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

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Bibliographic Details
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]
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Database: Engineering Source
Description
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]
ISSN:01677322
DOI:10.1016/j.molliq.2025.127427