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Modeling bacterial flow field with regularized singularities

Yaochen Yang, Daiki Matsunaga, Da Wei, Fanlong Meng

TL;DR

The model combining an anisotropically regularized stresslet with an isotropically regularized source dipole nicely reproduces the flow field around a swimming bacterium and can be utilised to study the collective responses of bacteria in dense suspensions.

Abstract

The flow field generated by a swimming bacterium serves as a fundamental building block for understanding hydrodynamic interactions between bacteria. Although the flow field generated by a force dipole (stresslet) well captures the fluid motion in the far field limit, the stresslet description does not work in the near-field limit, which can be important in microswimmer interactions. Here we propose the model combining an anisotropically regularized stresslet with an isotropically regularized source dipole, and it nicely reproduces the flow field around a swimming bacterium, which is validated by the experimental measurements of the flow field around \textit{E. coli} and our boundary-element-method simulations of a helical microswimmer, in both cases of the free space and the confined space with a no-slip wall. This work provides a practical tool for obtaining the flow field of the bacterium, and can be utilised to study the collective responses of bacteria in dense suspensions.

Modeling bacterial flow field with regularized singularities

TL;DR

The model combining an anisotropically regularized stresslet with an isotropically regularized source dipole nicely reproduces the flow field around a swimming bacterium and can be utilised to study the collective responses of bacteria in dense suspensions.

Abstract

The flow field generated by a swimming bacterium serves as a fundamental building block for understanding hydrodynamic interactions between bacteria. Although the flow field generated by a force dipole (stresslet) well captures the fluid motion in the far field limit, the stresslet description does not work in the near-field limit, which can be important in microswimmer interactions. Here we propose the model combining an anisotropically regularized stresslet with an isotropically regularized source dipole, and it nicely reproduces the flow field around a swimming bacterium, which is validated by the experimental measurements of the flow field around \textit{E. coli} and our boundary-element-method simulations of a helical microswimmer, in both cases of the free space and the confined space with a no-slip wall. This work provides a practical tool for obtaining the flow field of the bacterium, and can be utilised to study the collective responses of bacteria in dense suspensions.
Paper Structure (3 sections, 6 equations, 3 figures)

This paper contains 3 sections, 6 equations, 3 figures.

Table of Contents

  1. Theoretical model.
  2. Comparisons with experiments and simulations.
  3. Summary.

Figures (3)

  • Figure 1: The theoretical setup, with the ARS (anisotropically regularized stresslet) placed between the cell body and the flagellar bundle, and the IRSD (isotropically regularized source dipole) placed at the center of the cell body. The director of bacterium, $\bm{q}$, is set along the $+x$.
  • Figure 2: (a) Entire flow field (ARS + ISRD) given by the model in the free space. Colorbar indicates the magnitude of the in-plane flow velocity $|u| = \sqrt{u_x^2+u_y^2}$. Flow field of a stresslet of the same strength as the ARS is presented in the inset. ARS: anisotropically regularized stresslet, IRSD: isotropically regularized source dipole. (b) The head and side flow profile $|u_x(x,0,0)|$ (red) and $|u_y(0,y,0)|$ (blue). Experimental measurements are represented by dots, numerical simulations by diamonds. Theoretical predictions inside and outside the BEM cell body surface are shown as dashed and solid lines, respectively.
  • Figure 3: (a-b) Entire flow field given by the model in presence of a no-slip wall. Colorbar shows the magnitude of the in-plane flow velocity: (a) $|u| = \sqrt{u_x^2+u_y^2}$ and (b) $|u| = \sqrt{u_x^2+u_z^2}$. (c) The head and side flow profile $|u_x(x,0,0)|$ and $|u_y(0,y,0)|$. Experimental measurements are represented by dots, numerical simulations by diamonds. Theoretical predictions inside and outside the BEM cell body surface are shown as dashed and solid lines, respectively. The inset shows the side flow profile $u_y(0,y,0)$ around the inversion point.