Planar equilibrium shapes of a liquid drop on a membrane

Soft Matter ◽  
2015 ◽  
Vol 11 (46) ◽  
pp. 8960-8967 ◽  
Author(s):  
Chung-Yuen Hui ◽  
Anand Jagota
Keyword(s):  
Liquid Drop ◽  
Equilibrium Shape ◽  
Rigid Surface ◽  
Equilibrium Shapes ◽  
Young's Equation ◽  
Planar Equilibrium

The equilibrium shape of a small liquid drop on a smooth rigid surface is governed by the minimization of energy with respect to the change in configuration, represented by the well-known Young's equation.

scholarly journals Droplet impacts onto soft solids entrap more air

Soft Matter ◽  
2020 ◽  
Vol 16 (24) ◽  
pp. 5702-5710
Author(s):  
Kenneth R. Langley ◽  
Alfonso A. Castrejón-Pita ◽  
Sigurdur T. Thoroddsen
Keyword(s):  
Liquid Drop ◽  
Rigid Surface ◽  
Soft Solids ◽  
Droplet Impacts

A liquid drop impacting onto a soft solid will entrap more air in the central air disc than an equivalent drop impacting onto a rigid surface.

Two methods of deriving the equilibrium shapes of a liquid drop nucleus

1962 ◽  
Vol 25 (4) ◽  
pp. 817-837 ◽  
Author(s):  
S. Gallone ◽  
G. Ghilardotti
Keyword(s):  
Liquid Drop ◽  
Equilibrium Shapes

scholarly journals Numerical Studies on the Design of Self-Resetting Active Bistable Cross-Shaped Structure for Morphing Applications

Proceedings ◽  
2020 ◽  
Vol 64 (1) ◽  
pp. 16
Author(s):  
P. M. Anilkumar ◽  
A. Haldar ◽  
S. Scheffler ◽  
B. N. Rao ◽  
R. Rolfes
Keyword(s):  
Stable Equilibrium ◽  
Fibre Composite ◽  
Equilibrium Shape ◽  
Middle Portion ◽  
Stable Equilibrium State ◽  
Control Effort ◽  
Unsymmetric Laminates ◽  
Numerical Studies ◽  
Finite Element Package ◽  
Equilibrium Shapes

Multistable structures that possess more than one elastically stable equilibrium state are highly attractive for advanced shape-changing (morphing) applications due to the nominal control effort required to maintain the structure in any of its specific stable shapes. The aim of the paper is to develop a bistable cross-shaped structure consisting of symmetric and unsymmetric laminate actuated using Macro Fibre Composite (MFC) actuators. The critical snap-through voltages required to change the shapes are investigated in a commercially available finite element package. The use of MFC actuators to snap the bistable laminate from one equilibrium shape to another and back again (self-resetting) is demonstrated. A new cross-shaped design of active bistable laminate with MFC actuators is proposed where the cross-shape consist of four rectangles on the four legs and a square on the middle portion. All the rectangles are made up of unsymmetric laminates, and the central portion is designed with a symmetric laminate. MFC actuators are bonded on both sides of the four legs to trigger snap-through and snap-back actions. An attempt is made to address the possible design difficulties arising from the additional stiffness contribution by MFC layers on the naturally cured equilibrium shapes of cross-shaped bistable laminates.

Size-Dependent Equilibrium Shapes of Solid Pb Inclusions in Al

1997 ◽  
Vol 3 (S2) ◽  
pp. 629-630
Author(s):  
U. Dahmen ◽  
E. Johnson ◽  
S.Q. Xiao ◽  
S. Paciornik ◽  
A. Johansen
Keyword(s):  
Size Dependence ◽  
Equilibrium Shape ◽  
Alloy System ◽  
Lattice Parameter ◽  
Al Alloys ◽  
Size Dependent ◽  
Interfacial Energies ◽  
Relative Extent ◽  
Equilibrium Shapes ◽  
Melting And Solidification

Small Pb inclusions in Al have been studied by a number of investigators because the alloy system offers the possibility of observing the processes of melting and solidification directly. Both solids are fee, and the mutual solubility of solid Pb and Al is negligible. Despite a large difference in lattice parameter, it has been found that inclusions follow a parallel-cube orientation relationship and their equilibrium shape is a cuboctahedron, bounded by ﹛111﹜ and ﹛100﹜ facets [1]. Following Herring, the relative extent of the two types of facet directly indicates a ratio of interfacial energies γl00/γ111- However, recent investigations have shown that for inclusions in the range of a few to a few tens of nanometers the equilibrium shape becomes a function of size [2].In the present work, this size dependence of the equilibrium shape has been investigated further. Al alloys with about lat.% Pb were prepared by rapid solidification or by ion implantation, and equilibrated by annealing at about 300°C.

Shape training of Ge precipitates in an Al-1.8at% Ge alloy

1994 ◽  
Vol 52 ◽  
pp. 690-691
Author(s):  
S. Hinderberger ◽  
S. Q. Xiao ◽  
K. H. Westmacott ◽  
U. Dahmen
Keyword(s):  
Room Temperature ◽  
Equilibrium Shape ◽  
Bulk Sample ◽  
Temperature Cycling ◽  
Orientation Relationships ◽  
Rich Variety ◽  
Direct Observations ◽  
Equilibrium Shapes ◽  
Ice Water

Ge precipitates in Al are known to form in a rich variety of shapes and orientation relationships. In this work it is shown that initial non-equilibrium shapes such as plates, laths, needles and tetrahedra can be induced to change to the equilibrium shape of an octahedron by proper temperature cycling. Analysis of this effect in bulk samples was complemented by direct observations of its mechanisms during in-situ temperature cycling.A bulk sample of an Al-1.8at%Ge alloy was solid solution annealed at 420°C for 2h, quenched in ice water, pre-aged at room temperature for 72h and then annealed for 5h at 250°C. Subsequently, part of the sample was repeatedly cycled between 250°C and 360°C. TEM specimens were prepared from both the cycled and non-cycled bulk sample by conventional electropolishing and examined in a JEOL 200CX electron microscope. The in-situ temperature cycling was carried out in a Kratos 1.5 MeV HVEM equipped with a double tilt heating stage.

EQUILIBRIUM CONFIGURATIONS OF ADHERING TUBULAR VESICLES UNDER EXTERNAL LOADS

2006 ◽  
Vol 20 (10) ◽  
pp. 1201-1210
Author(s):  
DONG NI ◽  
HUIJI SHI ◽  
YAJUN YIN
Keyword(s):  
Theoretical Model ◽  
Boundary Conditions ◽  
External Force ◽  
Equilibrium Shape ◽  
Lipid Vesicles ◽  
Equilibrium Configurations ◽  
Applied Forces ◽  
Equilibrium Shapes ◽  
External Loads

A theoretical model is developed to describe the influence of external loads on the equilibrium shapes of adhering tubular lipid vesicles. In the case of nonspecific adhesion, the equilibrium shape equations and boundary conditions are derived through the method analogous to previous research. For a range of applied forces, locally stable bound shapes are simulated. Along with the increase or decrease the external force, the process for adhering vesicle disengaging from or sprawling to the substrate is predicted and analyzed.

Equilibrium Shapes of Small Strained Islands

1995 ◽  
Vol 399 ◽  
Author(s):  
Brian J. Spencer ◽  
J. Tersoff
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Chemical Potential ◽  
Equilibrium Shape ◽  
Two Dimensional ◽  
Asymptotic Results ◽  
Island Size ◽  
Equilibrium Shapes ◽  
Equilibrium Morphology

ABSTRACTWe calculate the equilibrium morphology of a strained layer, for the case where it wets the substrate (Stranski-Krastonow growth). Assuming isotropic surface energy and equal elastic constants in the film and substrate, we are able to calculate two-dimensional equilibrium shapes as a function of the island size and spacing. We present asymptotic results for the equilibrium shape of a thin island where the island height is much smaller than the island width. We also present numerical results of the full equations to describe the island shape when the islands are widely separated. From these solutions we are able to determine the chemical potential of the island as a function of island volume and the strain energy density along the surface of the island for small to medium-sized islands.

EQUILIBRIUM SHAPES FOR ISOTROPIC ELASTIC TUBES IN THE PLANAR CASE

2013 ◽  
Vol 27 (12) ◽  
pp. 1350083
Author(s):  
QING-HUA XU ◽  
XIAO-HUA ZHOU ◽  
YUAN-SHENG LIU ◽  
KE-JIAN WU ◽  
JUN WEN
Keyword(s):  
Blood Vessels ◽  
Varicose Vein ◽  
Equilibrium Shape ◽  
Elastic Shell ◽  
Elastic Tube ◽  
Elastic Behavior ◽  
Bending Energy ◽  
Planar Case ◽  
Elastic Tubes ◽  
Equilibrium Shapes

When making an isotropic elastic shell into a curving tube, the crimp energy and bending energy determine the equilibrium shapes of the tube. In this study, we established a model to explore the elastic behavior of a tube made of an elastic shell. Two typical shapes: torus shape and periodic shape are discussed by studying the equilibrium shape equations in the planar case. Our study reveals that the crimp energy for an isotropic elastic tube is innegligible and will induce abundant shapes. It also reveals that varicose vein is more likely to occur when the blood vessels become thicker, which is in accordance with the clinic experiments.

Equilibrium Shapes for Grain Boundaries and Surfaces with Anisotropic Surface Tension Functions

1983 ◽  
Vol 21 ◽  
Author(s):  
J.E. Taylor
Keyword(s):  
Surface Tension ◽  
Grain Boundaries ◽  
Equilibrium Shape ◽  
Mathematical Problem ◽  
Extreme Case ◽  
Wulff Shape ◽  
Surface Phenomena ◽  
Anisotropic Surface ◽  
Equilibrium Configurations ◽  
Equilibrium Shapes

ABSTRACTThe geometric configuration of grain boundaries and surfaces seems to play a significant role in phase transformations and surface phenomena. Determining the equilibrium configurations of such boundaries for a given surface tension function γ is additionally an interesting mathematical problem; it reduces in the case of isotropic surface tension to the minimal surface problem. A framework is given here for determining such configurations in the other extreme case, where the equilibrium shape of a crystal of fixed volume (the Wulff shape) is a polyhedron. Some results obtained within this framework are outlined.

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