Hydrodynamic interactions destroy motility-induced phase separation in active suspensions

Abstract

Motility-Induced Phase Separation (MIPS) is a distinctive phenomenon in active matter that arises from its inherent non-equilibrium nature. Despite recent progress in understanding MIPS in dry active systems, it has been debated whether MIPS can be observed in wet systems in which fluid-mediated hydrodynamic interactions (HI) are present. We use theory and large-scale {\it Active Fast Stokesian Dynamics} simulations of the so-called squirmer model to show that collision-induced pusher force dipoles, which are present even for the simplest neutral squirmers (stealth swimmers), destroy MIPS when HI are included. Both rotational and translational HI independently suppress phase separation: rotation by shortening a swimmer's persistence length (and thus reducing the swim pressure), translation by a confinement-scale advective fluid flow. We further clarify that collisional dipoles between swimmers and boundaries can generate attractive flows that promote particle aggregation observed in some previous simulations and experiments. Finally, we show how to recover MIPS in fluidic environments by tuning the magnitude of the HI through brush-like surface coatings on the active particles.

Figures (5)

• Figure 1: (A) Sketch of a neutral stealth swimmer. The surface slip velocity $U_S$ is a constant, hence no disturbance flow when swimming alone. (B) A swimmer confined in a liquid film of thickness $h$. At the liquid-air interfaces, zero shear-stress boundary conditions apply. The swimmer's motions are constrained in 2D. (C) Sketch of a collision-induced dipole. During a head-on collision, the hard-sphere repulsion between particles 1 and 2 induces a 'pusher'-like dipolar flow field at leading order.
• Figure 2: Simulation snapshots at steady states for persistent swimmers ($Pe_R=0$) at $\phi=0.6$. Particles are colored by their local crystalline order parameter $|\phi_6|$. (AB) Stealth swimmers $\beta=0$ with full HI at varying film thickness $h/a$. (CD) "pullers" ($\beta>0$) and "pushers" ($\beta<0$) at $h/a=10.0$.
• Figure 3: The effect of pure rotational HI. (A) $D_R^{\mathrm{eff}}$ scaling with packing density $\phi$ at $Pe_R=0.015$. Circles show simulation data for $h/a=5$ with only rotational HI, and squares show simulation data for $h/a=10$ with full HI. Black dash curve fits the scaling as in Eq. (\ref{['eq:DR-scaling']}). The inset shows the scaling fit in a log-log scale. (B) Pressure curves with vertical errorbars for $Pe_R=0.015$, $h/a=100$. Blue curve is the modified swim pressure constructed according to Eq. (\ref{['eq:modified-swim-pressure']}). Black curve is the measured collisional pressure. Purple curve is the hydrodynamic pressure. Red curve is the total mechanical pressure.
• Figure 4: The effects of pure translational HI. (AB) Simulation snapshot for persistent swimmers at $\phi=0.6$, with (A) $h/a=10$ and (B) $h/a=100$. (C) Steady state density profiles along the radial direction, solved from the local model Eq. (\ref{['eq:translationHI-nm']}) assuming axisymmetry. The lines vary from black solid, blue dots, red dash-dots to green dashes as the flow strength parameter $\alpha$ increases. $\alpha=0$ (black solid) corresponds to dry MIPS. The y-axis is normalized by $n$ at maximum packing.
• Figure 5: (A) Collision-induced dipole between a swimmer and wall generates an attractive flow. (B) A larger radius $b$ for the excluded volume interaction than the radius $a$ for the particle-fluid surface, possibly by brush-like surface coating. (C) Simulation snapshot with full HI for $Pe_R=0$, $b/a=2$, $h/a=3$ at steady state. Particles are visualized with excluded volume radius $b$.