Large-scale kinetic roughening behavior of coffee-ring fronts

TL;DR

This study investigates the kinetic roughening of coffee-ring aggregate fronts through numerical simulations, revealing a discontinuous pinning-depinning transition and complex scaling behaviors influenced by patch affinity parameters.

Contribution

It provides new insights into the morphological instability and anomalous scaling in ballistic aggregation models with patchy colloids, especially near the pinning transition.

Findings

Discontinuous pinning-depinning transition at r_AB=0

Intrinsic anomalous scaling with unusual exponents

Morphological instability induced by patch structure

Abstract

We have studied the kinetic roughening behavior of the fronts of coffee-ring aggregates via extensive numerical simulations of the off-lattice model considered for this context in [C.\ S.\ Dias {\it et al.}, Soft Matter {\bf 14}, 1903 (2018)]. This model describes ballistic aggregation of patchy colloids and depends on a parameter $r_\mathrm{AB}$ which controls the affinity of the two patches, A and B. Suitable boundary conditions allow us to elucidate a discontinuous pinning-depinning transition at $r_\mathrm{AB}=0$, with the front displaying intrinsic anomalous scaling, but with unusual exponent values $\alpha \simeq 1.2$, $\alpha_{\rm loc} \simeq 0.5$, $\beta\simeq 1$, and $z\simeq 1.2$. For $0<r_\mathrm{AB}\le 1$, comparison with simulations of standard off-lattice ballistic deposition indicates the occurrence of a morphological instability induced by the patch structure. As a result, we find that the asymptotic morphological behavior is dominated by macroscopic shapes. The intermediate time regime exhibits one-dimensional KPZ exponents for $r_\mathrm{AB}> 0.01$ and the system suffers a strong crossover dominated by the $r_\mathrm{AB}=0$ behavior for $r_\mathrm{AB}\le 0.01$. A detailed analysis of correlation functions shows that the aggregate fronts are always in the moving phase for $0<r_\mathrm{AB}\le 1$ and that their kinetic roughening behavior is intrinsically anomalous for $r_\mathrm{AB}\le 0.01$.