spreading coefficients. The effects of nanoscale structure and/or roughness on the proposed wetting metric are analyzed in detail. A model is developed that predicts the dependence of the proposed wetting parameter on intrinsic material wettability for rough, nano-structured surfaces. The model results demonstrate that the proposed metric is a more sensitive indicator of macroscopic wetting behavior than apparent contact angle when the surface is superhydrophilic. This characteristic of the proposed new metric is shown to have advantages over other wetting metrics in the specific case of superhydrophilic nanostructured surfaces. Application of the proposed wetting metric is demonstrated for some example nanostructured surfaces. The results of our study indicate that this proposed new metric can be particularly useful for characterizing the effects of variable wetting on vaporization processes on highly wetted nanostructured surfaces.

Wetting and Capillarity Effects On Bubble Formation From Orifice Plates Submerged in Pools of Water

2021 ◽  
Author(s):  
Sanjivan Manoharan ◽  
Raj M. Manglik ◽  
Milind A. Jog
Keyword(s):  
Contact Angle ◽  
Bubble Growth ◽  
High Speed ◽  
Bubble Formation ◽  
Minimum Energy ◽  
Hydrophobic Surface ◽  
Contact Angles ◽  
Orifice Diameter ◽  
Capillary Length ◽  
Critical Contact

Abstract An experimental study of bubble growth from submerged orifice plates in pools of water is carried out to scale and correlate the effects of surface wettability and orifice diameter D0 on ebullience. Measurements of bubble growth on surfaces with nine different contact angles (38° ≤ θ ≤ 128°) with varying air flow rates (1 to 300 ml/min) were made using high speed videography and image processing. In the static or constant-volume regime, below a critical contact angle θc, the bubble base remains attached to the orifice and the equivalent departure diameter Db is independent of contact angle θ. On the other hand, above the critical contact angle, the bubble base spreads on the surface resulting in larger Db. For θ > θc, Db is strongly dependent on θ and increases with it. Using minimum energy method, it is shown that the wettability effects can be scaled and correlated by a modified capillary length, defined as a function of the Laplace length and contact angle. The proposed correlation provides predictions of Db that agree with experimental data of this study as well as those available in the literature to within ±15 %. Moreover, for a hydrophobic surface when D0 > twice the modified capillary length, the bubble grows inside the orifice; for a hydrophilic surface this scales with twice the capillary length and effect of θ is not seen.

scholarly journals Thick drops climbing uphill on an oscillating substrate

2018 ◽  
Vol 840 ◽  
pp. 131-153 ◽  
Author(s):  
J. T. Bradshaw ◽  
J. Billingham
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Contact Angle Hysteresis ◽  
Contact Angles ◽  
Boundary Integral ◽  
Static Contact Angle ◽  
Rise Velocity ◽  
Contact Lines ◽  
Weakly Nonlinear ◽  
Static Contact

Experiments have shown that a liquid droplet on an inclined plane can be made to move uphill by sufficiently strong, vertical oscillations (Brunet et al., Phys. Rev. Lett., vol. 99, 2007, 144501). In this paper, we study a two-dimensional, inviscid, irrotational model of this flow, with the velocity of the contact lines a function of contact angle. We use asymptotic analysis to show that, for forcing of sufficiently small amplitude, the motion of the droplet can be separated into an odd and an even mode, and that the weakly nonlinear interaction between these modes determines whether the droplet climbs up or slides down the plane, consistent with earlier work in the limit of small contact angles (Benilov and Billingham, J. Fluid Mech. vol. 674, 2011, pp. 93–119). In this weakly nonlinear limit, we find that, as the static contact angle approaches $\unicode[STIX]{x03C0}$ (the non-wetting limit), the rise velocity of the droplet (specifically the velocity of the droplet averaged over one period of the motion) becomes a highly oscillatory function of static contact angle due to a high frequency mode that is excited by the forcing. We also solve the full nonlinear moving boundary problem numerically using a boundary integral method. We use this to study the effect of contact angle hysteresis, which we find can increase the rise velocity of the droplet, provided that it is not so large as to completely fix the contact lines. We also study a time-dependent modification of the contact line law in an attempt to reproduce the unsteady contact line dynamics observed in experiments, where the apparent contact angle is not a single-valued function of contact line velocity. After adding lag into the contact line model, we find that the rise velocity of the droplet is significantly affected, and that larger rise velocities are possible.

Numerical Study of Effect of Contact Angles on Flow Boiling Employing Thermal LBM Simulation

2018 ◽  
Author(s):  
Tingzhen Sun ◽  
Qian Liu ◽  
Nan Gui ◽  
Xingtuan Yang ◽  
Jiyuan Tu ◽  
...  
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Bubble Growth ◽  
Growth Stage ◽  
Numerical Study ◽  
Flow Boiling ◽  
Empirical Relation ◽  
Contact Angles ◽  
Equivalent Diameter ◽  
Two Stages

The influence of contact angle on bubble growth and detachment is investigated in this paper. The phase-change Lattice Boltzmann Method (LBM) which includes a SRT pseudo-potential LB model and a thermal LB model is used to simulate the flow boiling in vertical tube. To verify the correctness of the model, the coexistence curve obtained from the LBM simulations is compared to the analytical one. Then the relation between the diameter of bubble detachment and the wall superheat is compared with the empirical relation. The effect of contact angle on the bubble growth is investigated. The bubble growth with different contact angles is calculated. The bubble growth processes with different contact angles and the detached shape are shown in this paper. The bubble equivalent diameter and the length of contact line is investigated. The bubble equivalent diameter curve shows that bubble growth can be divided into two stages, initially isothermal growth stage, followed by isobaric growth stage. Bubbles show different characteristics at those two stages. The length of contact line curve shows there is a period of stagnation in the process of bubble growing up. This phenomenon can be explained by the theory of dynamic contact angle.

scholarly journals Salt creeping as a self-amplifying crystallization process

2019 ◽  
Vol 5 (12) ◽  
pp. eaax1853 ◽  
Author(s):  
M. J. Qazi ◽  
H. Salim ◽  
C. A. W. Doorman ◽  
E. Jambon-Puillet ◽  
N. Shahidzadeh
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Experimental Approach ◽  
Crystallization Process ◽  
Three Dimensional ◽  
The Self ◽  
Crystal Network ◽  
Exponential Increase ◽  
Dimensional Crystal ◽  
Critical Contact

Salt creeping is a ubiquitous phenomenon in which crystals precipitate far from an evaporating salt solution boundary, which constitutes a major problem in outdoor electronics, civil engineering, artworks, and agriculture. We report a novel experimental approach that allows to quantitatively describe the creeping mechanism and demonstrate its universality with respect to different salts. We show that there exists a critical contact angle below which salt creeping occurs, provided also the nucleation of multiple crystals is favored. The precipitation of new crystals happens ahead of the contact line by the meniscus that progressively advances over the crystals forming also nanometric precursor films. This enlarges the evaporative area, causing an exponential increase in the crystal mass in time. The self-amplifying process then results in a spectacular three-dimensional crystal network at macroscopic distances from the solution reservoir. These findings also allow us to control the creeping by using crystallization modifiers.

scholarly journals Superhydrophobicity and Contact-Line Issues

MRS Bulletin ◽  
2008 ◽  
Vol 33 (8) ◽  
pp. 747-751 ◽  
Author(s):  
Lichao Gao ◽  
Alexander Y. Fadeev ◽  
Thomas J. McCarthy
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Contact Angle Hysteresis ◽  
Water Repellency ◽  
Contact Angles ◽  
Single Step ◽  
Contact Lines ◽  
Lotus Effect ◽  
Three Phase ◽  
Solid Liquid

AbstractThe wettability of several superhydrophobic surfaces that were prepared recently by simple, mostly single-step methods is described and compared with the wettability of surfaces that are less hydrophobic. We explain why two length scales of topography can be important for controlling the hydrophobicity of some surfaces (the lotus effect). Contact-angle hysteresis (difference between the advancing, θA, and receding, θR, contact angles) is discussed and explained, particularly with regard to its contribution to water repellency. Perfect hydrophobicity (θA/θR = 180°/180°) and a method for distinguishing perfectly hydrophobic surfaces from those that are almost perfectly hydrophobic are described and discussed. The Wenzel and Cassie theories, both of which involve analysis of interfacial (solid/liquid) areas and not contact lines, are criticized. Each of these related topics is addressed from the perspective of the three-phase (solid/liquid/vapor) contact line and its dynamics. The energy barriers for movement of the three-phase contact line from one metastable state to another control contact-angle hysteresis and, thus, water repellency.

scholarly journals Dependency of Contact Angles on Three-Phase Contact Line: A Review

2021 ◽  
Vol 5 (1) ◽  
pp. 8
Author(s):  
H. Yildirim Erbil
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Contact Angle Hysteresis ◽  
Contact Angles ◽  
Contact Radius ◽  
Phase Contact ◽  
Sessile Droplet ◽  
Line Energy ◽  
Three Phase ◽  
Tension Term

The wetted area of a sessile droplet on a practical substrate is limited by the three-phase contact line and characterized by contact angle, contact radius and drop height. Although, contact angles of droplets have been studied for more than two hundred years, there are still some unanswered questions. In the last two decades, it was experimentally proven that the advancing and receding contact angles, and the contact angle hysteresis of rough and chemically heterogeneous surfaces, are determined by interactions of the liquid and the solid at the three-phase contact line alone, and the interfacial area within the contact perimeter is irrelevant. However, confusion and misunderstanding still exist in this field regarding the relationship between contact angle and surface roughness and chemical heterogeneity. An extensive review was published on the debate for the dependence of apparent contact angles on drop contact area or the three-phase contact line in 2014. Following this old review, several new articles were published on the same subject. This article presents a review of the novel articles (mostly published after 2014 to present) on the dependency of contact angles on the three-phase contact line, after a short summary is given for this long-lasting debate. Recently, some improvements have been made; for example, a relationship of the apparent contact angle with the properties of the three-phase line was obtained by replacing the solid–vapor interfacial tension term, γSV, with a string tension term containing the edge energy, γSLV, and curvature of the triple contact line, km, terms. In addition, a novel Gibbsian thermodynamics composite system was developed for a liquid drop resting on a heterogeneous multiphase and also on a homogeneous rough solid substrate at equilibrium conditions, and this approach led to the same conclusions given above. Moreover, some publications on the line energy concept along the three-phase contact line, and on the “modified” Cassie equations were also examined in this review.

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