scholarly journals A conservative saint-venant type model to describe the dynamics of thin partially wetting films with regularized forces at the contact line

2020 ◽  
Vol 69 ◽  
pp. 79-103
Author(s):  
Pierre Trontin ◽  
Julien Lallement ◽  
Philippe Villedieu
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Driving Forces ◽  
Mesh Size ◽  
Capillary Forces ◽  
Liquid Films ◽  
Industrial Applications ◽  
Type Model ◽  
Finite Volume Scheme ◽  
Mesh Resolution

This paper deals with the numerical simulation of thin liquid films flowing on partially wetting solid substrates. A 2D Saint-Venant like model is proposed. Its originality lies in the conservative formulation of the capillary forces and in the model used for the disjoining pressure that accounts for the contact line capillary forces. A finite volume scheme is proposed for the resolution of the system and various numerical examples are presented and discussed. In particular, when the mesh resolution is fine enough, the model is proved to be able to predict correctly the spreading of a film with the exact contact angle in the vicinity of the contact line. When the mesh size is larger than the film thickness (which could be the case for many industrial applications), it is of course no longer possible to recover the contact angle. However, the model is proved to correctly predict the spreading of the film. This important feature is related to the thermodynamic consistency of the model in the sense that the latter ensures by construction the decrease of the film total free energy in the absence of external driving forces.

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.

Sculpting and Aerosolizing Pinned Liquid Films With Localized Acoustic Pressures of Surface Acoustic Waves

2012 ◽  
Author(s):  
Daniel Taller ◽  
Hsueh-Chia Chang ◽  
David B. Go
Keyword(s):  
Contact Angle ◽  
Numerical Modeling ◽  
Contact Line ◽  
Acoustic Waves ◽  
Acoustic Pressure ◽  
Surface Acoustic Waves ◽  
Liquid Films ◽  
Solid Substrate ◽  
Planar Surface ◽  
Bulk Film

Due to viscous decay, a planar surface acoustic wave (SAW) diffracting from a solid substrate into a liquid film produces a time-averaged, exponentially decaying acoustic pressure in the film. We show that if the film is pinned against a bounding wall, the localized acoustic pressure generates a sequence of surface drops at the contact line, whose dimensions decay in the same exponential manner as the localized acoustic pressure. The undulating interfacial profile near the contact line also inherits this exponential decay, such that the averaged contact angle is exponentially small. The bulk film topology and the aerosolization mechanism are hence insensitive to the wettability of the surface but are controlled only by the localized acoustic pressure and the decaying undulations it produces at the contact line. The size distribution of surface drops is collapsed under the exponential scaling that depends only on the SAW decay rate and amplitude. Numerical modeling based on the Young-Laplace equation is used to model the liquid profile and to predict two aerosolization regimes.

Self-Assembly of Monolayers of Submicron Sized Particles on Thin Liquid Films

2013 ◽  
Author(s):  
Shriram Pillapakkam ◽  
N. A. Musunuri ◽  
P. Singh
Keyword(s):  
Electric Field ◽  
Self Assembly ◽  
Uv Light ◽  
Capillary Forces ◽  
Liquid Films ◽  
Thin Liquid Films ◽  
Liquid Interfaces ◽  
Uv Curable ◽  
Particle Monolayer ◽  
Uv Curable Resin

In this paper, we present a technique for freezing monolayers of micron and sub-micron sized particles onto the surface of a flexible thin film after the self-assembly of a particle monolayer on fluid-liquid interfaces has been improved by the process we have developed where an electric field is applied in the direction normal to the interface. Particles smaller than about 10 microns do not self-assemble under the action of lateral capillary forces alone since capillary forces amongst them are small compared to Brownian forces. We have overcome this problem by applying an electric field in the direction normal to the interface which gives rise to dipoledipole and capillary forces which cause the particles to arrange in a triangular pattern. The technique involves assembling the monolayer on the interface between a UV-curable resin and another liquid by applying an electric field, and then curing the resin by applying UV light. The monolayer becomes embedded on the surface of the solidified resin film.

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.

Capillary Forces Described by Effective Contact Angle Distributions via Simulations of the Centrifuge Technique

MRS Advances ◽  
2016 ◽  
Vol 1 (31) ◽  
pp. 2237-2245
Author(s):  
Myles Thomas ◽  
Elizabeth Krenek ◽  
Stephen Beaudoin
Keyword(s):  
Surface Roughness ◽  
Contact Angle ◽  
Smooth Surface ◽  
Adhesion Force ◽  
Capillary Forces ◽  
Angle Distribution ◽  
Particle Adhesion ◽  
Multiple Factors ◽  
Effective Contact ◽  
Condensed Moisture

ABSTRACTUnderstanding particle adhesion is vital to any industry where particulate systems are involved. There are multiple factors that affect the strength of the adhesion force, including the physical properties of the interacting materials and the system conditions. Surface roughness on the particles and the surfaces to which they adhere, including roughness at the nanoscale, is critically important to the adhesion force. The focus of this work is on the capillary force that dominates the adhesion whenever condensed moisture is present. Theoretical capillary forces were calculated for smooth particles adhered to smooth and rough surfaces. Simulations of the classical centrifuge technique used to describe particle adhesion to surfaces were performed based on these forces. A model was developed to describe the adhesion of the particles to the rough surface in terms of the adhesion to a smooth surface and an ‘effective’ contact angle distribution.

Anomalous Contact Angle Hysteresis of a Captive Bubble: Advancing Contact Line Pinning

Langmuir ◽  
2011 ◽  
Vol 27 (11) ◽  
pp. 6890-6896 ◽  
Author(s):  
Siang-Jie Hong ◽  
Feng-Ming Chang ◽  
Tung-He Chou ◽  
Seong Heng Chan ◽  
Yu-Jane Sheng ◽  
...  
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Contact Angle Hysteresis ◽  
Contact Line Pinning

scholarly journals Contact Angle Profiles for Droplets on Omniphilic Surfaces in the Presence of Tangential Forces

2019 ◽  
Vol 3 (4) ◽  
pp. 60 ◽  
Author(s):  
Kostoglou ◽  
Karapantsios
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Theoretical Perspective ◽  
Three Dimensional ◽  
Real Life ◽  
Suggested Approach ◽  
Droplet Shape ◽  
Tangential Forces ◽  
Contact Line Motion ◽  
Static Conditions

In real life, sessile droplets usually have a three-dimensional shape, making it difficult to understand their forced wetting behavior, both from an experimental and a theoretical perspective. Even in the case of spreading under quasi-static conditions, where the droplet shape is described by the Young–Laplace equation, there is no fundamental approach to describe the contact line evolution. In the present work, a few existing approaches on this issue are analyzed and assessed. It is shown that an experimentally inspired fixed shape for the contact line of droplets that are spreading under the action of tangential forces can be considered equivalent to a theory for contact line motion. There is a lack of experimental data for contact line evolution under arbitrary scenarios of forces. Such data will be very helpful for the further development of the suggested approach to contact line motion. Of particular interest is the case of small contact angle droplets, for which a top view can clearly indicate the contact line location. On the contrary, in such droplets, the direct experimental measurement of contact angle profile is very difficult. This must be estimated theoretically; thus, a special approach has been developed here for this purpose.

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.

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