Stochastic pattern formation in coupled chemo-mechanical surface erosion: A KS–KPZ interface model

We investigate surface pattern formation induced by the coupled effects of chemical ablation and particle-impact erosion in reactive particle-laden flows. A reduced stochastic interface equation of the Kuramoto–Sivashinsky–Kardar–Parisi–Zhang (KS–KPZ) type is derived from Arrhenius-based surface reaction kinetics and a stochastic description of particle impacts. The resulting model introduces an effective curvature coefficient that captures the competition between chemical and mechanical erosion mechanisms. Linear stability analysis predicts a transition to pattern-forming instability when this coefficient becomes negative and provides a characteristic wavelength selected by the balance between destabilizing curvature effects and higher-order surface relaxation. Numerical simulations based on a pseudospectral scheme combined with Monte Carlo particle forcing reveal three distinct regimes: smooth ablation, organized pattern formation, and irregular roughening. The regime behavior is governed by key dimensionless parameters, including the Damköhler number, Stokes number, and erosion ratio. In a controlled campaign with M = 16 –128 domains, the initial instability at λ * is followed by finite-time spectral migration toward lower wavenumbers and then by finite-domain stochastic saturation. The discrete spectral peak, low- q and high- q slopes, and roughness growth rate depend on the time and wavenumber windows used for their estimation; they therefore serve as effective diagnostics rather than a single universal ( n, α, β ) triplet. The late-time width as a function of domain size is the robust ensemble observable. Switching off the discrete particle process isolates its contribution as an additive roughening source on top of the continuum stochastic forcing. These results establish a mechanistic framework for interpreting reactive erosion-driven surface morphologies and for mapping governing parameters to qualitative morphological regimes in complex multiphase flow environments.