scholarly journals Non-isothermal droplet spreading/dewetting and its reversal

2015 ◽  
Vol 776 ◽  
pp. 74-95 ◽  
Author(s):  
Yi Sui ◽  
Peter D. M. Spelt
Keyword(s):  
Slip Length ◽  
Spreading Rate ◽  
Contact Angles ◽  
Lubrication Theory ◽  
Drop Diameter ◽  
Droplet Spreading ◽  
Spherical Cap ◽  
Drop Shape ◽  
Rate Versus ◽  
O 10

Axisymmetric non-isothermal spreading/dewetting of droplets on a substrate is studied, wherein the surface tension is a function of temperature, resulting in Marangoni stresses. A lubrication theory is first extended to determine the drop shape for spreading/dewetting limited by slip. It is demonstrated that an apparent angle inferred from a fitted spherical cap shape does not relate to the contact-line speed as it would under isothermal conditions. Also, a power law for the thermocapillary spreading rate versus time is derived. Results obtained with direct numerical simulations (DNS), using a slip length down to $O(10^{-4})$ times the drop diameter, confirm predictions from lubrication theory. The DNS results further show that the behaviour predicted by the lubrication theory – that a cold wall promotes spreading, and a hot wall promotes dewetting – is reversed at sufficiently large contact angles and/or viscosity of the surrounding fluid. This behaviour is summarized in a phase diagram, and a simple model that supports this finding is presented. Although the key results are found to be robust when accounting for heat conduction in the substrate, a critical thickness of the substrate is identified above which wall conduction significantly modifies wetting behaviour.

Inertial effects in droplet spreading: a comparison between diffuse-interface and level-set simulations

2007 ◽  
Vol 576 ◽  
pp. 287-296 ◽  
Author(s):  
HANG DING ◽  
PETER D. M. SPELT
Keyword(s):  
Level Set ◽  
Slip Length ◽  
Stress Singularity ◽  
Spreading Rate ◽  
Diffuse Interface ◽  
Universal Relation ◽  
Inertial Effects ◽  
Ohnesorge Number ◽  
Droplet Spreading ◽  
Moving Contact

Axisymmetric droplet spreading is investigated numerically at relatively large rates of spreading, such that inertial effects become important. Results from two numerical methods that use different means to alleviate the stress singularity at moving contact lines (a diffuse interface, and a slip-length-based level-set method) are shown to agree well. An initial inertial regime is observed to yield to a regime associated with Tanner's law at later times. The spreading rate oscillates during the changeover between these regimes. This becomes more significant for a fixed (effective) slip length when decreasing the value of an Ohnesorge number. The initial, inertia-dominated regime is characterized by a rapidly extending region affected by the spreading, giving the appearance of a capillary wave travelling from the contact line. The oscillatory behaviour is associated with the rapid collapse that follows the point at which this region extends to the entire droplet. Results are presented for the apparent contact angle as a function of dimensionless spreading rate for various values of Ohnesorge number, slip length and initial conditions. The results indicate that there is no such universal relation when inertial effects are important.

scholarly journals Validation and modification of asymptotic analysis of slow and rapid droplet spreading by numerical simulation

2013 ◽  
Vol 715 ◽  
pp. 283-313 ◽  
Author(s):  
Yi Sui ◽  
Peter D. M. Spelt
Keyword(s):  
Numerical Simulation ◽  
Asymptotic Analysis ◽  
Contact Line ◽  
Slip Length ◽  
Interface Shape ◽  
Droplet Spreading ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Line Region ◽  
Modified Theory

AbstractUsing a slip-length-based level-set approach with adaptive mesh refinement, we have simulated axisymmetric droplet spreading for a dimensionless slip length down to $O(1{0}^{\ensuremath{-} 4} )$. The main purpose is to validate, and where necessary improve, the asymptotic analysis of Cox (J. Fluid Mech., vol. 357, 1998, pp. 249–278) for rapid droplet spreading/dewetting, in terms of the detailed interface shape in various regions close to the moving contact line and the relation between the apparent angle and the capillary number based on the instantaneous contact-line speed, $\mathit{Ca}$. Before presenting results for inertial spreading, simulation results are compared in detail with the theory of Hocking & Rivers (J. Fluid Mech., vol. 121, 1982, pp. 425–442) for slow spreading, showing that these agree very well (and in detail) for such small slip-length values, although limitations in the theoretically predicted interface shape are identified; a simple extension of the theory to viscous exterior fluids is also proposed and shown to yield similar excellent agreement. For rapid droplet spreading, it is found that, in principle, the theory of Cox can predict accurately the interface shapes in the intermediate viscous sublayer, although the inviscid sublayer can only be well presented when capillary-type waves are outside the contact-line region. However, $O(1)$ parameters taken to be unity by Cox must be specified and terms be corrected to ${\mathit{Ca}}^{+ 1} $ in order to achieve good agreement between the theory and the simulation, both of which are undertaken here. We also find that the apparent angle from numerical simulation, obtained by extrapolating the interface shape from the macro region to the contact line, agrees reasonably well with the modified theory of Cox. A simplified version of the inertial theory is proposed in the limit of negligible viscosity of the external fluid. Building on these results, weinvestigate the flow structure near the contact line, the shear stress and pressure along the wall, and the use of the analysis for droplet impact and rapid dewetting. Finally, we compare the modified theory of Cox with a recent experiment for rapid droplet spreading, the results of which suggest a spreading-velocity-dependent dynamic contact angle in the experiments. The paper is closed with a discussion of the outlook regarding the potential of using the present results in large-scale simulations wherein the contact-line region is not resolved down to the slip length, especially for inertial spreading.

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 $\tilde{b}_{m}$.

Determining Parametric Effects for Droplet Evaporation on Nanoporous Superhydrophillic Surfaces Using Machine Learning Techniques

2021 ◽  
Author(s):  
Emma R. McClure ◽  
Van P. Carey
Keyword(s):  
Machine Learning ◽  
Cooling System ◽  
Spray Cooling ◽  
Droplet Evaporation ◽  
Contact Angles ◽  
Machine Learning Techniques ◽  
Metallic Surfaces ◽  
Droplet Spreading ◽  
Droplet Vaporization ◽  
Speed Accuracy

Abstract Experimental results demonstrate that droplet vaporization on metal surfaces can be significantly enhanced with the application of a nanoporous, superhydrophilic surface coating. A thin layer of ZnO nanopillars can be easily seeded and grown on most metallic surfaces to achieve nanoscale pores between pillars, and ultra-low apparent contact angles. These surface coatings have the potential to improve spray cooling processes, and can be easily scaled up to larger and more complex heat exchangers. In order to characterize the potential improvement to a spray cooling system it is important to understand the dependence on system parameters, and to have a clear model of droplet vaporization on such surfaces. There are a number of surface and impact parameters that will affect the droplet spreading and subsequent vaporization on the surface. The surface contact angle, wicking speed and impact velocity all interact to affect the maximum spread of the droplet and the speed at which the droplet reaches this state. Along with variations in droplet volume and wall superheat, the model for droplet vaporization becomes more complex and nonlinear. Instead of exploring a single parameter at a time, machine learning tools can be utilized to determine the dependence of droplet evaporation time on these parameters simultaneously. In this study a genetic algorithm and a neural network were used to develop a droplet evaporation model for these superhydrophilic surfaces. Each algorithm demonstrated clear advantages depending on whether speed, accuracy, or an explicit mathematical model was prioritized.

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.

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.

scholarly journals Molecular Dynamics Simulation and Measurement of Contact Angle of Water Droplet on a Platinum Surface

2001 ◽  
Author(s):  
Satish G. Kandlikar ◽  
Shigeo Maruyama ◽  
Mark E. Steinke ◽  
Tatsuto Kimura
Keyword(s):  
Molecular Dynamics ◽  
Liquid Droplet ◽  
Contact Region ◽  
Pair Potential ◽  
Heat Bath ◽  
Spreading Rate ◽  
Contact Angles ◽  
Dynamics Simulation ◽  
Platinum Surface ◽  
Receding Contact

Abstract A water liquid droplet in contact with a platinum surface was simulated by the molecular dynamics method. Water molecules were modeled by SPC/E and one layer of harmonic molecules represented the platinum surface with the constant temperature heat bath model using the phantom molecules. Here, the water-platinum pair potential developed by Spohr (1989) based on extended Hückel calculations was employed. In the spreading process of the liquid droplet on the platinum surface, the area of contact region between water and platinum expanded just in proportional to the one-third power of time. This spreading rate was clearly in contrast to the case of Lennard-Jones droplet. The contact angles of water on a platinum surface under saturated conditions are measured. The measurements are made in a vacuum container using de-ionized and degassed water on a clean platinum surface. The equilibrium static, advancing and receding contact angles are measured by changing the orientation of the platinum surface. The droplets of different masses are placed on the horizontal platinum surface. The surface is the inclined to 20, 30 and 40 degrees. The advancing and receding contact angles under these conditions are measured.

Coupled oscillations of deformable spherical-cap droplets. Part 1. Inviscid motions

2013 ◽  
Vol 714 ◽  
pp. 312-335 ◽  
Author(s):  
J. B. Bostwick ◽  
P. H. Steen
Keyword(s):  
Contact Angles ◽  
Solid Support ◽  
Linear Operators ◽  
Harmonic Oscillators ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Spherical Cap ◽  
Spherical Drop ◽  
Coupled Oscillations ◽  
Latitudinal Belt

AbstractA spherical drop is constrained by a solid support arranged as a latitudinal belt. This belt support splits the drop into two deformable spherical caps. The edges of the support are given by lower and upper latitudes yielding a ‘spherical belt’ of prescribed extent and position: a two-parameter family of constraints. This is a belt-constrained Rayleigh drop. In this paper we study the linear oscillations of the two coupled spherical-cap surfaces in the inviscid case, and the viscous case is studied in Part 2 (Bostwick & Steen, J. Fluid Mech., vol. 714, 2013, pp. 336–360), restricting to deformations symmetric about the axis of constraint symmetry. The integro-differential boundary-value problem governing the interface deformation is formulated as a functional eigenvalue problem on linear operators and reduced to a truncated set of algebraic equations using a Rayleigh–Ritz procedure on a constrained function space. This formalism allows mode shapes with different contact angles at the edges of the solid support, as observed in experiment, and readily generalizes to accommodate viscous motions (Part 2). Eigenvalues are mapped in the plane of constraints to reveal where near-multiplicities occur. The full problem is then approximated as two coupled harmonic oscillators by introducing a volume-exchange constraint. The approximation yields eigenvalue crossings and allows post-identification of mass and spring constants for the oscillators.

A laser interferometric study of sessile drop shape and contact angle

1985 ◽  
Vol 63 (8) ◽  
pp. 2339-2340 ◽  
Author(s):  
R. N. O'brien ◽  
Paul Saville
Keyword(s):  
Contact Angle ◽  
Sessile Drop ◽  
Contact Angles ◽  
Glass System ◽  
Drop Shape ◽  
Measured Angle ◽  
Interferometric Study ◽  
Laser Interferometric ◽  
Equal Thickness

Small contact angles, such as water on glass, have been shown to be measurable interferometrically using fringes of equal thickness after the fashion of Newton's rings. The measured angle for the water on glass system was 0.049 ± 0.006 degrees of arc.

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