Dissipation and microstructure in sheared active suspensions of squirmers

Abstract

We study the energy expenditure and structural correlations in semi-dilute to concentrated suspensions of squirmers using active fast Stokesian dynamics simulations. Specifically, we simulate apolar active suspensions of squirmers, or 'shakers,' and show that shear enhances the total dissipation but reduces the relative viscosity for both puller- and pusher-type shakers. At low shear rates where activity dominates, pushers dissipate more energy than pullers, and more so at higher volume fractions, in contrast to bacterial suspensions displaying a 'superfluid' transition. At high shear rates where shear dominates, pullers and pushers behave effectively as passive spheres, generating negative normal stress differences due to shear-induced collision. Remarkably, the rate-dependent rheological responses are accompanied by unusual microstructural signatures of an enhanced nematic order and anisotropic pair correlation, both of which contribute to a higher viscosity under shear. Further simulations of self-propelled, neutral squirmers exhibit similar but weaker shear-thinning, highlighting the importance of activity over motility, underpinned by hydrodynamic interactions. Overall, our results elucidate the interplay of internal activity and external flow on the dissipation and microstructure in sheared active suspensions of squirmers.

Figures (13)

• Figure 1: Suspensions of 1024 shakers under shear ($B_2=0.2$, $\dot\gamma = 0.1$), colored by their instantaneous dissipation (darker particles are more dissipative), at various $\phi$.
• Figure 2: Dissipation in suspensions of shakers without shear. (a) Temporal evolutions of the internal dissipation, relative to that of isolated shakers at the same volume fraction $\phi$, for pulling and pushing shakers at $\phi=10\%$ and 40%. Three random initial conditions are plotted in each case. (b) Average dissipation at steady state for both pullers and pushers, where the vertical bars represent one standard deviation (same in other similar plots). Inset shows the temporal evolutions of $\Phi_0/\Phi_\text{iso}$, as well as its hydrodynamic and interparticle contributions, for pullers and pushers (same color legend as in a) at $\phi=40\%$.
• Figure 3: (a) Total dissipation under shear $\Phi$, relative to its value without shear $\Phi_0$, as a function of Pe at different volume fractions $\phi$ for suspensions of pullers and pushers; see panel (b) for the legends. Inset shows a decomposition of $\Phi$ into $\Phi_\text{ext}$ and $\Phi_\text{int}$ for pulling shakers at $\phi=10\%$. (b) Relative dissipation $\varepsilon_r$ as a function of Pe at different $\phi$.
• Figure 4: Relative viscosity $\eta_r$. (a) Rate-dependence of $\eta_r$ at different volume fractions $\phi$ for suspensions of pulling or pushing shakers. (b) $\phi$-dependence of $\eta_r$ for pulling or pushing shakers at Pe $\approx 1$ and $10^3$, as well as for passive particles as Pe $\to \infty$ (by turning off activity). The experimental results of Rafai2010 at Pe $\approx 0.1$ are also plotted; c.f. Fig. 2b therein. Lines are the Einstein viscosity or fits to Eq. \ref{['eq:kd']}.
• Figure 5: (a) Relative viscosity as a function of Pe for ABPs, shakers, and C. reinhardtii (extracted from Fig. 2(a) in Rafai2010, based on $a=5$$\mu$m and $D=995$$\mu$m$^2/s$) at 10% volume fraction. The dashed line is the theoretical prediction of Takatori2017 at $\ell_{p,0}/a=1.5$. Inset shows the ABP viscosity as a function of Pe. (b) The normalized cross-diffusivity, $D_{xy}/D_{0}$, as a function of Pe for ABPs at $\phi=10\%$ (data with large uncertainties are removed). Inset shows the theoretical relative viscosity predicted from the particle dynamics, where markers correspond to direct application of the swim stress-diffusivity relation using the fitted $D_{xy}$, and lines are calculations based on Eq. \ref{['eq:Takatori']} (same color coding as in the main figure).