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Retraction of a liquid drop in a Hele-Shaw cell

  • Luke Neville
  • Paul R. Kaneelil
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Abstract

When a long liquid drop is confined in a Hele-Shaw cell, the pull of surface tension produces a rapid retraction of its tip, causing it to bulge out as it draws up the excess liquid. Using numerical simulations, we demonstrate that this retraction is self-similar at long times, with the speed of retraction slowing like t−1/2, where t is the duration of retraction. After showing how this scaling can be understood using force and mass balance, we perform an asymptotic analysis of the Hele-Shaw equations to derive both the shape of the retracting drop, as well as prefactors of the scaling laws. Excellent agreement is found between our simulations and theory, and the experimental consequences are pointed out.

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Cite

BibTeXRIS
BibTeX
@misc{neville2026retraction,
  title = {{Retraction of a liquid drop in a Hele-Shaw cell}},
  author = {Luke Neville and Paul R. Kaneelil},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19056},
  eprint = {2610.19056},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19056},
}
RIS
TY  - UNPB
TI  - Retraction of a liquid drop in a Hele-Shaw cell
AU  - Luke Neville
AU  - Paul R. Kaneelil
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.19056
UR  - https://arxiv.org/abs/2610.19056
AB  - When a long liquid drop is confined in a Hele-Shaw cell, the pull of surface tension produces a rapid retraction of its tip, causing it to bulge out as it draws up the excess liquid. Using numerical simulations, we demonstrate that this retraction is self-similar at long times, with the speed of retraction slowing like t^−1/2, where t is the duration of retraction. After showing how this scaling can be understood using force and mass balance, we perform an asymptotic analysis of the Hele-Shaw equations to derive both the shape of the retracting drop, as well as prefactors of the scaling laws. Excellent agreement is found between our simulations and theory, and the experimental consequences are pointed out.
ER  -