How are mobility and friction related in viscoelastic fluids?

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The motion of a colloidal probe in a viscoelastic fluid is described by friction or mobility, depending on whether the probe is moving with a velocity or feeling a force. While the Einstein relation describes an inverse relationship valid for Newtonian solvents, both concepts are generalized to time-dependent memory kernels in viscoelastic fluids. We theoretically and experimentally investigate their relation by considering two observables: the recoil after releasing a probe that was moved through the fluid and the equilibrium mean squared displacement (MSD). Applying concepts of linear response theory, we generalize Einstein's relation and thereby relate recoil and MSD, which both provide access to the mobility kernel. With increasing concentration, however, MSD and recoil show distinct behaviors, rooted in different behaviors of the two kernels. Using two theoretical models, a linear two-bath particle model and hard spheres treated by mode-coupling theory, we find a Volterra relation between the two kernels, explaining differing timescales in friction and mobility kernels under variation of concentration.

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ISO 690CASPERS, Juliana, Nikolas DITZ, Karthika Krishna KUMAR, Félix GINOT, Clemens BECHINGER, Matthias FUCHS, Matthias KRÜGER, 2023. How are mobility and friction related in viscoelastic fluids?. In: The Journal of Chemical Physics. American Institute of Physics (AIP). 2023, 158(2), 024901. ISSN 0021-9606. eISSN 1089-7690. Available under: doi: 10.1063/5.0129639
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@article{Caspers2023mobil-59417,
  year={2023},
  doi={10.1063/5.0129639},
  title={How are mobility and friction related in viscoelastic fluids?},
  number={2},
  volume={158},
  issn={0021-9606},
  journal={The Journal of Chemical Physics},
  author={Caspers, Juliana and Ditz, Nikolas and Kumar, Karthika Krishna and Ginot, Félix and Bechinger, Clemens and Fuchs, Matthias and Krüger, Matthias},
  note={Article Number: 024901}
}
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