Fig. 1.

Confinement effect on flow stability and collective motion. Lines indicate calculated confined critical volume fraction ${\varphi }_c\left(H\right)$, according to CKT using Eq. 4 and the experimentally measured ${\varphi }_c\left(H=400\hspace{0.17em}\mathrm{\mu }\text{m}\right)\approx 0.75\%$ (Fig. 4 I and J) as ${\varphi }_c^{\infty }$. ${\varphi }_c\left(H\right)$ defines the boundary between stable (below) and unstable (above) pusher suspensions for different persistence time $\tau$ of the swimmers, as indicated in the key, with speed $v=15\hspace{0.17em}\mathrm{\mu }\text{m}\hspace{0.17em}{\text{s}}^{-1}$. Symbols: experimental observation of flow with (filled squares) and without (open squares) banding; and with (filled circles) or without (open circles) large correlation length-scale $l$, based on rheo-imaging (squares) and phase-contrast imaging (no flow; circles), respectively. See Fig. 4 and related main text for more details. Red: Data from ref. 15 at $H=60\hspace{0.17em}\mathrm{\mu }\text{m}$ (an $x$ offset is applied to squares for better visualization).