Theoretical modelling and mechanistic investigation of Richtmyer–Meshkov instability nonlinear evolution in large Stokes number particle-laden flows

This study develops a novel theoretical model for predicting the nonlinear evolution of Richtmyer–Meshkov instability (RMI) in particle-laden flows at large Stokes numbers. We construct a coupled multiphase potential flow theory framework incorporating two key models: (i) a postshock interface velocity attenuation model based on exponential decay accounting for momentum dissipation and (ii) a unified bubble and spike growth model for multiphase conditions. The multiphase-unified model maintains compatibility with classical single-phase RMI theories in the dilute limit, meanwhile revealing stronger particle-induced nonlinear decay in the amplitude growth rate. Model validation demonstrates good quantitative agreement across key predictive metrics – including dilute to dense particle volume fractions, Atwood numbers, particle sizes and initial perturbation amplitudes. This wide-range predictive capability for nonlinear instability growth may improve theoretical understanding of phenomena relevant to engineering applications. The results reveal that increased particle loading significantly reduces the growth rate of interface disturbances due to enhanced damping effects, leading to the blunting of spikes and flattening of bubbles. Vorticity dynamics analysis further shows that particle-induced vorticity weakens baroclinic production, thereby stabilizing the flow and inhibiting RMI development.