Hydrodynamic Attraction of Swimming Microorganisms by Surfaces

Cells swimming in confined environments are attracted by surfaces. We measure the steady-state distribution of smooth-swimming bacteria (Escherichia coli) between two glass plates. In agreement with earlier studies, we find a strong increase of the cell concentration at the boundaries. We demonstrate theoretically that hydrodynamic interactions of the swimming cells with solid surfaces lead to their reorientation in the direction parallel to the surfaces, as well as their attraction by the closest wall. A model is derived for the steady-state distribution of swimming cells, which compares favorably with our measurements. We exploit our data to estimate the flagellar propulsive force in swimming E. coli.

Figure 1

Representation of the experimental procedure. (a) Smooth-swimming E. coli cells are mixed with a density-matched fluid. (b) The cell mixture is deposited between two glass plates (separation distance $H$). (c) The distribution of swimming cells is imaged as a function of the distance $y$ from the lower surface. (d) Example of an image obtained from data acquisition in the first layer above the glass surface.

Figure 2

Experimental data: number of swimming cells $n$ as a function of the distance to the bottom cover slip $y$ when the distance between the surfaces is $H=100\mu \mathrm{m}$ (top) and $H=200\mu \mathrm{m}$ (bottom). The lines are fits to the data with the model of Eq. (6) with $n_0=1.5$ and $L_{\perp }=34.8\mu \mathrm{m}$ (top, solid line), $n_0=0.3$ and $L_{\perp }=59.1\mu \mathrm{m}$ (top, dashed line), and $n_0=3.9$ and $L_{\perp }=26.4\mu \mathrm{m}$ (bottom, solid line).

Figure 3

Attraction of microorganisms to solid surfaces. (a) The flow field around a swimming cell is well approximated by a force dipole of strength $p>0$, represented by two arrows pointing in opposite directions. (b) Hydrodynamic attraction of a force dipole by a no-slip surface due to the image system on the other side of the surface (force dipole, force quadrupole, source quadrupole). (c) Notations for the model.