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DY: Fachverband Dynamik und Statistische Physik

DY 44: Droplets, Wetting, Complex Fluids, and Soft Matter (joint session DY/CPP)

DY 44.5: Vortrag

Freitag, 21. März 2025, 10:45–11:00, H47

Displacements in thin fluid and elastic films — •Andreas M. Menzel — Otto von Guericke University Magdeburg, Germany

We address the displacements of comparatively small objects in flat thin fluid films under low-Reynolds-number conditions or in flat thin elastic sheets under linear elasticity.
It is well-known that the fundamental solution of the corresponding continuum equations for forced in-plane displacements diverges logarithmically in strictly two-dimensional systems, the so-called Stokes paradox. We provide an illustrative way of interpretation and demonstrate how the divergence cancels under pairwise interactions and confinement [1,2]. Interestingly, logarithmic spatial dependencies prevail under rectangular clamping of elastic membranes [3]. Moreover, the divergence is still present in free-standing sheets of finite thickness, unless they are stabilized, for instance, by substrates [4,5].
We are confident that our analytical results will prove useful in corresponding quantitative experimental evaluations.
[1] S. K. Richter, A. M. Menzel, Phys. Rev. E 105, 014609 (2022).
[2] T. Lutz, S. K. Richter, A. M. Menzel, Phys. Rev. E 106, 054609 (2022).
[3] A. R. Sprenger, H. Reinken, T. Richter, A. M. Menzel, EPL (Europhys. Lett.) 147, 17002 (2024).
[4] T. Lutz, A. M. Menzel, A. Daddi-Moussa-Ider, Phys. Rev. E 109, 054802 (2024).
[5] A. Daddi-Moussa-Ider, E. Tjhung, T. Richter, A. M. Menzel, J. Phys.: Condens. Matter 36, 445101 (2024).

Keywords: thin fluid films; elastic membranes; displacements; Stokes paradox; analytical results