Rheology and Velocity Distribution of Couette Flow for Protoplasmic Streaming

Tomoya Souma; Fumitake Kato; Hiroshi Koibuchi

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arXiv · 2611.05732

Rheology and Velocity Distribution of Couette Flow for Protoplasmic Streaming

Tomoya Souma·Fumitake Kato·Hiroshi Koibuchi

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Abstract

We investigate two-dimensional Couette flow between parallel plates as a model of protoplasmic streaming in plant cells using a combined Langevin and Navier?Stokes simulation. The interaction between the fluid and biological materials is implemented using a Finsler geometry (FG) modeling technique, in which the interaction strength, represented by quantities such as relative viscosity, effectively varies with an internal degree of freedom (IDOF) associated with the biological materials. The simulations demonstrate that the Couette flow exhibits a linear velocity profile along the vertical direction perpendicular to the plates, as well as a peak structure in the velocity distribution consistent with reported experimental observations obtained by laser light scattering. The simulations also demonstrate that the model exhibits shear-thinning behavior typical of non-Newtonian fluids, with the viscosity minimized in the boundary region. Additionally, we find that the rheological properties are connected to the conformal transformation of the interaction between the fluid and the IDOF. Within the FG modeling framework, the conformally flat configuration of the IDOF, which is neither anisotropic nor randomly isotropic, is introduced as a minimum-energy state that characterizes the shear-thinning rheological properties of two-dimensional Couette flow.

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Tomoya Souma, Fumitake Kato, Hiroshi Koibuchi. 2026-11-03. Rheology and Velocity Distribution of Couette Flow for Protoplasmic Streaming. https://arxiv.org/abs/2611.05732

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