Coarsening dynamics

As was shown before, if phase separation is forced by a stationary and spatially periodic temperature modulation, the coarsening dynamics is interrupted above some critical value of the forcing amplitude a and it is locked to the periodicity of the external forcing. However, if this forcing is pulled by a velocity v 0, the traveling periodic solutions of (61) exist only in a certain range of v depending on a. 

Tanaka, H., Sigehuzi, T. Surface-pattern evolution in a selling gel under a geometrical constraint - direct observation of fold structure and its coarsening dynamics. Phys. Rev. E 49(1), R39-R42 (1994)... 

Coarsening Dynamics of Phase Separation During the Late Stages... 

Due to the relative complexity of the nematic order parameter, its coarsening dynamics has been the subject of numerous experiments and... 

In order to analyze the coarsening dynamics, we compute the orientational correlation along the x-direction in the middle of the cell ... 

Chuang, I., Turok, N., and Yurke, B Late-time coarsening dynamics in a nematic liquid crystal, Phys. Rev. Lett., 66, 2472-2475 (1991). 

Foam rheology has been a challenging area of research of interest for the yield behavior and stick-slip flow behavior (see the review by Kraynik [229]). Recent studies by Durian and co-workers combine simulations [230] and a dynamic light scattering technique suited to turbid systems [231], diffusing wave spectroscopy (DWS), to characterize coarsening and shear-induced rearrangements in foams. The dynamics follow stick-slip behavior similar to that found in earthquake faults and friction (see Section XU-2D). 

The phase separation process at late times t is usually governed by a law of the type R t) oc f, where R t) is the characteristic domain size at time t, and n an exponent which depends on the universality class of the model and on the conservation laws in the dynamics. At the presence of amphiphiles, however, the situation is somewhat complicated by the fact that the amphiphiles aggregate at the interfaces and reduce the interfacial tension during the coarsening process, i.e., the interfacial tension depends on the time. This leads to a pronounced slowing down at late times. In order to quantify this effect, Laradji et al. [217,222] have proposed the scaling ansatz... 

A. A. Chernov. Formation of crystals in solutions. Contemp Phys 30 251,1989 J. P. V. d. Eerden, H. Muller-Krumbhaar. Dynamic coarsening of crystal surfaces. Phys Rev Lett 57 2431, 1986. 

In Figs. 27 and 28 we also show the dynamics of the characteristic length scales and snapshots for a driving amplitude slightly below the critical one. One can see that at t 103 there is competition between the influence of the forcing and the coarsening process, which finally wins. 

The kinetics of particle coarsening was followed by applying the dynamic scaling analysis to sequential in-situ and ex-situ STM images of columnar-structured Pt and Au films on conducting substrates. 

To relate the flowing and trapped textures, the work of Friedmann et al. (39) is followed and local equilibrium is assumed. We argue that during coinjection of gas and liquid, the trapped fraction is dynamic. Some portion of the trapped bubbles coarsen and remobilize to be replaced by subsequent trapping of flowing bubbles. Flowing and stationary texture are thus approximately the same. In the simulations to follow, nf is set equal to n. ... 

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