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

Technical Deep Dive: Non-equilibrium (Thermo)dynamics of Colloids under Mobile Piston Compression

Overview

This work investigates the non-equilibrium compression of a confined colloidal fluid driven by a mobile boundary using dynamic density functional theory (DDFT). The system consists of a hard-sphere fluid confined between two parallel walls, with one wall acting as an overdamped piston subjected to a sudden increase in external pressure. The piston mobility, parametrized by a mobility coefficient $K$, is varied over several orders of magnitude to explore different dynamical regimes.

Methodology

• The DDFT framework is used to describe the time evolution of the one-body particle density field under the influence of the external piston-driven potential.
• The piston motion is modeled as an overdamped dynamics, where the piston velocity is linearly proportional to the pressure imbalance between the fluid and the externally imposed pressure.
• The non-equilibrium thermodynamics is analyzed by tracking the evolution of the free energy, entropy production, and mechanical work injected by the piston.

Results

Microscopic Dynamics

• For slow piston mobilities ($K^* \ll 1$), the system evolves quasi-statically, with the density profiles closely following the instantaneous piston position.
• As the piston mobility increases, strong non-equilibrium effects emerge, characterized by pronounced asymmetries in the density and current profiles.
• In the high-mobility regime ($K^* \gg 1$), the piston rapidly adjusts, and the subsequent dynamics becomes controlled by the intrinsic diffusive relaxation of the confined fluid.

Macroscopic Dynamics

• The piston position, pressure, and mean fluid velocity exhibit distinct dynamical regimes controlled by the piston mobility $K^*$.
• For slow mobilities, the piston motion follows a universal scaling form. For fast mobilities, the system exhibits a two-stage relaxation with an initial rapid piston adjustment followed by a slower diffusion-limited regime.
• The injected mechanical work and entropy production are bounded from above, reflecting fundamental constraints imposed by diffusive transport.

Thermodynamics

• The entropy change of the thermal bath interpolates between the reversible limit (compensating the configurational entropy loss of the fluid) and a strongly driven regime dominated by irreversible dissipation.
• The evolution of the configurational entropy and external potential energy reveals a dynamical decoupling between geometric confinement and structural relaxation, including transient non-monotonic behavior in the high-mobility regime.

Interpretation

• The competition between mechanical driving and diffusive relaxation controls the observed non-equilibrium features.
• The piston mobility $K^*$ acts as a control parameter that determines the degree of non-equilibrium during the compression process.
• The results provide a quantitative thermodynamic characterization of boundary-driven compression and uncover generic non-equilibrium features governed by a single mobility parameter.

Limitations & Uncertainties

• The DDFT approach relies on the adiabatic approximation, neglecting hydrodynamic interactions and inertial effects.
• The study is limited to a one-dimensional hard-sphere fluid; extensions to more complex fluids and geometries would be valuable.

What Comes Next

• Investigating memory effects in compression and expansion protocols.
• Incorporating interaction-induced dissipation within a Power Functional Theory framework to account for nonlocal dynamical correlations.
• Exploring the non-equilibrium thermodynamics of colloidal systems with responsive particle sizes.