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<p>Certain rod-shaped bacteria may move over surfaces without the assistance of external appendages like flagella, cilia, or pili thanks to a process known as gliding motility. In this work, the dynamics of an undulating sheet are used to represent the methods by which these bacteria migrate over a Williamson slime layer on a rigid substrate. The bacterial surface is approximated as a two-dimensional complex wavy sheet. The study examines how various physical factors influence bacterial gliding speed, flow rate, energy loss, and slime layer velocity by transforming partial differential equations into a fourth-order nonlinear ordinary differential equation under Stokes flow, analyzed with the regular perturbation method. Expressions for the stream function and pressure gradient are obtained and subsequently employed in the integrals representing dynamic equilibrium conditions. We utilized Wolfram Mathematica’s NIntegrate and FindRoot commands to calculate gliding speed and flow rate. These calculated pairs are further employed in the integral of power dissipation. The perturbed results are validated with MATLAB’s bvp5c approach. With potential uses in medical treatments and the development of sophisticated microfluidic systems, the results, which are displayed through visual analysis, provide insightful information about managing microbial motility.</p>

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Mathematical analysis of the Shear-thinning slime layer flowing beneath an active bacterial surface

  • 期刊论文

  • 发表日期：

    2025年1月31日

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  • Rehman Ali Shah,
  • Zeeshan Asghar,
  • Muhammad Waqas,
  • Muhammad Asif Gondal

摘要

Certain rod-shaped bacteria may move over surfaces without the assistance of external appendages like flagella, cilia, or pili thanks to a process known as gliding motility. In this work, the dynamics of an undulating sheet are used to represent the methods by which these bacteria migrate over a Williamson slime layer on a rigid substrate. The bacterial surface is approximated as a two-dimensional complex wavy sheet. The study examines how various physical factors influence bacterial gliding speed, flow rate, energy loss, and slime layer velocity by transforming partial differential equations into a fourth-order nonlinear ordinary differential equation under Stokes flow, analyzed with the regular perturbation method. Expressions for the stream function and pressure gradient are obtained and subsequently employed in the integrals representing dynamic equilibrium conditions. We utilized Wolfram Mathematica’s NIntegrate and FindRoot commands to calculate gliding speed and flow rate. These calculated pairs are further employed in the integral of power dissipation. The perturbed results are validated with MATLAB’s bvp5c approach. With potential uses in medical treatments and the development of sophisticated microfluidic systems, the results, which are displayed through visual analysis, provide insightful information about managing microbial motility.