Stochastic fluid dynamics simulations of the velocity distribution in protoplasmic streaming

Vladislav Egorov (1) , Olga Maksimova (1) , Irina Andreeva-Sussin (2) , Hiroshi Koibuchi (3) , Satoshi Hongo (3) , Shinichiro Nagahiro (3) , Toshiyuki Ikai (3) , Madoka Nakayama (3) , Shuta Noro (3) , Tetsuya Uchimoto (4, 5) , Jean-Paul Rieu (6)

1 Cherepovets State University
2 SPbPU - Peter the Great St. Petersburg Polytechnic University
3 KOSEN - National Institute of Technology
4 ELyTMaX
5 IFS - Institute of Fluid Sciences [Sendai]
6 iLM - BIOPHYSIQUE - iLM - Biophysique

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

Mots clés: Cell structure; Partial differential equations; Fluid dynamics simulation; Computer simulation; Brownian motion; Cell membranes; Stochastic processes; Navier Stokes equations; Langevin dynamics; Molecular motor

Domaines: Sciences de l'ingénieur [physics]; Chimie; Physique [physics]

Vladislav Egorov, Olga Maksimova, Irina Andreeva-Sussin, Hiroshi Koibuchi, Satoshi Hongo, et al.. Stochastic fluid dynamics simulations of the velocity distribution in protoplasmic streaming. Physics of Fluids, 2020, 32 (12), pp.121902. ⟨10.1063/5.0019225⟩. ⟨hal-03093645⟩