Large-scale kinetic roughening behavior of coffee-ring fronts

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 $\alpha \simeq 1.2$, ${\alpha }_{\mathrm{loc}}\simeq 0.5$, $\beta \simeq 1$, 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 $r_{\mathrm{AB}}\le 0.01$.

arXiv comment16 pages and 20 figures. Final version published in PRE

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