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.

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.

The nucleation of cavities at grain boundaries

1987 ◽  
Vol 45 ◽  
pp. 288-291
Author(s):  
P. J. Goodhew
Keyword(s):  
Surface Tension ◽  
Surface Energy ◽  
Grain Boundaries ◽  
Radiation Damage ◽  
Impurity Concentration ◽  
Driving Force ◽  
Nucleation And Growth ◽  
Phase Boundaries ◽  
Cavity Nucleation ◽  
Spherical Bubble

Cavity nucleation and growth at grain and phase boundaries is of concern because it can lead to failure during creep and can lead to embrittlement as a result of radiation damage. Two major types of cavity are usually distinguished: The term bubble is applied to a cavity which contains gas at a pressure which is at least sufficient to support the surface tension (2g/r for a spherical bubble of radius r and surface energy g). The term void is generally applied to any cavity which contains less gas than this, but is not necessarily empty of gas. A void would therefore tend to shrink in the absence of any imposed driving force for growth, whereas a bubble would be stable or would tend to grow. It is widely considered that cavity nucleation always requires the presence of one or more gas atoms. However since it is extremely difficult to prepare experimental materials with a gas impurity concentration lower than their eventual cavity concentration there is little to be gained by debating this point.

The stability of pendent liquid drops. Part 2. Axial symmetry

1974 ◽  
Vol 63 (3) ◽  
pp. 487-508 ◽  
Author(s):  
E. Pitts
Keyword(s):  
Surface Tension ◽  
Energy Change ◽  
Maximum Volume ◽  
Experimental Conditions ◽  
Liquid Drops ◽  
Stable Equilibria ◽  
Equilibrium Shapes ◽  
The Stability ◽  
The Many ◽  
Horizontal Support

In a drop of liquid which hangs below a horizontal support or a t the end of a tube, the forces due to surface tension, pressure and gravity are in equilibrium. Amongst the many possible equilibrium shapes of the drop, only those which are stable occur naturally. The calculus of variations has been used to determine theoretically the stable equilibria, by calculating the energy change when the liquid in equilibrium experiences axially symmetrical perturbations under physically realistic constraints. If the energy change can be made negative, the drop is unstable. With this criterion, stable equilibria have been identified through which the naturally growing drops evolve until they reach a maximum volume, when they become unstable. These results are illustrated by calculations relating to typical experimental conditions.

Embryonic tissues are viscoelastic materials

2000 ◽  
Vol 78 (3) ◽  
pp. 243-251 ◽  
Author(s):  
D A Beysens ◽  
G Forgacs ◽  
J A Glazier
Keyword(s):  
Surface Tension ◽  
Metastatic Potential ◽  
Relevant Information ◽  
Specific Cell ◽  
Biologically Relevant ◽  
Embryonic Tissues ◽  
Differential Adhesion ◽  
Equilibrium Configurations ◽  
Experimental Findings ◽  
Differential Adhesion Hypothesis

Early embryonic development is characterized by spectacular morphogenetic processes such as sorting or spreading of tissues. Analogy between viscoelastic fluids and certain properties of embryonic tissues turned out to be useful in interpreting some aspects of these morphogenetic phenomena. In accordance with the differential adhesion hypothesis, the values of tissue-specific surface tensions have been shown to be consistent with the equilibrium configurations such tissues reach in the course of sorting and spreading. A method to measure tissue surface tension and viscoelastic properties is described. Notions like the Laplace's equation relating surface tension to radii of curvature, or the Kelvin model of viscoelasticity are used to analyze the results of these measurements. The fluid analogy is extended to time-dependent phenomena, in particular, to the analysis of cellular pattern evolution in the course of spreading. On the basis of recent experimental findings, we demonstrate that the kinetics of spreading and nucleation in binary fluids can be analyzed using the same formalism. We illustrate how our results can be used to obtain biologically relevant information on the strength of binding between specific cell adhesion molecules under near physiological conditions. We also suggest a diagnostic application of our method to monitor the metastatic potential of tumors. PACS No.: 03.65Ge

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