MIPS is a Maxwell fluid with an extended and non-monotonic crossover

Abstract

Understanding the mechanical properties of active suspensions is crucial for their potential applications in materials engineering. Among the various phenomena in active matter that have no analogue in equilibrium systems, motility-induced phase separation (MIPS) in active colloidal suspensions is one of the most extensively studied. However, the mechanical properties of this fundamental active state of matter remain poorly understood. This study investigates the rheology of a suspension of active colloidal particles under constant and oscillatory shear. Systems consisting of pseudo-hard active Brownian particles exhibiting co-existence of dense and dilute phases behave as a viscoelastic Maxwell fluid at low and high frequencies, displaying exclusively shear thinning across a wide range of densities and activities. Remarkably, the cross-over point between the storage and loss moduli is non-monotonic, rising with activity before the MIPS transition but falling with activity after the transition, revealing the subtleties of how active forces and intrinsically out-of-equilibrium phases affect the mechanical properties of these systems.

Figures (4)

• Figure 1: Storage moduli $G'$ (closed circles) and loss moduli $G"$ (open squares) with oscillation amplitude $A_x/L_y=5\%$ (SAOS regime) for $\rho=0.5$ and different activities $\text{Pe}_\text{a} = 0$ (blue), $42$ (green) and $120$ (red). Dashed and straight lines are visual guides to show the expected Maxwell scaling of $\omega^1$ and $\omega^2$.
• Figure 2: Dimensionless crossover frequency $\text{Pe}_\text{s}^\dagger= \frac{A_xd^2}{L_y D_t} \omega_c$ for storage $G'$ and loss $G"$ moduli shown in Fig. \ref{['fig:fig1']} as a function of dimensionless activity $\text{Pe}_\text{a}$ at density $\rho =0.5$ for oscillation amplitude $A_x/L_y=5\%$ (SAOS regime). Shaded area represents the MIPS phase separation boundary (see SI SI). Insets: Snapshots corresponding to the colored points and semi-log plot. The dashed curve fits to $\omega_c\sim a_\omega+b_\omega\, \text{Pe}_\text{a}^2$ for $\text{Pe}_\text{a}<5$ and continuous curve fits to $\omega_c \sim a_\omega'+b'_\omega\, \text{Pe}_\text{a}$ for $5<\text{Pe}_\text{a}<30$ (see SI for more details).
• Figure 3: Effective viscosity $\eta$ as a function of dimensionless frequency $\text{Pe}_\text{s}$ with oscillation amplitude $A_x/L_y=5\%$ (SAOS regime) for density $\rho=0.5$ and different activities: $\text{Pe}_\text{a} =0$ (blue), $42$ (green) and $120$ (red). Viscosity computed from Fig. \ref{['fig:fig1']} using Eq. \ref{['eq:visc']}. Inset: Zero-shear limit $\eta_0=\lim_{\text{Pe}_\text{s}\to0}\eta$ as a function of activity. Colored points are the same as in Fig. \ref{['fig:fig2']}
• Figure 4: (a) Average out-of-diagonal stress component $\langle \sigma_{xy}\rangle$ for constant shearing as a function of dimensionless shear rate $\text{Pe}_\text{s}$ for density $\rho=0.5$ and dimensionless activities $\text{Pe}_\text{a}$=6 (blue), 42 (green), 66 (orange) and 120 (red). (b) Power law exponents for the curves shown in panel (a) as a function of dimensionless activity $\text{Pe}_\text{a}$ for $\rho=0.5$. Inset: The dependency of the exponent $n$ on density $\rho$ for $\text{Pe}_\text{a}=120$.