Critical contact angles for liquid drops on inclined surfaces

2004 ◽  
pp. 57-62
Author(s):  
A. I. ElSherbini ◽  
A. M. Jacobi
Keyword(s):  
Contact Angles ◽  
Liquid Drops ◽  
Inclined Surfaces ◽  
Critical Contact

Numerical Modeling of Liquid Drop Spreading Behavior on Inclined Surfaces

2009 ◽  
Author(s):  
Young-Gil Park ◽  
Anthony M. Jacobi
Keyword(s):  
Solid Surface ◽  
Liquid Drop ◽  
Numerical Study ◽  
Contact Angle Hysteresis ◽  
Contact Angles ◽  
Quasi Equilibrium ◽  
Liquid Drops ◽  
Spreading Behavior ◽  
Inclined Surfaces ◽  
Liquid Vapor

A numerical study was conducted on the spreading behavior of liquid drops on flat solid surfaces. The model predicts the shape of liquid-vapor interface under static equilibrium using an unstructured surface grid composed of triangular elements. Incremental movement of base contour, i.e. solid-liquid-vapor contact line, is also captured such that the constrained boundary conditions, i.e. advancing and receding contact angles, can be satisfied. The numerical model is applied to a common experiment that studies the behavior of liquid drops on inclined surfaces, where the shape of the drops change in response to an alteration of total volume or gravitational direction. On a heterogeneous surface that has contact angle hysteresis, the shape of the base contour on the solid surface is not determined uniquely but rather dependent upon history. This study demonstrates such dependence by comparing the spreading of a liquid drop on a solid surface with different quasi-equilibrium paths.

Simulation Analysis of Contact Angles and Retention Forces of Liquid Drops on Inclined Surfaces

Langmuir ◽  
2012 ◽  
Vol 28 (32) ◽  
pp. 11819-11826 ◽  
Author(s):  
M. J. Santos ◽  
S. Velasco ◽  
J. A. White
Keyword(s):  
Simulation Analysis ◽  
Contact Angles ◽  
Liquid Drops ◽  
Inclined Surfaces

The stability of pendent liquid drops. Part 1. Drops formed in a narrow gap

1973 ◽  
Vol 59 (4) ◽  
pp. 753-767 ◽  
Author(s):  
E. Pitts
Keyword(s):  
Contact Angles ◽  
Two Dimensional ◽  
Narrow Gap ◽  
Cross Sectional ◽  
Liquid Drops ◽  
Maximum Area ◽  
Area Increase ◽  
Equilibrium Profiles ◽  
The Stability ◽  
Horizontal Support

We consider a drop of liquid hanging from a horizontal support and sandwiched between two vertical plates separated by a very narrow gap. Equilibrium profiles of such ‘two-dimensional’ drops were calculated by Neumann (1894) for the case when the angle of contact between the liquid and the horizontal support is zero. This paper gives the equilibrium profiles for other contact angles and the criterion for their stability. Neumann showed that, as the drop height increases, its cross-sectional area increases until a maximum is reached. Thereafter, as the height increases, the equilibrium area decreases. This behaviour is shown to be typical of all contact angles. When the maximum area is reached, the total energy is a minimum. It is shown that the drops are stable as long as the height and the area increase together.

The surface energies of cation substituted Laponite

Clay Minerals ◽  
1993 ◽  
Vol 28 (1) ◽  
pp. 1-11 ◽  
Author(s):  
J. Norris ◽  
R. F. Giese ◽  
P. M. Costanzo ◽  
C. J. van Oss
Keyword(s):  
Divalent Cations ◽  
Contact Angles ◽  
Lewis Base ◽  
Silicate Layer ◽  
Natural Material ◽  
Exchangeable Cation ◽  
Monovalent Cations ◽  
Liquid Drops ◽  
Glass Slides ◽  
Silicate Surface

AbstractLaponite RD forms stable, coherent films which adhere strongly to glass slides. Such films are capable of supporting liquid drops allowing the direct measurement of contact angles for five liquids of which, two were apolar (0:-bromonaphthalene and diiodomethane) and three were polar (water, formamide, glycerol); surface tension components and parameters (γLw, γ⊕ and γ⊖) were determined by solving the Young equation. These determinations were made for homoionic samples saturated with Li, Na, K, Rb, Cs, Mg, Ca, Sr, Ba and NH4 as well as the natural material. Whereas the values of γLw (the apolar Lifshitz-van der Waals component) varied only within narrow limits (41-44 mJ/m2), the Lewis base parameter varied comparatively widely (24-41 mJ/m2). The Lewis acid parameter was small and relatively constant (1·3-3·0 mJ/m2). The variation of γ⊖ as a function of the exchangeable cation suggests that the divalent cations are shielded from the silicate surface by the water molecules of their sphere of hydration, whereas the monovalent cations are in direct contact with the oxygen atoms of the silicate surface. Furthermore, the divalent cations may screen the Lewis base sites to a greater degree than do the monovalent cations. Lithium behaves anomalously and this may indicate that it physically enters into the ditrigonal hole in the silicate layer.

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.

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