Wetting of rough surfaces: a homogenization approach

2005 ◽  
Vol 461 (2053) ◽  
pp. 79-97 ◽  
Author(s):  
Giovanni Alberti ◽  
Antonio DeSimone
Keyword(s):  
Contact Angle ◽  
Solid Surface ◽  
Transition Layer ◽  
Variational Formulation ◽  
Variational Approach ◽  
Rough Surfaces ◽  
Vapour Phase ◽  
Homogenization Theory ◽  
Minimal Energy ◽  
Homogenization Approach

The contact angle of a drop in equilibrium on a solid is strongly affected by the roughness of the surface on which it rests. We study the roughness–induced enhancement of the hydrophobic or hydrophilic properties of a solid surface through homogenization theory. By relying on a variational formulation of the problem, we show that the macroscopic contact angle is associated with the solution of two cell problems, giving the minimal energy per unit macroscopic area for a transition layer between the rough solid surface and a liquid or vapour phase. Our results are valid for both chemically heterogeneous and homogeneous surfaces. In the latter case, a very transparent structure emerges from the variational approach: the classical laws of Wenzel and Cassie–Baxter give bounds for the optimal energy, and configurations of minimal energy are those leading to the smallest macroscopic contact angle in the hydrophobic case, to the largest one in the hydrophilic case.

The rose petal effect and the modes of superhydrophobicity

2010 ◽  
Vol 368 (1929) ◽  
pp. 4713-4728 ◽  
Author(s):  
Bharat Bhushan ◽  
Michael Nosonovsky
Keyword(s):  
Contact Angle ◽  
Rough Surface ◽  
Solid Surface ◽  
Tilt Angle ◽  
Rough Surfaces ◽  
Strong Adhesion ◽  
Rose Petal ◽  
The Rose ◽  
Rose Petal Effect ◽  
Active Investigation

The wetting of rough surfaces remains a subject of active investigation by scientists. The contact angle (CA) is a traditional parameter used to characterize the hydrophobicity/philicity of a solid surface. However, it was found recently that high CAs can coexist with strong adhesion between water and a solid surface in the case of the so-called ‘rose petal effect’. Several additional parameters have been proposed to characterize the interaction of water with a rough solid surface, including the CA hysteresis, the ability of water droplets to bounce off a solid surface, the tilt angle needed to initiate the flow of a droplet, and the normal and shear adhesion. It is clear now that wetting is not characterized by a single parameter, since several modes or regimes of wetting of a rough surface can exist, including the Wenzel, Cassie, lotus and petal. Understanding the wetting of rough surfaces is important in order to design non-adhesive surfaces for various applications.

scholarly journals Electric Transverse Emissivity of Sinusoidal Surfaces Determined by a Differential Method: Comparison with Approximation of Geometric Optics

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Taoufik Ghabara
Keyword(s):  
Transition Layer ◽  
Numerical Study ◽  
Rough Surfaces ◽  
Method Comparison ◽  
Electromagnetic Theory ◽  
Differential Method ◽  
Homogenization Theory ◽  
Geometric Optics ◽  
Optical Index ◽  
Validity Limit

We present in this paper a numerical study of the validity limit of the optics geometrical approximation in comparison with a differential method which is established according to rigorous formalisms based on the electromagnetic theory. The precedent studies show that this method is adopted to the study of diffraction by periodic rough surfaces. For periods much larger than the wavelength, the mechanism is analog to what happens in a cavity where a ray is trapped and undergoes a large number of reflections. For gratings with a period much smaller than the wavelength, the roughness essentially behaves as a transition layer with a gradient of the optical index. Such a layer reduces the reflection there by increasing the absorption. The code has been implemented for TE polarization. We determine by the two methods such as differential method and the optics geometrical approximation the emissivity of gold and tungsten cylindrical surfaces with a sinusoidal profile, for a wavelength equal to 0.55 microns. The obtained results for a fixed height of the grating allowed us to delimit the validity domain of the optic geometrical approximation for the treated cases. The emissivity calculated by the differential method and that given on the basis of the homogenization theory are satisfactory when the period is much smaller than the wavelength.

scholarly journals Is contact angle a cause or an effect? – A cautionary tale

2020 ◽  
Vol 146 ◽  
pp. 03004
Author(s):  
Douglas Ruth
Keyword(s):  
Contact Angle ◽  
Solid Surface ◽  
Contact Angles ◽  
Two Dimensions ◽  
Experimental Results ◽  
Flow In Porous Media ◽  
Two Dimensional ◽  
Wide Range ◽  
Fluid Drop ◽  
Surrounding Fluid

The most influential parameter on the behavior of two-component flow in porous media is “wettability”. When wettability is being characterized, the most frequently used parameter is the “contact angle”. When a fluid-drop is placed on a solid surface, in the presence of a second, surrounding fluid, the fluid-fluid surface contacts the solid-surface at an angle that is typically measured through the fluid-drop. If this angle is less than 90°, the fluid in the drop is said to “wet” the surface. If this angle is greater than 90°, the surrounding fluid is said to “wet” the surface. This definition is universally accepted and appears to be scientifically justifiable, at least for a static situation where the solid surface is horizontal. Recently, this concept has been extended to characterize wettability in non-static situations using high-resolution, two-dimensional digital images of multi-component systems. Using simple thought experiments and published experimental results, many of them decades old, it will be demonstrated that contact angles are not primary parameters – their values depend on many other parameters. Using these arguments, it will be demonstrated that contact angles are not the cause of wettability behavior but the effect of wettability behavior and other parameters. The result of this is that the contact angle cannot be used as a primary indicator of wettability except in very restricted situations. Furthermore, it will be demonstrated that even for the simple case of a capillary interface in a vertical tube, attempting to use simply a two-dimensional image to determine the contact angle can result in a wide range of measured values. This observation is consistent with some published experimental results. It follows that contact angles measured in two-dimensions cannot be trusted to provide accurate values and these values should not be used to characterize the wettability of the system.

Influence of solid surface, temperature and concentration on contact angle of water-FeC nanofluid

2021 ◽  
Vol 128 ◽  
pp. 105650
Author(s):  
Angel Huminic ◽  
Gabriela Huminic ◽  
Claudiu Fleaca ◽  
Florian Dumitrache ◽  
Ion Morjan
Keyword(s):  
Contact Angle ◽  
Surface Temperature ◽  
Solid Surface

Contact angle measurement on rough surfaces

2004 ◽  
Vol 274 (2) ◽  
pp. 637-644 ◽  
Author(s):  
Tammar S. Meiron ◽  
Abraham Marmur ◽  
I.Sam Saguy
Keyword(s):  
Contact Angle ◽  
Rough Surfaces ◽  
Contact Angle Measurement ◽  
Angle Measurement

Analysis of Water Adsorption on Chitosan and Its Blends with Hydroxypropylcellulose

e-Polymers ◽  
2007 ◽  
Vol 7 (1) ◽  
Author(s):  
Maria Mucha ◽  
Kazimierz Wańkowicz ◽  
Jacek Balcerzak
Keyword(s):  
Hydrogen Bonds ◽  
Thermodynamic Parameter ◽  
Solid Surface ◽  
Mass Fraction ◽  
Water Adsorption ◽  
Vapour Phase ◽  
Heat Of Adsorption ◽  
Water Molecules ◽  
Monomolecular Layer ◽  
Adsorption Of Water

AbstractChitosan (CH) and hydroxypropylcellulose (HPC) adsorb water easily by hydrogen bonds formed with hydroxyl and amide groups present in their structures. Heat of adsorption is a thermodynamic parameter which is used to estimate the type of adsorbate molecule bond on a solid surface, among the others. Adsorption of water from vapour phase on chitosan, hydroxypropylcellulose and blends of both biopolymers in the form of films were carried out. Isotherms of water adsorption in the samples were described by the GAB equation. Correlations between mass fraction of chitosan in the sample (wf) and the values of GAB coefficients were obtained. From parameter c in the GAB equation mean heat of adsorption of the first monomolecular layer of water molecules E1, and pure molar heat of adsorption q were determined.

Macroscopic Wetting Behavior and a Method for Measuring Contact Angles

1990 ◽  
Vol 112 (3) ◽  
pp. 289-295 ◽  
Author(s):  
K. Katoh ◽  
H. Fujita ◽  
H. Sasaki
Keyword(s):  
Contact Angle ◽  
Solid Surface ◽  
Liquid Surface ◽  
Contact Angles ◽  
Critical Height ◽  
Solid Cone ◽  
Wetting Behavior ◽  
Conventional View ◽  
The Subject ◽  
Thermodynamic Instability

Macroscopic wetting behavior is investigated theoretically from a thermodynamic viewpoint. The axisymmetric liquid meniscus formed under a conical solid surface is chosen as the subject of the theoretical analysis. Using the meniscus configuration obtained by the Laplace equation, the total free energy of the system is calculated. In the case of the half vertical angle of the cone φ = 90 deg (horizontal plate), the system shows thermodynamic instability when the meniscus attaches to the solid surface at the contact angle. This result, unlike the conventional view, agrees well with the practical wetting behavior observed in this study. On the other hand, when 0 deg < φ < 90 deg, the system shows thermodynamic stability at the contact angle. However, when the solid cone is held at a position higher than the critical height from a stationary liquid surface, the system becomes unstable. It is possible to measure the contact angle easily using this unstable phenomenon.

Variational Approach to Beams Resting on Two-Parameter Tensionless Elastic Foundations

2012 ◽  
Vol 79 (2) ◽  
Author(s):  
A. Nobili
Keyword(s):  
Variational Formulation ◽  
Variational Approach ◽  
Multiple Solutions ◽  
Numerical Solutions ◽  
Bernoulli Beam ◽  
Scaling Invariance ◽  
Two Parameters ◽  
Euler Bernoulli Beam ◽  
Two Parameter ◽  
Nonlinear Nature

This paper presents a Hamiltonian variational formulation to determine the energy minimizing boundary conditions (BCs) of the tensionless contact problem for an Euler–Bernoulli beam resting on either a Pasternak or a Reissner two-parameters foundation. Mathematically, this originates a free-boundary variational problem. It is shown that the BCs setting the contact loci, which are the boundary points of the contact interval, are always given by second order homogeneous forms in the displacement and its derivatives. This stands for the nonlinear nature of the problem and calls for multiple solutions in the displacement, together with the classical result of multiple solutions in the contact loci position. In particular, it is shown that the Pasternak soil possesses an extra solution other than Kerr’s, although it is proved that such solution must be ruled out owing to interpenetration. The homogeneous character of the BCs explains the well-known load scaling invariance of the contact loci position. It is further shown that the Reissner foundation may be given two mechanical interpretations, which lead to different BCs. Comparison with the established literature is drawn and numerical solutions shown which confirm the energy minimizing nature of the assessed BCs.

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