Spreading fronts: numerical simulations on discrete models and continuous equations

TL;DR

The thesis investigates spreading fronts and kinetic roughening in nonequilibrium systems through extensive Monte Carlo simulations of discrete thin-film growth models and direct numerical integration of continuum equations, with a focus on universal scaling exponents and fluctuation statistics. It reveals that precursor films in wetting exhibit intrinsic anomalous scaling with temperature-dependent exponents and geometry-sensitive fluctuation distributions, hinting at a KPZ-related universality subclass in 1D front dynamics. The work extends to numerical PDE integration on Bethe lattices, showing strong boundary effects that challenge mean-field infinite-dimensional limits for KPZ/EW classes. It also develops a discrete lattice-gas model to study oil extraction via Surface Acoustic Waves, demonstrating the pivotal role of acoustic radiation pressure in promoting oil film formation and separation from emulsions. Together, these studies establish methodological tools (jackknife uncertainty, correlation-length estimation in oscillatory regimes, network-PDE integration) and map universal features of front dynamics across geometries, informing theory and potential applications in wetting, thin-film growth, and SAW-assisted separations.

Abstract

Out-of-equilibrium systems, inherently complex and challenging to understand, are prevalent across various disciplines, including physics where they arise in contexts such as fluid dynamics. In particular, critical out-of-equilibrium systems combine this complexity with the scaling laws and universality classes observed in critical phenomena, with kinetic surface roughening, the study of how a flat surface becomes progressively rougher over time, serving as a prime example. This behavior manifests in a wide variety of contexts, including metal corrosion, cell proliferation, and, notably, the growth of thin films, which can emerge as a result of wetting processes. In this thesis, we conduct extensive numerical simulations to study critical fluctuations and identify universal features of several rough interfaces, generated by simulating discrete models of thin film growth and by performing direct numerical integration of continuum equations. To explore the universal behavior of these interfaces, we identify the critical exponents that characterize the spatio-temporal fluctuations of the front. Additionally, we analyze the dynamics of thin films across different physical scenarios to deepen our understanding of their behavior in out-of-equilibrium conditions, especially in the case where these films are formed by the action of an external force such as Surface Acoustic Waves.

Figures (77)

• Figure 1: Example of a particle aggregate of lateral size $L$. The local heights $h(x,t)$ (blue dots) define the front. The system evolves over time, as more particles are aggregated, and the heights grow in the vertical direction. The mean front $\bar{h}(t)$ and the width $w(L,t)$ are represented by a solid orange line and a magenta arrow, respectively. Reproduced from Ref. GarciaBarreales2024.
• Figure 2: Diagrams of particle sticking rules in deposition models: random deposition, random deposition with relaxation, and ballistic deposition. Reproduced from Ref. GarciaBarreales2024.
• Figure 3: Particle aggregates for RD, RDSR, and BD models. As a reference, the substrate size is always $L=100$ in all cases, and the total number of particles in each morphology is 2000. Reproduced from Ref. GarciaBarreales2024.
• Figure 4: Example of the sticking rule in the RSOS model: Purple and yellow particles adhere to the surface, whereas the green particle does not, as the height difference on the left exceeds one. Reproduced from Ref. Sudijono2023.
• Figure 5: (a) Typical morphology of the DLA model. (b) Typical morphology of the Eden model. Reproduced from Ref. Tian2024.