Nonmonotonic diffusion in sheared active suspensions of squirmers

Abstract

We investigate how shear influences the dynamics of active particles in dilute to concentrated suspensions. Using apolar active suspensions of squirmers as model systems, we show how their long-time diffusive dynamics can surprisingly slow down and vary nonmonotonically with the shear rate arising from an interplay between the activity-induced persistent motion and shear-induced reorientation and diffusion. Further simulations of self-propelled particles with tunable persistence exhibit richer dynamics and confirm the observed coupling, suggesting that nonmonotonic diffusion may be a general feature of fluids endowed with an underlying microstructure and large persistence. Our results reveal a nonlinear effect of shear on diffusion in active suspensions, elucidate how internal and external forcing interact, and provide new possibilities to modulate transport in active fluids.

Figures (4)

• Figure 1: Nonmonotonic diffusion in sheared active suspensions. (a) Illustration of 1024 particles at 10% volume fraction ($\phi$) under shear. (b) Mean square displacements in the $yz$-plane for pulling shakers ($\phi=10\%$) at different Péclet numbers, Pe. The inset shows a few sample trajectories at Pe $=0$ and 77.5. (c) Relative diffusion coefficient, $D/D_0$, against Pe for pulling or pushing shakers at different $\phi$. Slopes are theoretical estimates (see text).
• Figure 2: Short-time dynamics and phase diagram. (a) Root-mean-square particle speeds under shear, normalized by their values without shear at all Pe and $\phi$. (b) Normalized velocity autocorrelation for passive particles at different $\phi$ (markers denote $\Phi_v(\dot\gamma \tau_d) = -10^{-2}$) and for pulling shakers under different Pe at $\phi=10\%$ (inset). (c) Phase diagram of all simulation results for shakers, divided by Pe $=1$ and 100 into three diffusive regimes with different scalings.
• Figure 3: Diffusivity of ABPs with different persistence length ($\ell_p$) at $\phi=10\%$. The main plot shows the relative diffusivity in the $y$ direction; the inset in $z$. The downarrows denote Pe$_0 \equiv \min(1,(a/\ell_p)^2)$; the uparrows Pe$_s \equiv \dot\gamma_s a^2/D_{0,\textrm{ABPs}}$, where $\dot\gamma_s \equiv \dot\gamma \tau_d/\min(\tau_s, \tau_r)$.
• Figure 4: Comparison of the different intrinsic and shear-induced diffusivities (in the same unit, $a^2/\tau_a$). The main plot compares the $D_0$ for pulling or pushing shakers with $D_s$ for passive particles at $\dot\gamma_s (\phi=0.2)$. The inset compares $D_{0,\textrm{ABPs}}$ at different $\ell_{p,0}$ (same color legend as in Fig. \ref{['fig:ABPs']}) with $D_s$ at $\dot\gamma_s (\phi=0.4, \ell_{p,0}/a=10)$.