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Investigating the effect of the fluid field on the vibrations of the curved microtubule based on the non-local couple stress theory

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Abstract

Microtubules play an essential role in many cellular processes, such as creating a platform for the intracellular transport of organelles and targeting microtubules for anticancer drugs using physical and chemical methods. Therefore, the investigation of microtubule mechanics is very crucial. In this study, the stability of a microtubule containing internal flow within the cytoplasm is investigated. To make the problem more realistic, curved microtubules are considered and the types of curvatures are examined. Considering that the dimensions of microtubule thickness are in the nanoscale, the size effects are considered using non-local couple stress theory in the solid part and velocity correction factor in the fluid part. The cytoplasm environment around the microtubule is simulated by the viscoelastic Kelvin–Voigt support. According to the fluid flow within the microtubule, Navier–Stokes equations are considered for this problem. In this study, a two-way fluid–solid interaction (FSI) model is employed. Hamilton principle is used for driving the Navier governing equation microtubule. To solve the governing differential equation, Galerkin numerical method and temporal differential equation analysis method were used. The gauss-Quadrature method was used for numerical integration. The results of this study showed that the effect of size is important and not considering the non-classical continuum mechanics has a significant error in solving the problem. The results showed by considering the non-local couple stress theory that both hardening and softening are predictable in this theory, so with this theory, many material properties are predictable. Furthermore, the results of this study showed that small curvatures have a great effect on the instability of the microtubule. In addition, increasing the fluid flow velocity increases the instability of the microtubule system. Moreover, with the increase of the fluid velocity inside the microtubule, the natural frequency of this system decreases. The type of fluid also had a great impact on the natural frequency of the system. Finally, it can be concluded that solving this problem will be of great help for the accurate modeling of microtubule systems along with experimental models.

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Data Availability Statement

All data that support the findings of this study are included within the article.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Yasouj University, Yasouj, Iran

    Rouzbeh Mahmoudi, Pourya Omidvar & Pedram Pournaderi

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  1. Rouzbeh Mahmoudi
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Correspondence to Pourya Omidvar or Pedram Pournaderi.

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Mahmoudi, R., Omidvar, P. & Pournaderi, P. Investigating the effect of the fluid field on the vibrations of the curved microtubule based on the non-local couple stress theory. Eur. Phys. J. Plus 138, 642 (2023). https://doi.org/10.1140/epjp/s13360-023-04131-w

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