Shear-Induced Collective Shape Oscillations in Dense Soft Suspensions

TL;DR

This work addresses how dense suspensions of deformable particles respond to external flow. Using a two-dimensional multi-phase-field model, it shows that steady shear first induces positional and orientational order and then drives robust self-sustained shape oscillations via repeated T1 neighbor exchanges. A minimal one-degree-of-freedom model, built around the lattice angle $\phi$ and an orientation angle $\theta$, reproduces the oscillations through a piecewise, clocked dynamics for $\theta$ and a nonlinear ODE for the elongation $r$, with $\phi(t)$ fit by $\phi(t) = (\pi/12)\cos^2(\omega t) + \pi/4$. The approach demonstrates a generic route to time-dependent collective behavior in dense soft suspensions and shows that the mechanism persists under Poiseuille flow, implying potential rheological consequences for emulsions, vesicles, capsules, and cells.

Abstract

Dense suspensions of deformable particles can exhibit rich nonequilibrium dynamics arising from complex flow-structure coupling. Using a multi-phase field model, we show that steady shear drives an initially disordered, dense, soft suspension into a positionally and orientationally ordered state, within which particles undergo robust self-sustained shape oscillations. These oscillations originate from repeated T1 neighbor exchanges that force the ordered particle lattice to cyclically traverse different ordered configurations, coupling particle deformation to evolving lattice topology. By identifying the lattice angle as a key variable, we construct a minimal one-degree-of-freedom model that quantitatively captures the limit cycle oscillation. Because these mechanisms rely only on deformability, packing, and shear, they provide a generic route to collective time-dependent behavior in dense soft suspensions.

Figures (6)

• Figure 1: Order emerges from induced shear flow. a) Bond and nematic order as a function of shear rate. The order parameters were calculated using the last $50$ time frames of the simulations, each with a total of $250$ time frames. These results were averaged over $10$ different samples. The shaded region represents the standard deviation of this average. b) Schematic representations of the phase field simulations, where the axis of elongation is placed at the center of each phase field in red. Each schematic corresponds to one of the vertical dashed lines in panel a).
• Figure 2: Shape oscillations in the phase field model. a) Snapshots of phase field configurations (top) and corresponding Voronoi constructions (bottom) at different times during one period of shape oscillation. For each, the angle of the orientation ($\theta$) and the lattice angle ($\phi$), taken from the Delaunay neighbors of each phase field, are shown, for different points in time. b) Period of shape oscillations as a function of the shear rate for the phase field model with regular initial conditions. The axis are in logscale and a line with slope one is drawn, highlighting the linear dependence of the period with shear rate. Two limit cycles in polar coordinates are shown which correspond to $\dot{\gamma}=0.0778$ and $\dot{\gamma}=0.3857$ (green and red respectively). The radial coordinate corresponds to the elongation of particles $r$, and the polar angle to their nematic director from the $x$-axis ($2\theta$).
• Figure 3: Comparison of shape oscillations between models with increasing shear rate. Plots of the elongation, $r(t)$ for different values of the shear rate. $\dot{\gamma} = (0.0778, 0.1487, 0.3857)$ for $a), b)$ and $c)$ respectively. Red lines represent the solutions calculated numerically from the minimal model in Eq. \ref{['r:eqn']}, while the green dots correspond to the results from phase-field simulations.
• Figure 4: Single phase field under shear flow. Elongation of the phase field as a function of time for shear rate, $\dot{\gamma}=1$.
• Figure 5: Lattice configuration fits to simulation data. Fitting curves (red) of the function $\phi=A\cos^2(kt)$ to simulations data (green), for $A=10.6$. In a) fitting is shown for $\dot{\gamma}=0.0778$ and in b) for $\dot{\gamma}=0.3857$. The fitting parameter $k=0.01$ is independent of shear rate.