Langevin and Navier–Stokes simulation of three-dimensional protoplasmic streaming

• Published in: Physica A: Statistical Mechanics and its Applications
• Main Authors: Noro, Shuta, Hongo, Satoshi, Nagahiro, Shin-Ichiro, Ikai, Hisatoshi, Koibuchi, Hiroshi, Nakayama, Madoka, Uchimoto, Tetsuya, Diguet, Gildas
• Other Authors: National Institute of Technology (KOSEN), Hokkaido University Sapporo, Japan, Institute of Fluid Sciences Sendai (IFS), Tohoku University Sendai, ELyTMaX, École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Tohoku University Sendai -Centre National de la Recherche Scientifique (CNRS)
• Format: Article in Journal/Newspaper
• Language: English
• Published: HAL CCSD 2023
• Subjects: Langevin simulations; Brownian motion; Navier-Stokes; Fluctuation-dissipation relation; Protoplasmic streaming; Velocity distribution; [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]; Nitella flexilis
• Online Access: https://hal.science/hal-04399527; https://hal.science/hal-04399527/document; https://hal.science/hal-04399527/file/PHYSA-231496-R2.pdf; https://doi.org/10.1016/j.physa.2023.129154

International audience In this paper, we report the numerical results obtained using the Langevin Navier-Stokes (LNS) simulation of the velocity distribution of three-dimensional (3D) protoplasmic streaming in plant cells, such as those of Nitella flexilis. The LNS simulations are performed on 3D cylinders discretized by regular cubes in which fluid velocities are activated by boundary velocities parallel and nonparallel to the longitudinal direction and a random Brownian force with strength D. We find that, for a finite D, the velocity distribution h(V), V = | ⃗ V |, has two different peaks at a small non-zero V and a finite V , and the distribution h(V z) for |V z | along the longitudinal direction also has a peak at finite V z. These results are in good agreement with the reported velocity distributions observed using laser Doppler velocimetry. Moreover, we study the effects of the Brownian force on biological material mixing and find that mixing along the ⃗ V direction enhanced by the nonparallel circular motion is further improved by the Brownian force in the experimentally relevant region of D. In addition, the experimentally relevant D is found to be consistent with the expectation from the fluctuation dissipation relation between the random stress and viscosity in the LNS equation of Landau and Lifschitz for incompressible fluids.