Dynamics of surface roughening in disordered media

Csahók, Zoltán; Honda, Katsuya; Vicsek, Tamás

doi:10.1088/0305-4470/26/5/001

Cited by 58 publications

(60 citation statements)

References 15 publications

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“…Averaging over several independent runs, we found that for the QKPZ system the growth exponent is β = 0 61 ± 0 02. This result is in excellent agreement with previous simulations of the QKPZ equation where the growth exponent was found to be β ≈ 0 6 [7,8] and β = 0 61 ± 0 06 [16].…”

Section: Qkpz Equation Simulationsupporting

confidence: 92%

“…4 for a single run). We find that the roughness exponent, averaged over several runs, is α = 0 72 ± 0 02 in good agreement with previous results [8,16]. We also find that there is a crossover behavior of the interface width from small to large scale, as shown in Fig.…”

Section: Qkpz Equation Simulationsupporting

confidence: 92%

“…Both models are well known and were partially studied before with respect to interface dynamics. The QKPZ equation was studied in the context of its kinetic roughening exponents [7,8,16], but not for its persistence. On the other hand, the persistence of the Ising model was calculated before [11,12], but the kinetic roughening exponents were not.…”

Section: Introductionmentioning

confidence: 99%

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Can Ising model and/or QKPZ equation properly describe reactive-wetting interface dynamics?

Efraim

Taitelbaum

2009

Open Physics

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Abstract:The reactive-wetting process, e.g. spreading of a liquid droplet on a reactive substrate is known as a complex, non-linear process with high sensitivity to minor fluctuations. The dynamics and geometry of the interface (triple line) between the materials is supposed to shed light on the main mechanisms of the process. We recently studied a room temperature reactive-wetting system of a small (∼ 150 µm) Hg droplet that spreads on a thin (∼ 4000 Å) Ag substrate. We calculated the kinetic roughening exponents (growth and roughness), as well as the persistence exponent of points on the advancing interface.In this paper we address the question whether there exists a well-defined model to describe the interface dynamics of this system, by performing two sets of numerical simulations. The first one is a simulation of an interface propagating according to the QKPZ equation, and the second one is a landscape of an Ising chain with ferromagnetic interactions in zero temperature. We show that none of these models gives a full description of the dynamics of the experimental reactivewetting system, but each one of them has certain common growth properties with it. We conjecture that this results from a microscopic behavior different from the macroscopic one. The microscopic mechanism, reflected by the persistence exponent, resembles the Ising behavior, while in the macroscopic scale, exemplified by the growth exponent, the dynamics looks more like the QKPZ dynamics.

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Section: Qkpz Equation Simulationsupporting

confidence: 92%

Section: Qkpz Equation Simulationsupporting

confidence: 92%

Section: Introductionmentioning

confidence: 99%

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Can Ising model and/or QKPZ equation properly describe reactive-wetting interface dynamics?

Efraim

Taitelbaum

2009

Open Physics

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“…Three distinct growth processes were discovered in the evaporating colloidal suspensions by tuning particle shapedependent capillary interactions and thus varying the microscopic rules of deposition. The substantial shape fluctuations of the growth line of spheres are readily explained via a Poisson-like deposition process; slightly anisotropic particles exhibit weaker fluctuations characteristic of KPZ class behavior, and very anisotropic ellipsoids exhibit behavior consistent with the KPZ class in the presence of quenched disorder [20][21][22].…”

mentioning

confidence: 99%

“…Previous work found that if quenched disorder prevents interfacial growth in a particular region, then a new universality class (the KPZQ class) was produced with ¼ 0:68 and ¼ 0:63 [20]. The measured roughness exponent is ¼ 0:61ð2Þ [ Fig.…”

mentioning

confidence: 99%

Effects of Particle Shape on Growth Dynamics at Edges of Evaporating Drops of Colloidal Suspensions

et al. 2013

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We study the influence of particle shape on growth processes at the edges of evaporating drops. Aqueous suspensions of colloidal particles evaporate on glass slides, and convective flows during evaporation carry particles from drop center to drop edge, where they accumulate. The resulting particle deposits grow inhomogeneously from the edge in two-dimensions, and the deposition front, or growth line, varies spatio-temporally. Measurements of the fluctuations of the deposition front during evaporation enable us to identify distinct growth processes that depend strongly on particle shape. Sphere deposition exhibits a classic Poisson like growth process; deposition of slightly anisotropic particles, however, belongs to the Kardar-Parisi-Zhang (KPZ) universality class, and deposition of highly anisotropic ellipsoids appears to belong to a third universality class, characterized by KPZ fluctuations in the presence of quenched disorder.

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Driven interface depinning in a disordered medium

et al. 1997

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Abstract. The dynamics of a driven interface in a medium with random pinning forces is analyzed. The interface undergoes a depinning transition where the order parameter is the interface velocity v, which increases as v N ( F -F,)' for driving forces F close to its threshold value F,. We consider a Langevin-type Eq. which is expected to be valid close to the depinning transition of an interface in a statistically isotropic medium. By a functional renormalization group scheme the critical expo- Here, we present details of the perturbative calculation and of the derivation of the functional flow Eq. for the random-force correlator. The fixed point function of the correlator has a cusp singularity which is related to a finite value of the threshold F,, similar to the mean field theory. We also present extensive numerical simulations and compare them with our analytical results for the critical exponents. For E = I the numerical and analytical results deviate from each other by only a few percent. The deviations in lower dimensions E = 2,3 are larger and suggest that the roughness exponent is somewhat larger than the value [ = ~/ 3 of an interface in thermal equilibrium.

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Dynamics of surface roughening in disordered media

Cited by 58 publications

References 15 publications

Can Ising model and/or QKPZ equation properly describe reactive-wetting interface dynamics?

Can Ising model and/or QKPZ equation properly describe reactive-wetting interface dynamics?

Effects of Particle Shape on Growth Dynamics at Edges of Evaporating Drops of Colloidal Suspensions

Driven interface depinning in a disordered medium

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