Phase Coexistence and Edge Currents in the Chiral Lennard-Jones Fluid

We study a model chiral fluid in two dimensions composed of Brownian disks interacting via a Lennard-Jones potential and a nonconservative transverse force, mimicking colloids spinning at a given rate. The system exhibits a phase separation between a chiral liquid and a dilute gas phase that can be characterized using a thermodynamic framework. We compute the equations of state and show that the surface tension controls interface corrections to the coexisting pressure predicted from the equal-area construction. Transverse forces increase surface tension and generate edge currents at the liquid-gas interface. The analysis of these currents shows that the rotational viscosity introduced in chiral hydrodynamics is consistent with microscopic bulk mechanical measurements. Chirality can also break the solid phase, giving rise to a dense fluid made of rotating hexatic patches. Our Letter paves the way for the development of the statistical mechanics of chiral particles assemblies.

Figure 1

(a) Phase diagram at $k_{B}T=0.47$ comprising a gas (white), chiral liquid (blue), and solid (gray) phases, and a coexistence region (brown). Filled symbols are obtained from density distributions, and the empty ones from the pressure. Black circles come from the analysis of the hexatic order parameter. (b)–(d) Snapshots of the system corresponding to $(\varphi ,\mathrm{\Omega })=(0.3,10)$ (b), (0.7,5) (c), and (0.7,1) (d). Particles are colored according to the projection of the local hexatic order ${\psi }_6(r_i)$ on the global mean orientation.

Figure 2

(a) Equation of state for different values of $\mathrm{\Omega }$ at $k_{B}T=0.47$. The dotted lines correspond to the equal-area construction applied to $\mathrm{\Omega }=0$, 20 curves. (b),(c) Slab configurations at (b) $\mathrm{\Omega }=0$ and (c) $\mathrm{\Omega }=20$ with a detailed view. (d) Corresponding profiles of the difference ${\sigma }^{yy}-{\sigma }^{xx}$ and resulting (e) surface tension $\gamma$ (left $y$ scale), and area $A$ of the pressure loop ($\times {10}^3$) (right $y$ scale).

Figure 3

(a) A chiral drop at $k_{B}T=0.35$ and $\mathrm{\Omega }=5.0$. The global density of the system is $\varphi =0.2$ with $N=16384$ particles. Particles are colored according to their velocity (normalized by the fastest particle one, in log scale). (b) Detailed view of the configuration showing the velocity field. (c) Tangential velocity as a function of the distance from the droplet center for $\mathrm{\Omega }=1\dots 9$. The exponential fits (discontinuous lines) allow to extract the values of $w$ shown in the inset, with the dotted line representing the average value $w=2.57\pm 0.42$. (d) Dependence of the edge velocity $v_e$ with $\mathrm{\Omega }$, showing a linear growth. Inset: ${\eta }_R(\varphi )$, from the computation of ${\sigma }^{xy}$ for $\mathrm{\Omega }=3.0$ (yellow) and $\mathrm{\Omega }=10.0$ (blue) together with the estimation from the edge currents ${\eta }_R=1.32\pm 0.22$ (dotted line).

Figure 4

(a) Global hexatic order $|{\mathrm{\Psi }}_6|$ as a function of $\mathrm{\Omega }$ at fixed $k_{B}T=0.35$ for three different densities. The solid line is a hyperbolic tangent fit. (b) Exponential decay of $G_6(r)$ for systems at $\varphi =0.70$ and different values of $\mathrm{\Omega }$, shown in the color map. Inset: corresponding correlation lengths $\xi$. (c) Displacement field $\delta \mathit{r}$ in a chiral liquid configuration ($k_{B}T=0.35$, $\varphi =0.70$, $\mathrm{\Omega }=3.0$) (darker arrows indicate larger displacements). (d) Detailed view showing the local bond orientation $\mathrm{Arg}({\psi }_6)$ together with particle displacements.