Publisher’s Note: Minimal Model for Phase Separation under Slow Cooling [Phys. Rev. Lett.<b>98</b>, 115701 (2007)]

Vollmer, J.; Auernhammer, Günter K.; Vollmer, Doris

doi:10.1103/physrevlett.98.139903

Cited by 20 publications

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“…The cell is placed in a computer controlled thermostat, and its temperature is varied smoothly away from the phase coalescence temperature T c , at a rate de-scribed by a variable ξ which has dimensions of inverse time (defined by equation (4) below). Several examples of this type of experiment have been reported: [5][6][7][8][9]. The experiments show similar quantitative results: both layers show a variation in turbidity, which is approximately periodic, with period ∆t.…”

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confidence: 59%

A test-tube model for rainfall

Wilkinson¹

2014

EPL

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If the temperature of a cell containing two partially miscible liquids is changed very slowly, so that the miscibility is decreased, microscopic droplets nucleate, grow and migrate to the interface due to their buoyancy. The system may show an approximately periodic variation of the turbidity of the mixture, as the mean droplet size fluctuates. These precipitation events are analogous to rainfall from warm clouds. This paper considers a theoretical model for these experiments. After nucleation the initial growth is by Ostwald ripening, followed by a finite-time runaway growth of droplet sizes due to larger droplets sweeping up smaller ones. The model predicts that the period ∆t and the temperature sweep rate ξ are related by ∆t ∼ Cξ −3/7 , and is in good agreement with experiments. The coefficient C has a power-law divergence approaching the critical point of the miscibility transition: C ∼ (T − Tc) −η , and the critical exponent η is determined.

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confidence: 59%

A test-tube model for rainfall

Wilkinson¹

2014

EPL

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“…In this way, the condensation is similar to the formation and growth of rain droplets in orographic rain formation, where clouds cools slowly due to adiabatic expansion (e.g. Shaw, 2003), to the formation of droplets in laboratory experiments where binary fluid mixtures are slowly pushed into a phase coexistence region by an applied temperature drift (Lapp et al, 2012;Vollmer et al, 2007), and to the formation of slow dust in Enceladus' plume from the condensation of water (Schmidt et al, 2008). Understanding of phase separation in such settings is presently a subject of active research due to the importance of clouds in climate dynamics (Bodenschatz et al, 2010;Pierrehumbert, 2010).…”

Section: A Particle Generationmentioning

confidence: 95%

The journey of hydrogen to quantized vortex cores

Bewley

Vollmer

2013

Phys. Scr.

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Nanoscale hydrogen particles in superfluid helium track the motions of quantized vortices. This provides a way to visualize turbulence in the superfluid. Here, we trace the evolution of the hydrogen from a gas to frozen particles migrating toward the cores of quantized vortices. Not only are the intervening processes interesting in their own right, but understanding them better leads to more revealing experiments.

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“…Note that the present design of the guiding field is different from the homogeneous (overall) cooling that was used in most of the previous studies of non-autonomous CH models, see e.g. [27][28][29][30]. As we shall demonstrate, a simple guiding field is sufficient to generate crossover between regular and inverse patterns.…”

Section: Introductionmentioning

confidence: 97%

Guiding fields for phase separation: Controlling Liesegang patterns

et al. 2007

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Liesegang patterns emerge from precipitation processes and may be used to build bulk structures at submicron lengthscales. Thus they have significant potential for technological applications provided adequate methods of control can be devised. Here we describe a simple, physically realizable patterncontrol based on the notion of driven precipitation meaning that the phase-separation is governed by a guiding field such as, for example, a temperature or a pH field. The phase-separation is modeled through a non-autonomous Cahn-Hilliard equation whose spinodal is determined by the evolving guiding field. Control over the dynamics of the spinodal gives control over the velocity of the instability front which separates the stable and unstable regions of the system. Since the wavelength of the pattern is largely determined by this velocity, the distance between successive precipitation bands becomes controllable. We demonstrate the above ideas by numerical studies of a 1D system with diffusive guiding field. We find that the results can be accurately described by employing a linear stability analysis (pulled-front theory) for determining the velocity -local-wavelength relationship. From the perspective of the Liesegang theory, our results indicate that the so-called revert patterns may be naturally generated by diffusive guiding fields.

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Publisher’s Note: Minimal Model for Phase Separation under Slow Cooling [Phys. Rev. Lett.98, 115701 (2007)]

Cited by 20 publications

References 0 publications

A test-tube model for rainfall

A test-tube model for rainfall

The journey of hydrogen to quantized vortex cores

Guiding fields for phase separation: Controlling Liesegang patterns

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