Fig. 6: (Modeling results) A continuous active fluid simulation reveals that the mixing time of ATP depends on the dimensionless molecular diffusion coefficient of ATP and the dimensionless activity level of active fluid.
From: Self-mixing in microtubule-kinesin active fluid from nonuniform to uniform distribution of activity
a Table of ATP concentration (top panels) and active fluid flow speed (bottom panels) maps for various dimensionless activity levels \({\alpha }_{0}^{*}\) and molecular diffusion coefficients \({D}^{*}\). When the fluid has no activity (\({\alpha }_{0}^{*}=0\); left column), ATP disperses to the right side of the system only by molecular diffusion; the dispersion is enhanced when the active fluid starts to flow and actively transport ATP (\({\alpha }_{0}^{*}=25\); middle column). The dispersion is further enhanced when ATP diffuses significantly faster (\({D}^{*}=\) 64; right column) (Supplementary Movie 4). b Evolution of normalized multiscale norm for \({\alpha }_{0}^{*}=\) 0–25 while keeping \({D}^{*}=\) 16. The normalized multiscale norms decay exponentially with time: \(\hat{s}={{\exp }}\left(-{t}^{*}/{t}_{0}^{*}\right)\), where \({t}_{0}^{*}\) is the dimensionless mixing time. Inset: Dimensionless mean speed of active fluid in active region \({\bar{v}}_{{{{{{\rm{ab}}}}}}}^{*}\) monotonically increases with dimensionless activity level \({\alpha }_{0}^{*}\). c Dimensionless ATP mixing times, \({t}_{0}^{*}\), as a function of dimensionless activity level, \({\alpha }_{0}^{*}\), for various dimensionless molecular diffusion coefficients, \({D}^{*}\). Increasing both \({\alpha }_{0}^{*}\) and \({D}^{*}\) decreases mixing time monotonically. Each error bar in \({t}_{0}^{*}\) represents the fitting error of \(\hat{s}\) vs. \({t}^{*}\) to \({{{{{\rm{ln}}}}}}\hat{s}=-{t}^{*}/{t}_{0}^{*}\) (Panel b). Inset: Active-inactive interface progression exponent \(\gamma\) as a function of dimensionless activity level \({\alpha }_{0}^{*}\) for dimensionless molecular diffusion coefficients \({D}^{*}=\) 2 (dark blue), 4 (dark green), and 8 (light green). Each error bar in \(\gamma\) represents the slope fitting error as in Fig. 2a. Increasing \({D}^{*}\) decreases \(\gamma\) (from dark blue to light green curve), whereas increasing \({\alpha }_{0}^{*}\) increases \(\gamma\) (dark green curve).
