Engineering Ratchet-Based Particle Separation via Shortcuts to Isothermality

Abstract

Microscopic particle separation plays vital role in various scientific and industrial domains. In this Letter, we propose a universal non-equilibrium thermodynamic approach, employing the concept of Shortcuts to Isothermality, to realize controllable separation of overdamped Brownian particles. By utilizing a designed ratchet potential with temporal period $\tau$, we find in the slow-driving regime that the average particle velocity $\Bar{v}_s\propto\left(1-D/D^*\right)τ^{-1}$, indicating that particles with different diffusion coefficients $D$ can be guided to move in distinct directions with a preset $D^{\ast }$. Furthermore, we reveal that there exists an extra energetic cost with a lower bound $W_{\rm{ex}}^{(\rm{min})}\propto\mathcal{L}^{2}\Bar{v}_s$, alongside a quasi-static work consumption. Here, $\mathcal{L}$ is the thermodynamic length of the driving loop in the parametric space. We numerically validate our theoretical findings and illustrate the optimal separation protocol (associated with $W_{\mathrm{ex}}^{(\min )}$) with a sawtooth potential. This study establishes a bridge between thermodynamic process engineering and particle separation, paving the way for further explorations of thermodynamic constrains and optimal control in ratchet-based particle separation.

5 pages, 3 figures + Supplemental Materials (10 pages, 4 figures). Comments are welcome!

References in corpus (10)

• Separation of microscale chiral objects by shear flow
• Realization of a feedback controlled flashing ratchet
• Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics
• Tunable mass separation via negative mobility
• Collective advantages in finite-time thermodynamics
• Inertial effects on rectification and diffusion of active Brownian particles in an asymmetric channel
• Active sieving across driven nanopores for tunable selectivity
• Using Thermal Ratchet Mechanism to Achieve Net Motility in Magnetic Microswimmers
• Microscopic low-dissipation heat engine via shortcuts to adiabaticity and shortcuts to isothermality
• Geodesic bound of the minimum energy expense to achieve membrane separation within finite time

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