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

Abstract

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.

Reactive wetting in metal–metal systems

“…The growth exponent, which is the slope of the width versus the shifted time in log-log scale, was found to be β = 0.62 ± 0.039. This result resembles the growth exponent that was found in the Hg-Ag reactive wetting system [24]. The last regime is where the interface saturates and the roughness exponent α becomes relevant.…”

“…Roughening does not appear to be a CL instability but rather the growth of a new phase in the CL region. This phenomenon was originally identified by Taitelbaum and co-workers [22][23][24] who studied the room temperature wetting of Ag and Au coatings on glass by liquid Hg. These authors also considered different time regimes, related to those regimes being discussed here [25,26].…”

Persistence in reactive-wetting interfaces

“…Averaging over all the experiments, the growth exponent β in this regime is found to be β = 0.67 ± 0.06. This value is in agreement with former experiments in a similar system and with simulation results of the quenched Kardar-Parisi-Zhang (QKPZ) equation [17,[20][21][22]. This also means that relation (5) is valid in the growth regime, θ + β = 1.04 ± 0.07.…”

Kinetic roughening of magnetic flux fronts in Bi2Sr2CaCu2OBarness1, Efraim2, Taitelbaum3 et al. 2012Phys. Rev. B

“…However, as the system approaches 40 K, the exponents tend to the set of exponents (β = 0.6, α = 0.75), which, as mentioned above, associates the front dynamics with the QKPZ equation for nonlinear front evolution in quenched disorder. 12,25,28 The fact that the gross features of the front morphology are reproducible supports the argument that the front roughening is governed by the quenched noise, as expected by the QKPZ description. This description is consistent with that found in some experiments involving fronts moving in the critical state for type-II thin superconducting films.…”

“…We note that the fronts have backbends, especially at the final stages of the experiment; in the kinetic roughening analysis, we define h(x,t) as the maximal value of the front at each x coordinate, as it is the real front of the process. 24,25 Figures 4(a) and 4(b) show log-log plots of the front width W at T = 40 K as a function of time for L = 180 μm and as a function of the length scale L for t = 64 s (above the estimated 26 t x ≈ 60 s), respectively. The solid red lines in Figs.…”