Engineering Ratchet-Based Particle Separation via Shortcuts to Isothermality
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| Format: | Preprint |
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2023
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| author | Zhao, Xiu-Hua Tu, Z. C. Ma, Yu-Han |
| author_facet | Zhao, Xiu-Hua Tu, Z. C. Ma, Yu-Han |
| contents | 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 $τ$, 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 $D^*$. 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 $W_{\rm{ex}}^{(\rm{min})}$) 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_16823 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Engineering Ratchet-Based Particle Separation via Shortcuts to Isothermality Zhao, Xiu-Hua Tu, Z. C. Ma, Yu-Han Statistical Mechanics Mesoscale and Nanoscale Physics Applied Physics Chemical Physics 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 $τ$, 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 $D^*$. 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 $W_{\rm{ex}}^{(\rm{min})}$) 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. |
| title | Engineering Ratchet-Based Particle Separation via Shortcuts to Isothermality |
| topic | Statistical Mechanics Mesoscale and Nanoscale Physics Applied Physics Chemical Physics |
| url | https://arxiv.org/abs/2311.16823 |