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

Resumen:

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.

Resumen divulgativo:

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.

Palabras Clave: 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)

Índice de impacto JCR-JIF y cuartil WoS: 3,800 - Q1 (2025)

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

Publicado en papel: Enero 2026.

Publicado on-line: Enero 2026.

Cita:
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, Enero 2026. [Online: Enero 2026] doi: 10.1063/5.0304652