Stochastic Fluid Dynamics Simulations of the Velocity Distribution in Protoplasmic Streaming

TL;DR

This study uses stochastic Navier-Stokes simulations to replicate the velocity distribution in plant cell streaming, revealing the role of Brownian motion in forming observed velocity peaks.

Contribution

First numerical demonstration that stochastic NS equations can reproduce velocity distribution peaks in protoplasmic streaming, highlighting Brownian motion's importance.

Findings

Peaks at zero and finite velocity are reproduced by stochastic NS simulations.

Peak position shifts with the strength of Brownian force D.

Velocity peaks depend on physical parameters like viscosity and boundary velocity.

Abstract

Protoplasmic streaming in plant cells is directly visible in the cases of \textit{Chara corallina} and \textit{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 $V_x(\not=\!0)$, 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 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 $V_x(\not=\!0)$ 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.