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A new interpretation of the Einstein-Stokes-Smoluchowski relationship based on the forced harmonic oscillator model.

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Title: A new interpretation of the Einstein-Stokes-Smoluchowski relationship based on the forced harmonic oscillator model.
Authors: Freire, Fernando C.M.1 (AUTHOR) fcmfreire@gmail.com, Silva, Arthur E.T.1 (AUTHOR), Santana, Adriel J.1 (AUTHOR)
Source: Journal of Molecular Liquids. Jun2025, Vol. 427, pN.PAG-N.PAG. 1p.
Subjects: Problem solving, Viscosity, Velocity, Fluids, Ions
Abstract: The movement of ions in electrolytic solutions determines the conductivity of the fluid and, therefore, the impedance of the solution. Models explaining this behavior have been proposed for many years, such as circuit and diffusive models. Our modeling differs slightly from these two mentioned, but it contains all the necessary ingredients for understanding impedance and it is built upon an electro-mechanical model of damped and forced harmonic oscillation. It was possible to solve the problem analytically and obtain the dynamic behavior of the charged particles responsible for the electrical conduction of the medium, such as displacement and velocity amplitudes. We also provide a new interpretation for the Einstein-Stokes-Smoluchowski relations. Two variants of electro-mechanical model of increasing complexity are presented here in order to interprete and underline new results. The work provides a panoramic view of the dynamic behavior of the charged particles moving in an ionic fluid and, as a result, also provides extensions to the Einstein-Smoluchowski relations when analyzing viscosity, and therefore mobility and diffusion. • The work presents a new interpretation of the Einstein-Stokes-Smoluchowski equations. • Two variants of electro-mechanical model are presented here. • The complete model fits the experimental data optimally. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Molecular Liquids is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 185027701
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: A new interpretation of the Einstein-Stokes-Smoluchowski relationship based on the forced harmonic oscillator model.
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  Data: <searchLink fieldCode="AR" term="%22Freire%2C+Fernando+C%2EM%2E%22">Freire, Fernando C.M.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> fcmfreire@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Silva%2C+Arthur+E%2ET%2E%22">Silva, Arthur E.T.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Santana%2C+Adriel+J%2E%22">Santana, Adriel J.</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Molecular+Liquids%22">Journal of Molecular Liquids</searchLink>. Jun2025, Vol. 427, pN.PAG-N.PAG. 1p.
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  Data: <searchLink fieldCode="DE" term="%22Problem+solving%22">Problem solving</searchLink><br /><searchLink fieldCode="DE" term="%22Viscosity%22">Viscosity</searchLink><br /><searchLink fieldCode="DE" term="%22Velocity%22">Velocity</searchLink><br /><searchLink fieldCode="DE" term="%22Fluids%22">Fluids</searchLink><br /><searchLink fieldCode="DE" term="%22Ions%22">Ions</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: The movement of ions in electrolytic solutions determines the conductivity of the fluid and, therefore, the impedance of the solution. Models explaining this behavior have been proposed for many years, such as circuit and diffusive models. Our modeling differs slightly from these two mentioned, but it contains all the necessary ingredients for understanding impedance and it is built upon an electro-mechanical model of damped and forced harmonic oscillation. It was possible to solve the problem analytically and obtain the dynamic behavior of the charged particles responsible for the electrical conduction of the medium, such as displacement and velocity amplitudes. We also provide a new interpretation for the Einstein-Stokes-Smoluchowski relations. Two variants of electro-mechanical model of increasing complexity are presented here in order to interprete and underline new results. The work provides a panoramic view of the dynamic behavior of the charged particles moving in an ionic fluid and, as a result, also provides extensions to the Einstein-Smoluchowski relations when analyzing viscosity, and therefore mobility and diffusion. • The work presents a new interpretation of the Einstein-Stokes-Smoluchowski equations. • Two variants of electro-mechanical model are presented here. • The complete model fits the experimental data optimally. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Molecular Liquids is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=185027701
RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.molliq.2025.127427
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      – Code: eng
        Text: English
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        PageCount: 1
        StartPage: N.PAG
    Subjects:
      – SubjectFull: Problem solving
        Type: general
      – SubjectFull: Viscosity
        Type: general
      – SubjectFull: Velocity
        Type: general
      – SubjectFull: Fluids
        Type: general
      – SubjectFull: Ions
        Type: general
    Titles:
      – TitleFull: A new interpretation of the Einstein-Stokes-Smoluchowski relationship based on the forced harmonic oscillator model.
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            NameFull: Silva, Arthur E.T.
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            NameFull: Santana, Adriel J.
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            – D: 01
              M: 06
              Text: Jun2025
              Type: published
              Y: 2025
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              Value: 427
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