Deformable bodies in a 3-dimensional viscous flow: Vorticity-stream vector formulation

A. Gallén, J. Muñoz Biosca, M. Castro, A. Hernández-Machado

Physics of Fluids Vol. 38, nº. 1, pp. 013119

Summary:

When simulating three-dimensional flows interacting with deformable and elastic obstacles, current methods often encounter complexities in the governing equations and challenges in numerical implementation. In this work, we introduce a novel numerical formulation for simulating incompressible viscous flows at low Reynolds numbers in the presence of deformable interfaces. Our method employs a vorticity-stream vector formulation that significantly simplifies the fluid solver, transforming it into a set of coupled Poisson problems. The body–fluid interface is modeled using a phase field, allowing for the incorporation of various free-energy models to account for membrane bending and surface tension. In contrast to existing three-dimensional approaches, such as lattice Boltzmann methods or boundary-integral techniques, our formulation is lightweight and grounded in classical fluid mechanics principles, making it implementable with standard finite-difference techniques. We demonstrate the capabilities of our method by simulating the evolution of a single vesicle or droplet in Newtonian Poiseuille and Couette flows under different free-energy models, successfully recovering canonical axisymmetric shapes and stress profiles. Although this work primarily focuses on single-body dynamics in Newtonian suspending fluids, the framework can be extended to include body forces, inertial effects, and viscoelastic media.

Spanish layman's summary:

Se ha desarrollado un nuevo método computacional simplificado para simular con precisión cómo se deforman y se desplazan objetos blandos, como células o gotas, a través de fluidos microscópicos, lo que facilita avances en bioingeniería y en estudios sanguíneos.

English layman's summary:

We have developed a streamlined computational method to accurately simulate the deformation and motion of soft objects, such as cells and droplets, in microscopic fluids, paving the way for advancements in bioengineering and blood flow analysis.

Keywords: Microfluídica (Microfluidics); Dinámica de Fluidos Computacional (CFD); Flujo viscoso (Viscous flow); Biomecánica celular (Cell biomechanics): Bajo número de Reynolds (Low Reynolds number); Vorticidad (Vorticity); Campo de fase (Phase-field)

JCR-JIF Impact Factor and WoS quartile: 3,800 - Q1 (2025)

DOI reference: https://doi.org/10.1063/5.0304652

Published on paper: January 2026.

Published on-line: January 2026.

Citation:
A. Gallén, J. Muñoz Biosca, M. Castro, A. Hernández-Machado, "Deformable bodies in a 3-dimensional viscous flow: Vorticity-stream vector formulation", Physics of Fluids, Vol. 38, nº. 1, pp. 013119, January 2026. [Online: January 2026] doi: 10.1063/5.0304652