Journal ArticleDOI
The possible equilibrium shapes of static pendant drops.
P. T. Sumesh,Rama Govindarajan +1 more
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TLDR
It is shown analytically that a static pendant two-dimensional drop can never be longer than 3.42 times the capillary length, and there is no limit to the height of multiple-lobed Kelvin drops, but the total volume is finite, with the volume of successive lobes forming a convergent series.Abstract:
Analytical and numerical studies are carried out on the shapes of two-dimensional and axisymmetric pendant drops hanging under gravity from a solid surface. Drop shapes with both pinned and equilibrium contact angles are obtained naturally from a single boundary condition in the analytical energy optimization procedure. The numerical procedure also yields optimum energy shapes, satisfying Young's equation without the explicit imposition of a boundary condition at the plate. It is shown analytically that a static pendant two-dimensional drop can never be longer than 3.42 times the capillary length. A related finding is that a range of existing solutions for long two-dimensional drops correspond to unphysical drop shapes. Therefore, two-dimensional drops of small volume display only one static solution. In contrast, it is known that axisymmetric drops can display multiple solutions for a given volume. We demonstrate numerically that there is no limit to the height of multiple-lobed Kelvin drops, but the total volume is finite, with the volume of successive lobes forming a convergent series. The stability of such drops is in question, though. Drops of small volume can attain large heights. A bifurcation is found within the one-parameter space of Laplacian shapes, with a range of longer drops displaying a minimum in energy in the investigated space. Axisymmetric Kelvin drops exhibit an infinite number of bifurcations.read more
Citations
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Journal ArticleDOI
Stability of a compound sessile drop at the axisymmetric configuration.
TL;DR: Using the Laplace equations, the stability transition is verified for the axisymmetric configuration of compound sessile drops using a pair of fluids in which the density ratio can be tuned nearly independently of the interfacial tensions.
Journal ArticleDOI
Minimum energy shapes of one-side-pinned static drops on inclined surfaces.
TL;DR: On a solid surface capable of sustaining any amount of hysteresis, the global, and hence unique, minimum energy shape as a function of equilibrium contact angle, drop volume, and plate inclination is obtained.
Journal ArticleDOI
Pinning Effects of Wettability Contrast on Pendant Drops on Chemically Patterned Surfaces
TL;DR: The morphology and dynamics of the pendant drops attached to chemically patterned surfaces with different hydrophilic/hydrophobic contrasts were investigated experimentally and numerically and the maximum contact radius was presented as a key parameter for the pattern-pinned drops, which is directly related to the stability and themaximum volume of the drops.
Journal ArticleDOI
Hanging colloidal drop: A new photonic crystal synthesis route
TL;DR: In this paper, high quality photonic crystals (hundreds of micrometres in thickness) were grown by the free evaporation of a colloidal drop consisting of silica and polystyrene nanospheres with dimensions of 300nm, 500nm, and 1000nm.
Journal ArticleDOI
Trapped Liquid Drop at the End of Capillary
TL;DR: The liquid drop captured at the capillary end, which is observed in capillary valve and pendant drop technique, is investigated theoretically and experimentally and four regimes can be identified by three critical drop volumes.
References
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BookDOI
Capillarity and Wetting Phenomena
TL;DR: The first € price and the £ and $ price are net prices, subject to local VAT as discussed by the authors, and prices and other details are subject to change without notice. All errors and omissions excepted.
Book
Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves
TL;DR: Capillarity: Unconstrained Interfaces / Capillarity and gravity / Hysteresis and Elasticity of Triple Lines / Wetting and Long-Range Forces b/ Hydrodynamics of Interfaces -- Thin Films, Waves, and Ripples as discussed by the authors.
Book
The calculus of variations
TL;DR: Van Brunt as discussed by the authors presents an introductory account of the calculus of variations suitable for advanced undergraduate and graduate students of mathematics, physics, or engineering, assuming a course in multivariable calculus and some familiarity with the elements of real analysis and ordinary differential equations.
Journal ArticleDOI
Apparent contact angles on rough surfaces: the Wenzel equation revisited
Gershon Wolansky,Abraham Marmur +1 more
TL;DR: In this paper, it is shown that the Wenzel equation becomes axisymmetric even if the roughness of the solid surface is not, when the drop size becomes infinitely larger than the scale of roughness.