Fig. 5: (Experimental results) Dispersion of UV-activated fluorescent dyes in active-inactive fluid systems.

Active fluid flows promote mixing of UV-activated fluorescent dyes, which are initially activated in the left-hand side of the container only. a Dispersion of UV-activated fluorescent dyes (magenta) in inactive (\({\bar{v}}_{{{{{{\rm{ab}}}}}}}=\) 0; left column) and active (\({\bar{v}}_{{{{{{\rm{ab}}}}}}}=\) 8.2 µm/s; right column) microtubule-kinesin fluid. Active fluid flows actively transport fluorescent dyes and enhance their dispersion. Time stamps are hour:minute:second. (See also Supplementary Movie 3.) b Selected examples of normalized multiscale norm vs. time for different active bulk flow speeds, \({\bar{v}}_{{{{{{\rm{ab}}}}}}}\). Normalized multiscale norm \(\hat{s}\left(t\right)\) decreases faster in a faster-flowing active fluid system. Inset: The normalized multiscale norm, \(\hat{s}\left(t\right)\), in log-linear axes behaves as a straight line, which suggests that the norm decays exponentially with time. The decay time scale \({t}_{0}\) (or mixing time) is determined by fitting the normalized multiscale norm versus time data to \({{{{{\rm{ln}}}}}}\hat{s}=-t/{t}_{0}\) with \({t}_{0}\) as the fitting parameter (dashed blue line). c The mixing time decreases monotonically with Péclet number, which demonstrates that a stronger convection mechanism leads to faster mixing of suspended components. Each dot represents one experimental measurement. Each error bar in \({t}_{0}\) represents the slope fitting error in \({{{{{\rm{ln}}}}}}\hat{s}=-t/{t}_{0}\) (Panel b inset), and each error bar in \({{{{{\rm{Pe}}}}}}\) (defined as \({{{{{\rm{Pe}}}}}}\equiv {\bar{v}}_{{{{{{\rm{ab}}}}}}}{l}_{{{{{{\rm{c}}}}}}}/D\)) represents propagated uncertainties from \({\bar{v}}_{{{{{{\rm{ab}}}}}}}\) (see inset) and \({l}_{{{{{{\rm{c}}}}}}}\) (see Supplementary Fig. 5d). Inset: Mixing time, \({t}_{0}\), as a function of active bulk mean speed, \({\bar{v}}_{{{{{{\rm{ab}}}}}}}\). Each error bar in \({t}_{0}\) is the same as in Panel c, and each error bar in \({\bar{v}}_{{{{{{\rm{ab}}}}}}}\) represents the standard deviation of flow speeds in the active region. Notably, the mixing time of the inactive fluid system (\({\bar{v}}_{{{{{{\rm{ab}}}}}}}=\) 0) is 24 hours (top-left dot); minimally activating the fluid (\({\bar{v}}_{{{{{{\rm{ab}}}}}}}=\) 2 µm/s) reduces the mixing time to 8 hours.