Effects of Near-Field Hydrodynamic Interactions on Bacterial Dynamics Near a Solid Surface

Abstract

Near-field hydrodynamic interactions between bacteria and no-slip solid surfaces are the main mechanism underlying surface entrapment of bacteria. In this study, we employ a chiral two-body model to simulate bacterial dynamics near the surface. The simulation results show that as bacteria approach the surface, their translational velocities and diffusion coefficients decrease. Under the combination of near-field hydrodynamic interactions and DLVO forces, bacteria reach a stable fixed point in the phase plane and follow circular trajectories at this point. In particular, bacteria with left-handed helical flagella exhibit clockwise circular motion on the surface. During this process, as the stable height increases, the near-field hydrodynamic interactions weaken. Consequently, the translational velocity of the bacteria parallel to the surface increases while the rotational velocity perpendicular to the surface decreases, collectively increasing the radius of curvature. Ultimately, our findings demonstrate that near-field hydrodynamic interactions significantly prolong the surface residence time of bacteria. Additionally, smaller stable heights further amplify this effect, resulting in longer residence times and enhanced surface entrapment.

Figures (9)

• Figure 1: Schematic diagram of a bacterium model with a rigid helical flagellum and a spherical cell body swimming near a no-slip solid surface. $\mathbf{r}_{b}$ and $\mathbf{r}_{t}$ are the center positions of the cell body and flagellum, respectively. The closest distance between the cell body and solid surface is $h$, and the inclination angle is $\Psi$. The surface is located on the $xy$-plane.
• Figure 2: The scalar functions (a) $\bar{Y}_{\parallel}^{A}$, $\bar{Y}_{\perp}^{A}$, (b) $\bar{Y}^{B}$, (c) $\bar{Y}_{\parallel}^{C}$ and $\bar{Y}_{\perp}^{C}$ of the resistance matrix as a function of reduced height $h/R_{b}$. (d) DLVO forces of a sphere interacting with a solid surface as a function of the closest distance $h$ for different Debye lengths.
• Figure 3: The normalized velocities of a bacterium approaching the surface perpendicularly. (a) The vertical translational velocity $U_{z}$ as a function of reduced height $h/R_{b}$ normalized by the bulk velocity $U_{\infty}$. The inset is a schematic. (b) The vertical rotational velocity $W_{z}$ as a function of reduced height $h/R_{b}$ normalized by the bulk velocity $W_{\infty}$.
• Figure 4: (a) Stable heights $h^{*}$ and (b) stable inclination angles $\Psi^{*}$ as a function of Debye length for different values of zeta potentials $\zeta$.
• Figure 5: Bacterial velocities and radius of curvature of their circular motion in the surface swimming stage. (a) Horizontal translational velocity, $U_{\parallel}$, as a function of stable height $h^{*}$. (b) Vertical rotational velocity, $W_{\perp}$, as a function of stable height $h^{*}$. (c) Radius of curvature, $r$, as a function of stable height $h^{*}$. (d) Radius of curvature, $r$, as a function of horizontal translational velocity $U_{\parallel}$.