Molecular hydrodynamic theory of the velocity autocorrelation function
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2023
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| _version_ | 1866917644156796928 |
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| author | Seyler, Sean L Seyler, Charles E |
| author_facet | Seyler, Sean L Seyler, Charles E |
| contents | The velocity autocorrelation function (VACF) encapsulates extensive information about a fluid's molecular-structural and hydrodynamic properties. We address the following fundamental question: How well can a purely hydrodynamic description recover the molecular features of a fluid as exhibited by the VACF? To this end, we formulate a bona fide hydrodynamic theory of the tagged-particle VACF for simple fluids. Our approach is distinguished from previous efforts in two key ways: collective hydrodynamic modes are modeled by \emph{linear} hydrodynamic equations; the fluid's static kinetic energy spectrum is identified as a necessary initial condition for the momentum current correlation. Our formulation leads to a natural physical interpretation of the hydrodynamic VACF as a superposition of quasinormal hydrodynamic modes weighted commensurately with the static kinetic energy spectrum, which appears to be essential to bridging continuum hydrodynamical behavior and discrete-particle kinetics. Our methodology yields VACF calculations quantitatively on par with existing approaches for liquid noble gases and alkali metals; moreover, our hydrodynamic model for the self-intermediate scattering function extends the applicable domain to low densities where the Schmidt number is of order unity, enabling calculations for gases and supercritical fluids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_06546 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Molecular hydrodynamic theory of the velocity autocorrelation function Seyler, Sean L Seyler, Charles E Soft Condensed Matter Statistical Mechanics Chemical Physics Fluid Dynamics The velocity autocorrelation function (VACF) encapsulates extensive information about a fluid's molecular-structural and hydrodynamic properties. We address the following fundamental question: How well can a purely hydrodynamic description recover the molecular features of a fluid as exhibited by the VACF? To this end, we formulate a bona fide hydrodynamic theory of the tagged-particle VACF for simple fluids. Our approach is distinguished from previous efforts in two key ways: collective hydrodynamic modes are modeled by \emph{linear} hydrodynamic equations; the fluid's static kinetic energy spectrum is identified as a necessary initial condition for the momentum current correlation. Our formulation leads to a natural physical interpretation of the hydrodynamic VACF as a superposition of quasinormal hydrodynamic modes weighted commensurately with the static kinetic energy spectrum, which appears to be essential to bridging continuum hydrodynamical behavior and discrete-particle kinetics. Our methodology yields VACF calculations quantitatively on par with existing approaches for liquid noble gases and alkali metals; moreover, our hydrodynamic model for the self-intermediate scattering function extends the applicable domain to low densities where the Schmidt number is of order unity, enabling calculations for gases and supercritical fluids. |
| title | Molecular hydrodynamic theory of the velocity autocorrelation function |
| topic | Soft Condensed Matter Statistical Mechanics Chemical Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2302.06546 |