Flow characteristics of Chlamydomonas result in purely hydrodynamic scattering

It has long been believed that eukaryotic flagellated swimming cells feel solid boundaries through direct ciliary contact. Specifically, based on observations of behavior of green alga Chlamydomonas reinhardtii it has been reported that it is their “flagella [that] prevent the cell body from touching the surface” [Kantsler et al., Proc. Natl. Acad. Sci. USA 110, 1187 (2013)]. Here, via investigation of a model swimmer whose flow field closely resembles that of C. reinhardtii, we show that the scattering from a wall can be purely hydrodynamic and that no mechanical or flagellar force is needed for sensing and escaping the boundary.

Figure 1

(a) Schematic of the model swimmer, which combines harmonic oscillation of its body length with counter-rotation of propellers. (b) Schematic representation of the model swimmer scattering off a stationary solid wall. ${\theta }_{\mathrm{in}}$ and ${\theta }_{\mathrm{out}}$ are defined with respect to the axis normal to the wall. (c) Snapshots of the oscillatory flow field induced by a single model swimmer in an infinite fluid [19], which mimics the flow field around a C. reinhardtii cell [20]. The red thick bar represents chassis of the swimmer, blue lines demonstrate streamlines, and the timescale is $T=2\pi /{\omega }_s$.

Figure 2

Samples of the hydrodynamic sensing and escaping behavior of microswimmers swimming near a solid boundary (denoted by the thick brown solid line at $X_3=0$). The swimmers initially swim toward the wall with different incidence angles: ${\theta }_{\mathrm{in}}=0^{\circ }$ (a), $5^{\circ }$ (b), ${15}^{\circ }$ (c), ${30}^{\circ }$ (d), ${60}^{\circ }$ (e), and ${85}^{\circ }$ (f). The initial and final (after scattering) states of each case are shown. In each panel, the black thick bar represents the swimmer's body [cf. Fig. 1], trajectory of the swimmer is shown by a dashed line, the start points are denoted by asterisks, and arrows represent the initial direction.

Figure 3

Time variation of the vertical position of a model swimmer approaching the wall with ${\theta }_{\mathrm{in}}=0$, i.e., exactly normal to the wall. Inset is the zoomed view of the tail, which represents the very small-amplitude up-and-down oscillations.

Figure 4

Snapshots of the flow field generated by the model swimmer during scattering process off a solid boundary. The incidence angle is ${\theta }_{\mathrm{in}}={30}^{\circ }$, and panels correspond to $t=T$ (a), $5T$ (b), $10T$ (c), $15T$ (d), $20T$ (e), and $25T$ (f). Purple arrows represent the flow field, and green solid lines demonstrate the corresponding streamlines. Trajectory of the swimmer during $t\in [0,25T]$ is shown by a black dashed line, chassis of the swimmer is denoted by a black thick bar, and the blue (red) filled circles represents propellers initially on the left (right) side of the swimmer.

Figure 5

Comparison between the scattering angles (${\theta }_{\mathrm{out}}$) resulted from purely hydrodynamic numerical simulations of the model swimmer (black filled squares), and the experimental data (green circles) measured by Contino et al. [17] for wild-type C. reinhardtii cells. Angles are given in degrees.

Figure 6

The scattering angle (${\theta }_{\mathrm{out}}$) of the model swimmer and its minimum distance ($d_{\min }$) from the wall as a function of its incidence angle (${\theta }_{\mathrm{in}}$). The black (brown) axis on the left (right) measures the scattering angles (minimum distances from the wall). For each incidence angle, the scattering angle (minimum distance from the wall) of the swimmer is shown by a black unfilled (brown filled) square, right-triangle, and up-triangle for (a) $c_0=$ 5, 50, and 500, respectively; (b) $s_m/a=$ 1, 2, and 4, respectively; and (c) $h_0/a=$ 15, 20, and 25, respectively. The benchmark (also presented in Fig. 5) corresponds to $c_0=50$, $s_m/a=2$, and $h_0/a=20$.