Bacterial detachment from a wall with a bump line

The interactions of bacteria with surfaces have important implications in numerous areas of research, such as bioenergy, biofilm, biofouling, and infection. Recently, several experimental studies have reported that the adhesion of bacteria can be reduced considerably by microscale wall features. To clarify the effect of wall configurations, we numerically investigated the behavior of swimming bacteria near a flat wall with a bump line. The results showed that the effects of bump configuration are significant; a detachment time larger than several seconds can be achieved in certain parameter sets. These results illustrate that the number density of bacteria near the wall may be reduced by appropriately controlling the parameter sets. When background shear flow was imposed, the near-wall bacterium mainly moved towards the vorticity axis. The detachment time of cells increased significantly by adjusting the bump line to have ${45}^{\circ }$ relative to the flow direction. The knowledge obtained in this study is fundamental for understanding the interactions between bacteria and surfaces according to more complex geometries, and is useful for reducing the adhesion of cells to walls.

Figure 1

Schematic diagram of the bacterial model and the problem settings. A flat wall exists at $z=0$, and the bump line is aligned with the $y$ axis. $\mathit{e}$ is the unit orientation vector of the bacterium, and ${\mathit{e}}^{\prime }$ is the projection on the x-y plane. $\theta$ is the orientation angle relative to the bump line. Simple shear flow may be applied as $\mathit{u}=\dot{\gamma }z{\mathit{e}}_u$, where ${\mathit{e}}_u$ is the direction of flow and $\dot{\gamma }$ is the shear rate. $\phi$ is the orientation angle relative to the shear flow. Bacterial shape parameters are set as $2\pi /k=2.0$, $\mathrm{h}=0.25$, and the radius of the flagellum is $r_f=0.1$.

Figure 2

Sample bacterial trajectories and the minimum distance between the wall and the bacterium. (a) Case A, a cell crossing the wall ($\delta h=0.1,\delta w=1.6,{\theta }_0={135}^{\circ }$); (b) case B, a cell detaching and returning from the wall ($\delta h=1.0,\delta w=1.6,{\theta }_0=90{}^{\circ }$); and (c) case C, a cell detaching and crossing the wall ($\delta h=2.0,\delta w=1.6,{\theta }_0={135}^{\circ }$). (d) Time change of the minimum distance ${\varepsilon }_{\min }$ between the wall and the bacterium in cases A–C.

Figure 3

Time change of the minimum distance ${\varepsilon }_{\min }$ between the wall and the bacterium. (a) Effect of the bump height $\delta h(\delta w=1.6,\theta ={90}^{\circ }$). (b) Effect of the bump width $\delta w(\delta h=2.0,{\theta }_0={90}^{\circ }$). The inset indicates the final configuration of the bacterium in the case of $\delta w=1.6$. (c) Effect of the initial orientation angle ${\theta }_0(\delta h=2.0,\delta w=1.6$).

Figure 4

Color contour of the detachment time. Black lines separate the behaviors of bacteria between across and return cases: (a) diagram plotted in $\delta h\text{–}\delta w$ space with ${\theta }_0={90}^{\circ }$, and (b) diagram plotted in $\delta h\text{–}{\theta }_0$ space with $\delta w=1.6$.

Figure 5

Behaviors of bacteria in shear flow near a flat wall without the bump. Initially, the minimum distance was set as ${\varepsilon }_{\min }=4.5$, and the orientation relative to the shear flow ${\phi }_0$ was varied. (a) Trajectories with shear rate $\dot{\gamma }=0.1$, (b) trajectories with $\dot{\gamma }=0.01$, and (c) final orientation of bacteria as a function of $\dot{\gamma }$ and ${\phi }_0$. $e_y=1$ indicates that the bacterium is oriented with the positive $y$ axis, whereas $e_y=-1$ indicates that the bacterium is oriented with the negative $y$ axis.

Figure 6

Time change of the minimum separation distance ${\varepsilon }_{\min }$ with ${\theta }_0={90}^{\circ }$. The shear rate is $\dot{\gamma }=0.1$, and the bump configurations are $\delta w=3.2$ and $\delta \mathrm{h}=2.0$.

Figure 7

Behavior of bacteria with ${\theta }_0={45}^{\circ }$ and ${135}^{\circ }$. The shear rate is , and the bump configurations are $\delta w=1.6$ and $\delta \mathrm{h}=2.0$. (a) Trajectory and attitude of the bacterium with ${\theta }_0={45}^{\circ }$. (b) Trajectory and attitude of the bacterium with ${\theta }_0={135}^{\circ }$. (c) Time change of the minimum separation distance ${\varepsilon }_{\min }$.

Figure 8

Time change of the minimum separation distance ${\varepsilon }_{\min }$ of the bacteria with ${\theta }_0={45}^{\circ }$. The height of the bump is varied from 0.1 to 2.5. The shear rate is $\dot{\gamma }=0.1$, and the bump width is $\delta w=1.6$.