Giesekus Stick-Slip Singularity: Asymptotic Theory in the Log-Conformation Formulation

Abstract

In this paper, the log-conformation reformulation of a Giesekus fluid near a planar stick-slip singularity is investigated analytically. In what is, to our knowledge, the first use of the log-conformation formulation beyond its numerical purpose, we present results that match the asymptotic stress analysis of Evans [JNNFM 222 (2015) 24-33] for the stick, slip, and core regions under the assumption of a given Newtonian velocity field. Furthermore, the logarithmic reformulation allows us to extend the existing asymptotic theory substantially, showing, e.g., that the determinant of the conformation tensor is asymptotically constant, as well as thoroughly characterizing the transition behavior between the boundary layers and the core region. Combining these results, we obtain a composite asymptotic solution of the log-conformation equation that is valid uniformly throughout a close neighborhood of the singularity.

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BibTeX

@misc{becker2026giesekus,
  title = {{Giesekus Stick-Slip Singularity: Asymptotic Theory in the Log-Conformation Formulation}},
  author = {Florian Becker and Philipp Knechtges},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10836},
  eprint = {2609.10836},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10836},
}

RIS

TY  - UNPB
TI  - Giesekus Stick-Slip Singularity: Asymptotic Theory in the Log-Conformation Formulation
AU  - Florian Becker
AU  - Philipp Knechtges
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.10836
UR  - https://arxiv.org/abs/2609.10836
AB  - In this paper, the log-conformation reformulation of a Giesekus fluid near a planar stick-slip singularity is investigated analytically. In what is, to our knowledge, the first use of the log-conformation formulation beyond its numerical purpose, we present results that match the asymptotic stress analysis of Evans [JNNFM 222 (2015) 24-33] for the stick, slip, and core regions under the assumption of a given Newtonian velocity field. Furthermore, the logarithmic reformulation allows us to extend the existing asymptotic theory substantially, showing, e.g., that the determinant of the conformation tensor is asymptotically constant, as well as thoroughly characterizing the transition behavior between the boundary layers and the core region. Combining these results, we obtain a composite asymptotic solution of the log-conformation equation that is valid uniformly throughout a close neighborhood of the singularity.
ER  -

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