Persistence in reactive-wetting interfaces

Abstract

In this paper, we report on persistence results of reactive-wetting advancing interfaces performed with mercury on silver at room temperature. Earlier kinetic roughening studies of reactive-wetting systems at room temperature as well as at high temperatures revealed some limited information on the spatiotemporal behavior of these systems. However, by calculating the persistence exponent, we were able to identify two distinct kinetic time regimes in this process. In the first one, while the interface is moving but its width is not yet growing, the persistence exponent is θ=0.55±0.05, which is typical for a random, noisy behavior. In the second regime, there is an effective growth of the interface width with a growth exponent β=0.67±0.06 followed by saturation, according to the Family-Vicsek description of interface growth. The persistence exponent in this regime is θ=0.37±0.05, which indicates that the relation θ=1-β seems to hold even for this nonlinear experimental system.

Persistence and first-passage properties in nonequilibrium systems

“…As far as we know, this is yet to be verified experimentally. Finally, the relation θ s = 1 − β has also been verified recently for nonlinear reacting-wetting advancing interfaces in the experimental system of mercury on silver at room temperature [41]. In this system, the experimentally measured growth exponent β = 0.67 ± 0.06 and the persistence exponent θ s = 0.37 ± 0.05 are consistent with the relation θ s = 1 − β.…”

“…In these experiments, the persistence probability Q(t) that the local order parameter has not switched its state by the time t was found to decay algebraically Q(t) ∼ t −θ with a measured persistence exponent θ = 0.190 (31), in good agreement with analytical approximation [27] and numerical simulations [10,11]. These first results have been followed by a large numbers of other experimental measurements of the persistence probability in a variety of physical systems including NMR measurement of persistence in 1-d diffusion in Xenon gases [36], fluctuating step edges on crystals [37,38], advancing combustion fronts [39], two-dimensional Ostwald ripening [40], reactive-wetting interfaces [41] and liquid crystal turbulence [42]-some of these results will be discussed later in appropriate sections.…”

“…[271]. Apart from step edges on crystals, persistence of fluctuating interfaces have also been measured in a variety of other experimental systems, such as in combustion fronts in paper [39], for interfaces between phase-separated coloid-polymer mixtures [272], advancing interfaces or fronts in reactive-wetting systems such as mercury on silver [41] and growing droplets of turbulent phase in nematic liquid crystals [42].…”

Imaging how thermal capillary waves and anisotropic interfacial stiffness shape nanoparticle supracrystals

“…Beyond the quasi-equilibrium system we focus on here, where the surface profile is controlled by the balance between surface energy and thermal fluctuations, the imaging of surface profiles can allow mapping of other parameters on other fluctuating systems at the nanoscale. For example, one can measure the bending and stretching modulus in a fluctuating vesicle where inter-lipid interactions add rigidity to the vesicle during vesicle transformation 29 , or measure the deposition laws as the RMS roughness changes with time due to active materials deposition 27 , 53 . More studies can emerge to use our method to study fluctuations as liquid-phase TEM becomes more compatible with biological samples and out-of-equilibrium field application.…”

Persistence in Brownian motion of an ellipsoidal particle in two dimensions

“…The persistence probability p(t) of a stochastic variable is simply the probability that the variable has not changed sign up to time t. In physics, the persistence property has been investigated both theoretically and experimentally [25][26][27][28][29][30][31][32] in spatially extended systems that are out of equilibrium. For a more comprehensive review of the persistence probability in spatially extended systems, we invite the readers to look at the recent review by Bray et al 33 and the brief review by Majumdar 34 on the subject and the references therein.…”