Stochastic fluid dynamics simulations of the velocity distribution in protoplasmic streaming

• Published in: Physics of Fluids
• Main Authors: Egorov, Vladislav, Maksimova, Olga, Andreeva-Sussin, Irina, Koibuchi, Hiroshi, Hongo, Satoshi, Nagahiro, Shinichiro, Ikai, Toshiyuki, Nakayama, Madoka, Noro, Shuta, Uchimoto, Tetsuya, Rieu, Jean-Paul
• Other Authors: Cherepovets State University, Peter the Great St. Petersburg Polytechnic University (SPbPU), National Institute of Technology (KOSEN), ELyTMaX, École Centrale de Lyon (ECL), Université de Lyon-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), Institute of Fluid Sciences Sendai (IFS), Tohoku University Sendai, iLM - Biophysique (iLM - BIOPHYSIQUE), Institut Lumière Matière Villeurbanne (ILM), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)
• Format: Article in Journal/Newspaper
• Language: English
• Published: HAL CCSD 2020
• Subjects: Cell structure; Partial differential equations; Fluid dynamics simulation; Computer simulation; Brownian motion; Cell membranes; Stochastic processes; Navier Stokes equations; Langevin dynamics; Molecular motor; [SPI]Engineering Sciences [physics]; [CHIM]Chemical Sciences; [PHYS]Physics [physics]; Nitella flexilis
• Online Access: https://hal.science/hal-03093645; https://hal.science/hal-03093645/document; https://hal.science/hal-03093645/file/5.0019225.pdf; https://doi.org/10.1063/5.0019225

International audience Protoplasmic streaming in plant cells is directly visible in the cases of Chara corallina and Nitella flexilis , and this streaming is understood to play a role in the transport of biological materials. For this reason, related studies have focused on molecular transportation from a fluid mechanics viewpoint. However, the experimentally observed distribution of the velocity along the flow direction x, which exhibits two peaks at V x = 0 and at a finite V x (≠0), remains to be studied. In this paper, we numerically study whether this behavior of the flow field can be simulated by a 2D stochastic Navier–Stokes (NS) equation for Couette flow in which a random Brownian force is assumed. We present the first numerical evidence that these peaks are reproduced by the stochastic NS equation, which implies that the Brownian motion of the fluid particles plays an essential role in the emergence of these peaks in the velocity distribution. We also find that the position of the peak at V x (≠0) moves with the variation in the strength D of the random Brownian force, which also changes depending on physical parameters such as the kinematic viscosity, boundary velocity, and diameter of the plant cells.I. INTROD