Figure 1

Schematic of a right-handed helix in simple shear flow. Red shading and black shading show the top and bottom halves of the helix. Upper inset: The net force acting on one pitch of the helix is along $-\widehat{\mathbf{z}}$. Lower inset: Predicted normalized drift velocity $v/v_0$ versus helix orientation $\theta$. $\theta$ is the angle between a helix in the $x\mathrm{\text{−}}y$ plane and the flow, and $v_0$ is the drift velocity of a helix aligned with the flow ($\theta =0$).Reuse & Permissions

Figure 2

(a) Scanning electron micrograph (SEM) of L. biflexa flaB mutant, with typical dimensions (inset). The bent configuration is a result of SEM preparation and live organisms are nearly always straight. (b) Microchannel design with separate inlets for spirochetes and buffer. The color-coded squares refer to the locations of data collection [Fig. 3b]. (c) Schematic of the separation process (for one enantiomer) in the microchannel ($W=1\mathrm{mm}$, $H=90\mu \mathrm{m}$, $w\approx 100\mu \mathrm{m}$). The lateral drift direction depends on the sign of the shear $\dot{\gamma }$, resulting in divergence of top and bottom streams.Reuse & Permissions

Figure 3

The observed spirochete distribution across the channel at (a) $x=2\mathrm{cm}$ and (c) $x=107.5\mathrm{cm}$. Colors represent populations at different depths $y$: top (orange), mid (black), and bottom (blue) [see Fig. 2c]. The midpoint of each rectangle corresponds to the mean position ($\overline{z}$) of the distribution, while the half-width is 2 standard deviations ($2\sigma$). (b) Probability density function of spirochete distribution at various distances $x$ along the channel [see Fig. 2b]. The thick pink and green profiles correspond to (a) and (c), respectively. (d)–(f) Quantification of lateral drift and separation along $x$. (d) Mean position of the population at three depths. (e) Divergence between the top and bottom populations. (f) Separation efficiency. In all panels, full circles refer to spirochete data, lines are linear fits, and empty squares are experiments with spherical beads. Over 10 000 spirochetes were imaged and located at each position ($x,y$).Reuse & Permissions

Figure 4

Size limit for separation of isometric helices of length $L$ and equivalent aspect ratio $r=70$. Dashed contours show constant Re (spaced by a factor of 10) and the thick contour is $\mathrm{Re}=0.1$. Solid contours show constant Pe. The gray scale shows $\overline{v}/v_0$, where $v_0$ is the drift velocity of a helix aligned with the flow. The smallest helices which can be separated for a given shear rate, determined by $\overline{v}/v_0=0.66$ ($\mathrm{Pe}=50$, marked by circle on inset) and $\mathrm{Re}<0.1$, have $L\approx 20$ (square), 80 (circle), and 400 nm (diamond) for $\dot{\gamma }\approx {10}^8$, ${10}^6$, and ${10}^4{\mathrm{s}}^{-1}$, respectively. Full symbols mark the parameter regimes of our experiments: $\mathrm{Re}=0.03$ (triangle) and $\mathrm{Re}=5$ (hexagon). Inset: $\overline{v}/v_0$ vs Pe.Reuse & Permissions