Algorithmic Spherical Mode Decomposition and Rheological Analysis of Nonlinear Interactions in Variable Density Deformable Particle Domains*

This study investigates nonlinear interactions from pressure waves emitted during particle deformation in domains with variable particle density distributions. We propose a novel algorithm to generate irregular 3D shapes by combining spherical harmonic modes and decomposing them into dominant modes. The domain includes particles ranging from nanometers to millimeters. We examine the impact of centroid distance, initial shape, and material properties on interaction dynamics. Geometry and mesh generation are performed using GMSH, creating a structured quad mesh with smaller cell sizes near the particles to avoid mass diffusion. CFD modeling is conducted using the compressibleInterDyMFoam solver in OpenFOAM. The study includes rheological analysis via analytically derived equations and explores the use of physics-informed neural networks (PINNs) to predict dynamics of nonspherical deformable particles.

Preliminary findings indicate smaller particle sizes correlate with increased equilibrium pressure, higher peak frequency, and smaller deformation. Factors such as particle size, perturbation amplitude, and fluid compressibility influence damping effects and bubble stability. Our results provide insights into pressure wave behavior in non-uniform particle distributions, advancing the understanding of wave-particle interactions in heterogeneous media with significant implications for fluid dynamics and material science.