Fully resolved particle dynamics over long time scales in acoustofluidic flows: Theory and numerical simulations
Abstract
We present a perturbation-based theoretical framework, together with its immersed boundary/volume penalization implementation, for long-time simulations of fully resolved rigid-particle dynamics in acoustically actuated flows. A perturbation formulation separates the fast acoustic time scale from the slow mean dynamics, avoiding long-time direct integration of the fully compressible Navier-Stokes equations. The immersed rigid body is represented through a Brinkman penalization term in equations posed over a unified fluid-solid domain. The coupled fluid-particle system is decomposed into a time-harmonic first-order problem governing the acoustic response and a time-averaged second-order problem. A central challenge in this decomposition is the treatment of the moving fluid-solid interface. We derive order-consistent expressions for the structural velocities, comprising rigid-body and Stokes-drift contributions, and formulate the corresponding first- and second-order rigid-body equations of motion. For a circular particle in two dimensions, the simulations reveal substantial differences in the magnitude and structure of acoustic streaming around fixed and freely moving particles, highlighting the importance of two-way fluid-structure coupling. The results also show that particle-density effects are more complex than suggested by simplified descriptions based solely on the acoustic contrast factor. The framework captures the mean particle dynamics using time steps associated with the slow particle-motion scale rather than the much smaller acoustic time scale. Finally, simulations of an elliptical particle demonstrate the ability of the method to capture coupled translational and rotational motion. The proposed approach therefore provides an efficient route to fully resolved, long-time simulations of acoustically driven rigid-particle motion while retaining two-way fluid-structure coupling.
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BibTeX
@misc{kshetri2026fully,
title = {{Fully resolved particle dynamics over long time scales in acoustofluidic flows: Theory and numerical simulations}},
author = {Khemraj Gautam Kshetri and Amneet Pal Singh Bhalla and Nitesh Nama},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27228},
eprint = {2610.27228},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27228},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fully resolved particle dynamics over long time scales in acoustofluidic flows: Theory and numerical simulations
AU - Khemraj Gautam Kshetri
AU - Amneet Pal Singh Bhalla
AU - Nitesh Nama
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.27228
UR - https://arxiv.org/abs/2610.27228
AB - We present a perturbation-based theoretical framework, together with its immersed boundary/volume penalization implementation, for long-time simulations of fully resolved rigid-particle dynamics in acoustically actuated flows. A perturbation formulation separates the fast acoustic time scale from the slow mean dynamics, avoiding long-time direct integration of the fully compressible Navier-Stokes equations. The immersed rigid body is represented through a Brinkman penalization term in equations posed over a unified fluid-solid domain. The coupled fluid-particle system is decomposed into a time-harmonic first-order problem governing the acoustic response and a time-averaged second-order problem. A central challenge in this decomposition is the treatment of the moving fluid-solid interface. We derive order-consistent expressions for the structural velocities, comprising rigid-body and Stokes-drift contributions, and formulate the corresponding first- and second-order rigid-body equations of motion. For a circular particle in two dimensions, the simulations reveal substantial differences in the magnitude and structure of acoustic streaming around fixed and freely moving particles, highlighting the importance of two-way fluid-structure coupling. The results also show that particle-density effects are more complex than suggested by simplified descriptions based solely on the acoustic contrast factor. The framework captures the mean particle dynamics using time steps associated with the slow particle-motion scale rather than the much smaller acoustic time scale. Finally, simulations of an elliptical particle demonstrate the ability of the method to capture coupled translational and rotational motion. The proposed approach therefore provides an efficient route to fully resolved, long-time simulations of acoustically driven rigid-particle motion while retaining two-way fluid-structure coupling.
ER -