On the Shear Modulus of Two-Dimensional Liquid Foams: A Theoretical Study of the Effect of Geometrical Disorder

2006 ◽  
Vol 74 (3) ◽  
pp. 560-567 ◽  
Author(s):  
N. P. Kruyt
Keyword(s):  
Surface Tension ◽  
Shear Modulus ◽  
Theoretical Study ◽  
Two Dimensional ◽  
Liquid Content ◽  
Geometrical Characteristics ◽  
Liquid Foams ◽  
Theoretical Predictions ◽  
Nonaffine Deformation

The shear modulus of two-dimensional liquid foams in the dry limit of low liquid content has been studied theoretically. The focus is on the effect of geometrical disorder on the shear modulus (besides the influence of surface tension). Various theoretical predictions are formulated that are all based on the assumptions of isotropic geometrical characteristics, incompressible bubbles, and negligible edge curvature. Three of these predictions are based on a transformation of Princen’s theory that is strictly valid only for regular hexagonal bubbles. Another prediction takes into account variations in bubble areas by considering the foam as consisting of approximately regular hexagonal bubbles with varying areas. Two other predictions are solely based on the characteristics of the bubble edges. The first of these is based on the assumption of affine movement of bubble vertices, while the second accounts for nonaffine deformation by considering the interaction with neighboring edges. The theoretical predictions for the shear modulus are compared with the result from a single foam simulation. For the single simulation considered, all predictions, except that based on affine movement of bubble vertices, are close to the value obtained from this simulation.

The effects of surface tension and tube inclination on a two-dimensional rising bubble

1987 ◽  
Vol 184 ◽  
pp. 1-14 ◽  
Author(s):  
Benoit Couët ◽  
Gary S. Strumolo
Keyword(s):  
Surface Tension ◽  
Froude Number ◽  
Excellent Agreement ◽  
Experimental Results ◽  
Large Bubble ◽  
Continuous Derivative ◽  
Two Dimensional ◽  
Rising Bubble ◽  
Theoretical Predictions ◽  
Bubble Rising

The effects of surface tension σ and tube inclination β on the Froude number Fr of a large bubble rising in a two-dimensional duct is considered. It is found that there exists either one (for small σ and β > 0°) or a set (for any σ and β = 0°) of Fr-values for which the bubble has a continuous derivative at the nose. By selecting either this single Fr (or the maximum of the set), we obtain solutions in excellent agreement with both theoretical predictions and experimental results.

scholarly journals Free surface flow over an obstacle. Theoretical study of the fluvial case

2001 ◽  
Vol 6 (7) ◽  
pp. 413-429 ◽  
Author(s):  
D. Boukari ◽  
R. Djouadi ◽  
D. Teniou
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Implicit Function Theorem ◽  
Theoretical Study ◽  
Free Surface Flow ◽  
Stationary Flow ◽  
Surface Flow ◽  
Existence Theory ◽  
Two Dimensional ◽  
Implicit Function

The two-dimensional stationary flow of a fluid over an obstacle lying on the bottom of a stream is discussed. We take into account the gravity and we neglect the effects of the surface tension. An existence theory for the solution of this problem is established by the implicit function theorem, for small obstacles and Froude numbers in an interval included in]0,1[.

Polymers on a Random Liquid Surface

1989 ◽  
Vol 177 ◽  
Author(s):  
Bertrand Duplantier
Keyword(s):  
Surface Tension ◽  
Critical Exponents ◽  
Degrees Of Freedom ◽  
Liquid Membrane ◽  
Theoretical Study ◽  
Liquid Surface ◽  
Experimental Studies ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Universal Values

ABSTRACTWe report a recent theoretical study of polymers moving on a random two-dimensional fluid surface. The metric of the liquid membrane is free to fluctuate and these new degrees of freedom couple to those of the polymers - as a result, the critical exponents describing the polymers are changed, but are nevertheless related to those in two dimensions. The relation to possible experimental studies on membranes with vanishing surface tension, which should search for new universal values of exponents u and 7, is discussed.

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

Fluctuations and Shear Modulus of a Classical Two-Dimensional Electron Solid: Experiment

1982 ◽  
Vol 49 (3) ◽  
pp. 212-215 ◽  
Author(s):  
F. Gallet ◽  
G. Deville ◽  
A. Valdès ◽  
F. I. B. Williams
Keyword(s):  
Shear Modulus ◽  
Two Dimensional ◽  
Dimensional Electron

Interactions between steady and oscillatory convection in mushy layers

2010 ◽  
Vol 645 ◽  
pp. 411-434 ◽  
Author(s):  
PETER GUBA ◽  
M. GRAE WORSTER
Keyword(s):  
Standing Waves ◽  
Mushy Layer ◽  
Two Dimensional ◽  
Oscillatory Convection ◽  
Mushy Layers ◽  
Theoretical Predictions ◽  
Convection Patterns ◽  
The Stability ◽  
Nonlinear Solutions ◽  
Steady Convection

We study nonlinear, two-dimensional convection in a mushy layer during solidification of a binary mixture. We consider a particular limit in which the onset of oscillatory convection just precedes the onset of steady overturning convection, at a prescribed aspect ratio of convection patterns. This asymptotic limit allows us to determine nonlinear solutions analytically. The results provide a complete description of the stability of and transitions between steady and oscillatory convection as functions of the Rayleigh number and the compositional ratio. Of particular focus are the effects of the basic-state asymmetries and non-uniformity in the permeability of the mushy layer, which give rise to abrupt (hysteretic) transitions in the system. We find that the transition between travelling and standing waves, as well as that between standing waves and steady convection, can be hysteretic. The relevance of our theoretical predictions to recent experiments on directionally solidifying mushy layers is also discussed.

scholarly journals Shear modulus of two-dimensional colloidal crystals

2002 ◽  
Vol 57 (2) ◽  
pp. 219-225 ◽  
Author(s):  
A Wille ◽  
F Valmont ◽  
K Zahn ◽  
G Maret
Keyword(s):  
Shear Modulus ◽  
Colloidal Crystals ◽  
Two Dimensional
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