Stochastic fluid dynamics simulations of the velocity distribution in protoplasmic streaming

Author:

Egorov Vladislav1ORCID,Maksimova Olga1,Andreeva Irina2ORCID,Koibuchi Hiroshi3ORCID,Hongo Satoshi3,Nagahiro Shinichiro3,Ikai Toshiyuki3ORCID,Nakayama Madoka3,Noro Shuta3,Uchimoto Tetsuya45ORCID,Rieu Jean-Paul6ORCID

Affiliation:

1. Cherepovets State University (ChSU) 1 , Prospekt Lunacharskogo, 5, Cherepovets 162600, Vologda Oblast, Russian Federation

2. Peter the Great St.Petersburg Polytechnic University (SPbPU) 2 , Polytechnicheskaya, 29, St. Petersburg 195251, Russian Federation

3. National Institute of Technology (KOSEN), Sendai College 3 , 48 Nodayama, Medeshima-Shiote, Natori-shi, Miyagi 981-1239, Japan

4. ELyTMaX UMI 3757, CNRS-Université de Lyon-Tohoku University 4 , International Joint Unit, Tohoku University, 2-1-1 Katahira, Aoba-ku Sendai 980-8577, Japan

5. Institute of Fluid Science (IFS), Tohoku University 5 , 2-1-1 Katahira, Aoba-ku Sendai 980-8577, Japan

6. Univ. Lyon, Université Claude Bernard Lyon 1, CNRS UMR-5306, Institut Lumière Matière 6 , F-69622 Villeurbanne, France

Abstract

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 Vx = 0 and at a finite Vx(≠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 Vx(≠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.

Funder

National Institute of Technology, Sendai College

Institute of Fluid Science, Tohoku University

Publisher

AIP Publishing

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