Hybrid hydrodynamic models for active elastic particles driven by self-generated force couples

We present novel hybrid hydrodynamic phase-field models for studying the dynamics of active particles propelled by force couples in incompressible viscous fluids. Our approach integrates variable-viscosity Navier–Stokes equations, a nonlinear volume-preserving Allen–Cahn equation, and constitutive equations of viscous, elastic, or viscoelastic active particles valid within the particles. This hybrid formulation captures complex multiphase hydrodynamical interactions, offering a versatile framework for analyzing diverse active particle behaviors based on their material properties and activity mechanisms. Derived from the generalized Onsager principle, our model ensures thermodynamic consistency by maintaining energy dissipation in the absence of active forces. We develop a linearly decoupled, first-order time-marching numerical scheme that combines a projection approach in space with stabilization techniques. This scheme is rigorously validated for accuracy and asymptotic preservation with respect to model parameters and thermodynamic consistency. Numerical simulations demonstrate the efficacy and scalability of our models and numerical schemes in capturing and elucidating the complex dynamics of force couple-propelled active particles. The numerical results not only confirm some conventional wisdoms about swimmers, but also reveal the delicate hydrodynamic detail on how pushers and pullers interact with each other. This work provides a robust foundation for further investigations into active matter systems across various scales and applications.