Kinetic roughening in a realistic model of non-conserved interface growth

TL;DR

This paper investigates non-conserved interface growth using theoretical models and experiments, focusing on the validity of small-slope theories, morphological instabilities, and kinetic roughening in electrochemical deposition.

Contribution

It combines interfacial equations and phase-field models to quantitatively connect theory with experiments and analyze the limits of small-slope approximations.

Findings

Identifies the conditions under which small-slope theories fail.

Links anomalous scaling to the breakdown of small-slope assumptions.

Shows standard kinetic roughening re-emerges at long times under certain conditions.

Abstract

We provide a quantitative picture of non-conserved interface growth from a diffusive field making special emphasis on two main issues, the range of validity of the effective small-slopes (interfacial) theories and the interplay between the emergence of morphologically instabilities in the aggregate dynamics, and its kinetic roughening properties. Taking for definiteness electrochemical deposition as our experimental field of reference, our theoretical approach makes use of two complementary approaches: interfacial effective equations and a phase-field formulation of the electrodeposition process. Both descriptions allow us to establish a close quantitative connection between theory and experiments. Moreover, we are able to correlate the anomalous scaling properties seen in some experiments with the failure of the small slope approximation, and to assess the effective re-emergence of standard kinetic roughening properties at very long times under appropriate experimental conditions.