Breakup of an active chiral fluid

Abstract

The nonlinear breakup dynamics of a strip of active chiral fluid is considered, and it is shown that the strip thickness goes to zero as a power law in finite time. Applying slender body theory to the hydrodynamic equations of active chiral fluids, we predict the exponents analytically, and our predictions are shown to be in excellent agreement with numerical simulations. Qualitative agreement between experiment and simulation is also found.

Figures (4)

• Figure 1: (a) Experimental evidence of two dimensional strips of chiral fluid breaking up asymmetrically, provided courtesy of the William Irvine group. The arrow marks the direction of time, with the strip going unstable before breaking up into drops. The whole process happens in a few seconds. (b) Sketch of a strip of chiral fluid undergoing an instability leading to breakup. The top and bottom surfaces are at $z=\pm h^{\pm}(x)$, the characteristic vertical scale is $h_0$, the horizontal scale is $L$, and their ratio is $\epsilon=h_0/L$. The dot-dashed orange line marks the centerline of the strip at $z=c(x)$, and the arrows inside the strip show the chiral shear flows
• Figure 2: (a) Numerical solution of equations (\ref{['eqn:dimfull 1d equations']}) over a periodic domain. The light orange line shows the initial profile, and the sequence of darkening lines show the strip as time progresses; the black arrow marks the direction of time. (b) The thickness function $h$ is symmetric about $x=0$ as time progresses, and as breakup is approached the minimum strip thickness decreases to zero. In all plots lengths are measured in units of $\ell_R = \gamma(\eta+\eta_R)/(\eta\eta_R \Omega)$.
• Figure 3: A comparison between the experimental data from \ref{['fig:experimental break and schematic']}(a), shown in shades of orange, and numerical simulations, shown as dashed black lines. The simulations are initiated from an initial condition that smoothly approximated the experimental data, and each line in both sets are equally spaced in time. We see qualitative agreement between the experiment and simulation, with the timescale the only adjustable parameter.
• Figure 4: (a) Scaling of the minimum strip thickness as a function of the time to breakup, $t'$. The black line is from the PDE simulation, and the orange dashed line is the power law ${t'}^{1.24}$. (b) The scaling function $f$. The solid orange line gives the prediction from our scaling theory; the dashed, dot-dashed, and chain-dashed lines come from the PDE simulation at $t'=7\times 10^{-6},1.8\times 10^{-4},7\times 10^{-4}$. The agreement between the PDE results and theory improves as breakup is approached.