Hydrodynamic Trapping of Swimming Bacteria by Convex Walls

Swimming bacteria display a remarkable tendency to move along flat surfaces for prolonged times. This behavior may have a biological importance but can also be exploited by using microfabricated structures to manipulate bacteria. The main physical mechanism behind the surface entrapment of swimming bacteria is, however, still an open question. By studying the swimming motion of Escherichia coli cells near microfabricated pillars of variable size, we show that cell entrapment is also present for convex walls of sufficiently low curvature. Entrapment is, however, markedly reduced below a characteristic radius. Using a simple hydrodynamic model, we predict that trapped cells swim at a finite angle with the wall and a precise relation exists between the swimming angle at a flat wall and the critical radius of curvature for entrapment. Both predictions are quantitatively verified by experimental data. Our results demonstrate that the main mechanism for wall entrapment is hydrodynamic in nature and show the possibility of inhibiting cell adhesion, and thus biofilm formation, using convex features of appropriate curvature.

Figure 1

(a) A scanning electron micrograph of the PDMS-based microdevice containing several micropillars. The height of the posts is $75\mu \mathrm{m}$. The scale bar is $250\mu \mathrm{m}$. (b) A montage of fluorescence microscopy images of a bacterial cell following the curved surface of a micropillar. The time between each position of the cell shown is 2.5 s. The arrow indicates the swimming direction of the cell. The perimeter of the pillar is indicated by a solid red line. The scale bar is $100\mu \mathrm{m}$.

Figure 2

(a) The measured ratio of the cells that followed the wall of a pillar after collision (open circles) and the model prediction for the fraction of trapped cells (solid line). The dashed line represents the value for flat walls. The gray shaded area extends for one standard deviation above and below the predicted result. (b) The average tracing speed of bacteria near pillars. The dashed line represents the average speed in bulk. (c) The measured average residence time of bacteria for each pillar (open circles) and the model prediction (solid line). The error bars indicate standard errors.

Figure 3

A schematic illustration and notation for the hydrodynamic model proposed in the text.

Figure 4

A histogram of the average angles of orientation of individual cells with respect to the solid wall ($n=58$). The inset shows a montage of frames with a swimming bacterium near a planar solid wall. The red line shows the surface of the wall. The scale bar is $5\mu \mathrm{m}$.

Figure 5

(a) A representative fluorescence microscopy image showing the bacterial cells adhered to the surface of the micropillars. The scale bar is $200\mu \mathrm{m}$. (b) The fluorescence pixel intensity over a unit area in the vicinity ($3\mu \mathrm{m}$) of pillars and next to a planar wall. The dashed line represents the value for flat walls.