Viscosity as the product of its ideal low-concentration value times a thermodynamic function
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913938146328576 |
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| author | Marchioni, L. Di Muro, M. A. Hoyuelos, M. |
| author_facet | Marchioni, L. Di Muro, M. A. Hoyuelos, M. |
| contents | The behavior of viscosity, $η$, as a function of concentration in dense fluids remains an unsolved problem, as is the case with other transport coefficients. Boltzmann's theory and the Chapman-Enskog method predict the value of the viscosity at low concentrations, $η_0$. Here, the hypothesis $η=ϕ\, η_0$ is proposed, where $ϕ$ is a function of the thermodynamic state that represents the effects of interactions as concentration increases. We consider that $η_0$ is the viscosity in an ideal hypothetical system, where the condition of small interactions applies for the whole density range ($ϕ\to 1$ for low concentration). The method proposed to verify this hypothesis involves coupling the system with a solvent represented by a Langevin thermostat, characterized by a damping time $t_d$. Molecular dynamics simulations show that different values of noise intensity modify $η$ and $η_0$, but do not affect $ϕ$. This result supports the assumption that $ϕ$ is a state function, since the thermodynamic state remains unaltered by the presence of damping and noise. Simulations were conducted for particles that interact via a pseudo-hard sphere or a Lennard-Jones potential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15039 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Viscosity as the product of its ideal low-concentration value times a thermodynamic function Marchioni, L. Di Muro, M. A. Hoyuelos, M. Statistical Mechanics The behavior of viscosity, $η$, as a function of concentration in dense fluids remains an unsolved problem, as is the case with other transport coefficients. Boltzmann's theory and the Chapman-Enskog method predict the value of the viscosity at low concentrations, $η_0$. Here, the hypothesis $η=ϕ\, η_0$ is proposed, where $ϕ$ is a function of the thermodynamic state that represents the effects of interactions as concentration increases. We consider that $η_0$ is the viscosity in an ideal hypothetical system, where the condition of small interactions applies for the whole density range ($ϕ\to 1$ for low concentration). The method proposed to verify this hypothesis involves coupling the system with a solvent represented by a Langevin thermostat, characterized by a damping time $t_d$. Molecular dynamics simulations show that different values of noise intensity modify $η$ and $η_0$, but do not affect $ϕ$. This result supports the assumption that $ϕ$ is a state function, since the thermodynamic state remains unaltered by the presence of damping and noise. Simulations were conducted for particles that interact via a pseudo-hard sphere or a Lennard-Jones potential. |
| title | Viscosity as the product of its ideal low-concentration value times a thermodynamic function |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2408.15039 |