‘Effervescent’ atomization in two dimensions

2013 ◽  
Vol 714 ◽  
pp. 361-392 ◽  
Author(s):  
H. Lhuissier ◽  
E. Villermaux
Keyword(s):  
Nucleation Rate ◽  
Model Experiment ◽  
Drop Size ◽  
Surface Concentration ◽  
Two Dimensions ◽  
Air Bubbles ◽  
Two Dimensional ◽  
Atomization Process ◽  
Nucleation Sites ◽  
Size Dispersion

AbstractA planar Savart water sheet uniformly seeded with small air bubbles in a large surface concentration is studied as a model experiment of the so-called ‘effervescent’ atomization process. This two-dimensional setup allows for a quantitative observation of all the steps of the sheet’s disintegration into a collection of disjointed droplets. The bubbles are heterogeneous nucleation sites which puncture the sheet with holes. The dynamics of the opening of holes competes with the simultaneous nucleation rate of new holes in a statistically stationary fashion. The liquid constituting the sheet is then transiently concentrated in a web of ligaments of various lengths and diameters, at the junction between adjacent holes. Their breakup produces the final spray. We provide a complete description of the ligament web statistics when nucleation is synchronous, and we show that the drop size dispersion from the breakup of a single ligament is responsible for the shape of the overall spray drop size distribution.

Modelling of Two-Dimensional Grain Growth and Crystallization

1994 ◽  
Vol 362 ◽  
Author(s):  
William Krakow
Keyword(s):  
Grain Growth ◽  
Nucleation Rate ◽  
Growth Parameters ◽  
Effective Rate ◽  
Growth Conditions ◽  
Two Dimensional ◽  
Zone Size ◽  
Depletion Zone ◽  
Nucleation Sites ◽  
Area Growth

AbstractPC based computer programs have been developed to simulate twodimensional microstructural grain growth either by nucleation or transformation from an amorphous phase. By controlling the parameters of the rate of grain growth, nucleation rate, depletion zone size, and changes in these latter two variables most grain growth conditions can be achieved in practice. Several cases have been explored which include: constant nucleation rates, both increasing and decreasing rates, and the instantaneous saturation of nucleation sites. The evolution of domain sizes can be investigated which is dependent on the effective rate of nucleation during various stages of grain growth. Real time graphics displays are present the instantaneous growth parameters and their changes as well as information on fractional area growth.

Urbanicity, City Delegations, and Two-Dimensional Liberalism

2018 ◽  
Author(s):  
Thomas K. Ogorzalek
Keyword(s):  
National Level ◽  
Two Dimensions ◽  
Political Order ◽  
Two Dimensional ◽  
Local Institutions ◽  
Horizontal Integration ◽  
National Politics ◽  
United Front ◽  
Strategies For Success

This theoretical chapter develops the argument that the conditions of cities—large, densely populated, heterogeneous communities—generate distinctive governance demands supporting (1) market interventions and (2) group pluralism. Together, these positions constitute the two dimensions of progressive liberalism. Because of the nature of federalism, such policies are often best pursued at higher levels of government, which means that cities must present a united front in support of city-friendly politics. Such unity is far from assured on the national level, however, because of deep divisions between and within cities that undermine cohesive representation. Strategies for success are enhanced by local institutions of horizontal integration developed to address the governance demands of urbanicity, the effects of which are felt both locally and nationally in the development of cohesive city delegations and a unified urban political order capable of contending with other interests and geographical constituencies in national politics.

scholarly journals Interface Roughening in Two Dimensions

2021 ◽  
Vol 182 (3) ◽  
Author(s):  
Gernot Münster ◽  
Manuel Cañizares Guerrero
Keyword(s):  
Field Theory ◽  
Monte Carlo ◽  
Capillary Wave ◽  
System Size ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Wave Approximation ◽  
Statistical Field ◽  
Statistical Field Theory ◽  
Interface Roughening

AbstractRoughening of interfaces implies the divergence of the interface width w with the system size L. For two-dimensional systems the divergence of $$w^2$$ w 2 is linear in L. In the framework of a detailed capillary wave approximation and of statistical field theory we derive an expression for the asymptotic behaviour of $$w^2$$ w 2 , which differs from results in the literature. It is confirmed by Monte Carlo simulations.

scholarly journals Is contact angle a cause or an effect? – A cautionary tale

2020 ◽  
Vol 146 ◽  
pp. 03004
Author(s):  
Douglas Ruth
Keyword(s):  
Contact Angle ◽  
Solid Surface ◽  
Contact Angles ◽  
Two Dimensions ◽  
Experimental Results ◽  
Flow In Porous Media ◽  
Two Dimensional ◽  
Wide Range ◽  
Fluid Drop ◽  
Surrounding Fluid

The most influential parameter on the behavior of two-component flow in porous media is “wettability”. When wettability is being characterized, the most frequently used parameter is the “contact angle”. When a fluid-drop is placed on a solid surface, in the presence of a second, surrounding fluid, the fluid-fluid surface contacts the solid-surface at an angle that is typically measured through the fluid-drop. If this angle is less than 90°, the fluid in the drop is said to “wet” the surface. If this angle is greater than 90°, the surrounding fluid is said to “wet” the surface. This definition is universally accepted and appears to be scientifically justifiable, at least for a static situation where the solid surface is horizontal. Recently, this concept has been extended to characterize wettability in non-static situations using high-resolution, two-dimensional digital images of multi-component systems. Using simple thought experiments and published experimental results, many of them decades old, it will be demonstrated that contact angles are not primary parameters – their values depend on many other parameters. Using these arguments, it will be demonstrated that contact angles are not the cause of wettability behavior but the effect of wettability behavior and other parameters. The result of this is that the contact angle cannot be used as a primary indicator of wettability except in very restricted situations. Furthermore, it will be demonstrated that even for the simple case of a capillary interface in a vertical tube, attempting to use simply a two-dimensional image to determine the contact angle can result in a wide range of measured values. This observation is consistent with some published experimental results. It follows that contact angles measured in two-dimensions cannot be trusted to provide accurate values and these values should not be used to characterize the wettability of the system.

scholarly journals Calderón problem for Maxwell's equations in two dimensions

2016 ◽  
Vol 24 (3) ◽  
Author(s):  
Oleg Y. Imanuvilov ◽  
Masahiro Yamamoto
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell Equations ◽  
Maxwell's Equations ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Global Uniqueness ◽  
Calderón Problem ◽  
Dirichlet To Neumann Map

AbstractWe prove the global uniqueness in determination of the conductivity, the permeability and the permittivity of the two-dimensional Maxwell equations by the partial Dirichlet-to-Neumann map limited to an arbitrary subboundary.

Estimates of critical percolation probabilities for a set of two-dimensional lattices

1972 ◽  
Vol 71 (1) ◽  
pp. 97-106 ◽  
Author(s):  
D. G. Neal
Keyword(s):  
Monte Carlo ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Critical Percolation ◽  
Site Percolation

AbstractThis paper describes new detailed Monte Carlo investigations into bond and site percolation problems on the set of eleven regular and semi-regular (Archimedean) lattices in two dimensions.

Asymptotic analysis of some two-dimensional diffusion problems

1995 ◽  
Vol 448 (1933) ◽  
pp. 213-236 ◽  
Keyword(s):  
Linear Problem ◽  
Vacancy Concentration ◽  
Surface Concentration ◽  
Two Dimensional ◽  
Surface Source ◽  
Dimensional Diffusion ◽  
Equilibrium Vacancy ◽  
Equilibrium Vacancy Concentration ◽  
Dimensional Surface ◽  
Diffusion Problems

In this paper we discuss two-dimensional surface source and implant problems for a substitutional-interstitial diffusion model. We present asymptotic solutions in the limit of the surface concentration of impurity (or peak concentration of the implant) being far greater than the equilibrium vacancy concentration. Using leading order composite solutions we plot contours of constant impurity concentration. Some of these contours differ markedly from those of the corresponding linear problem, having the ‘bird’s beak’ shape which is frequently observed in experiments. We also discuss a two-dimensional surface source problem for a va­cancy model.

Crystal to Glass Transition and Melting in Two Dimensions

1993 ◽  
Vol 321 ◽  
Author(s):  
M. Li ◽  
W. L. Johnson ◽  
W. A. Goddard
Keyword(s):  
Glass Transition ◽  
Intermediate Phase ◽  
Orientational Order ◽  
Finite Size ◽  
Two Dimensions ◽  
Size Difference ◽  
Two Dimensional ◽  
Atomic Size ◽  
Bond Orientational Order ◽  
Dynamics Simulations

ABSTRACTThermodynamic properties, structures, defects and their configurations of a two-dimensional Lennard-Jones (LJ) system are investigated close to crystal to glass transition (CGT) via molecular dynamics simulations. The CGT is achieved by saturating the LJ binary arrays below glass transition temperature with one type of the atoms which has different atomic size from that of the host atoms. It was found that for a given atomic size difference larger than a critical value, the CGT proceeds with increasing solute concentrations in three stages, each of which is characterized by distinct behaviors of translational and bond-orientational order correlation functions. An intermediate phase which has a quasi-long range orientational order but short range translational order has been found to exist prior to the formation of the amorphous phase. The destabilization of crystallinity is observed to be directly related to defects. We examine these results in the context of two dimensional (2D) melting theory. Finite size effects on these results, in particular on the intermediate phase formation, are discussed.

scholarly journals THE EFFECT OF THE THIRD DIMENSION ON ROUGH SURFACES FORMED BY SEDIMENTING PARTICLES IN QUASI-TWO-DIMENSIONS

2002 ◽  
Vol 16 (08) ◽  
pp. 1217-1223 ◽  
Author(s):  
K. V. MCCLOUD ◽  
M. L. KURNAZ
Keyword(s):  
Two Dimensions ◽  
Scaling Analysis ◽  
Silica Spheres ◽  
Two Dimensional ◽  
One Dimensional ◽  
The Third ◽  
Roughness Exponent ◽  
Third Dimension ◽  
Dimensional Cell ◽  
Roughness Exponents

The roughness exponent of surfaces obtained by dispersing silica spheres into a quasi-two-dimensional cell is examined. The cell consists of two glass plates separated by a gap, which is comparable in size to the diameter of the beads. Previous work has shown that the quasi-one-dimensional surfaces formed have two roughness exponents in two length scales, which have a crossover length about 1 cm. We have studied the effect of changing the gap between the plates to a limit of about twice the diameter of the beads. If the conventional scaling analysis is performed, the roughness exponent is found to be robust against changes in the gap between the plates; however, the possibility that scaling does not hold should be taken seriously.

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