Non-equilibrium (thermo)dynamics of colloids under mobile piston compression

Abstract

We investigate the non-equilibrium compression of a confined hard-sphere colloidal fluid driven by a mobile boundary within dynamical density functional theory. The system consists of a fluid confined between two parallel walls, one acting as an overdamped piston subjected to a sudden increase in external pressure. The piston motion is controlled by a mobility parameter $K$, which sets the relative timescale between mechanical driving and diffusive relaxation. By varying $K$ over several orders of magnitude, we identify a crossover from quasi-static compression to a diffusion-limited strongly driven regime. For small $K$, the system evolves close to equilibrium and the total injected work approaches the equilibrium free-energy difference. For large $K$, the piston rapidly adjusts and the dynamics becomes governed by diffusive relaxation, leading to saturation in the piston trajectory, pressure--position relation, particle currents, and center-of-mass velocity. In this regime, the injected work and entropy production are bounded, reflecting constraints imposed by diffusive transport. The maximum injected power scales linearly with $K$, while the entropy-production peak exhibits a crossover from quadratic growth to saturation, with peak times displaying $1/K$ scaling. The entropy change of the thermal bath interpolates between a reversible limit and a strongly driven dissipative regime. Finally, the evolution of configurational entropy and external potential energy reveals a dynamical decoupling between confinement and structural relaxation, including transient non-monotonic behavior. These results provide a quantitative thermodynamic characterization of boundary-driven compression.

Figures (10)

• Figure 1: (a) Schematic illustration of a hard-sphere fluid confined between two parallel walls. The right boundary is an overdamped mobile piston subjected to an externally imposed pressure $P_{\mathrm{ext}}$. (b) Equilibrium density profiles of the hard-sphere fluid in the initial and final states (solid black and dashed blue lines, respectively), corresponding to an initial piston pressure $P_0^* = 0.128$ with wall separation $L^*_0 = 10$, and to the final compressed equilibrium state under $P^*_{\mathrm{ext}} = P_\infty = 0.5$ with final piston position $L^*_\infty = 6.158$, respectively. In both cases the reduced mean particle density is $\rho^* = 0.05$.
• Figure 2: (a) Time evolution of the non-equilibrium density profiles during the compression process. From top to bottom, the panels correspond to $K^* = 0.1$, $10$, and $1000$. In the top panel, square and triangle symbols indicate the limiting equilibrium density profiles obtained at reduced pressures $P_\mathrm{R}^* = 0.128$ and $P_\mathrm{R}^* = 0.5$, respectively.
• Figure 3: (a) Time evolution of the distance between walls during the compression process, $L^*(t)$, for values of the mobility parameter $K^*$ ranging from $0.1$ to $10000$. (b) Collapse of $L^*(t)$ onto a common master curve when plotted as a function of the normalized time $t/\tau_{\mathrm{K}}$ in the regime $K^* \ll 1$. The solid black line represents the theoretical master curve given by Eq. \ref{['eq:lamejorfuncion']}. (c) Time evolution of the pressure exerted by the hard-sphere fluid on the mobile hard wall, $P_\mathrm{R}^*(t)$, for values of $K^*$ between $0.1$ and $10000$. (d) Scaling collapse of $P_\mathrm{R}^*(t)$ as a function of $t/\tau_{\mathrm{K}}$ in the regime $K^* \ll 1$, yielding a universal curve described by Eq. \ref{['eq:lasegundamejorfuncion']}.
• Figure 4: (a) Comparison between the time evolution of the pressure on the hard and left walls. (b) Pressure on the hard wall as a function of the distance between walls, $P_\mathrm{R}^*(L)$ for values of $K^*$ from $0.01$ to $1000$ ($P_0^*=0.128$ and $P_\mathrm{ext}^*=0.5$). Square symbols represent the equilibrium equation of state (EoS) of the confined colloids obtained from equilibrium DFT, $P_\mathrm{eq}^*(L^*)$. Black dashed line represents the limiting behavior obtained for pistons with very high piston mobility ($K^*\rightarrow \infty$).
• Figure 5: Time evolution of the mean particle velocity for values of $K^*$ ranging from $0.1$ to $10000$. Negative values indicate that particles move, on average, toward the left as a result of the action of the compressing piston.