Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published January 2019 | Submitted + Supplemental Material + Published
Journal Article Open

Self-similar cuspidal formation by runaway thermocapillary forces in thin liquid films


Many physical systems give rise to dynamical behavior leading to cuspidal shapes which represent a singularity of the governing equation. The cusp tip often exhibits self-similarity as well, indicative of scaling symmetry invariant in time up to a change of scale. Cusp formation can even occur in liquid systems when the driving force for fluid elongation is sufficiently strong to overcome leveling by capillarity. In almost all cases reported in the literature, however, the moving interface is assumed to be \textit{shear-free} and the operable forces orient exclusively in the direction normal to the advancing boundary. Here we focus on a system in which a slender liquid film is exposed to large thermocapillary stresses, a system previously shown to undergo a linear instability resembling microlens arrays. We demonstrate by analytic and numerical means how in the nonlinear regime these surface forces undergo self-similar runaway behavior leading to cusp formation with a conical tip whose slope can be prescribed from the analytic relation derived. On a fundamental level, this finding broadens our understanding of known categories of flows capable of cusp formation. More practically, the system geometry proposed offers a potentially novel lithographic method for one-step non-contact fabrication of cuspidal microarrays.

Additional Information

© 2019 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Received 26 July 2018; Accepted 30 November 2018; Accepted Manuscript online 30 November 2018; Published 18 January 2019.

Attached Files

Published - Zhou_2019_New_J._Phys._21_013018.pdf

Submitted - 1808.01017.pdf

Supplemental Material - Zhou_Troian_Video_NJP_20180508.mp4


Files (8.0 MB)
Name Size Download all
4.7 MB Download
1.6 MB Preview Download
1.7 MB Preview Download

Additional details

August 19, 2023
October 18, 2023