On the transition to dripping of an inverted liquid film

Blyth, Mark G., Lin, Te-Sheng and Tseluiko, Dmitri (2023) On the transition to dripping of an inverted liquid film. Journal of Fluid Mechanics, 958. ISSN 0022-1120

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Abstract

The transition to dripping in the gravity-driven flow of a liquid film under an inclined plate is investigated at zero Reynolds number. Computations are carried out on a periodic domain assuming either a fixed fluid volume or a fixed flow rate for a hierarchy of models: two lubrication models with either linearised curvature or full curvature (the LCM and FCM, respectively), and the full equations of Stokes flow. Of particular interest is the breakdown of travelling-wave solutions as the plate inclination angle is increased. For any fixed volume, the LCM reaches the horizontal state where it attains a cosine-shaped profile. For sufficiently small volume, the FCM and Stokes solutions attain a weak Young-Laplace equilibrium profile, the approach to which is described by an asymptotic analysis generalising that of Kalliadasis & Chang (J. Fluid Mech., vol. 261, 1994, pp. 135-168) for the LCM. For large volumes, the bifurcation curves for the FCM and Stokes model have a turning point so that the fully inverted state is never reached. For fixed flow rate, the LCM blows up at a critical angle that is well predicted by asymptotic analysis. The bifurcation curve for the FCM either has a turning point or else reaches a point at which the surface profile has an infinite slope singularity, indicating the onset of multi-valuedness. The latter is confirmed by the Stokes model, which can be continued to obtain overturning surface profiles. Overall, the thin-film models either provide an accurate prediction for dripping onset or else supply an upper bound on the critical inclination angle.

Item Type:	Article
Additional Information:	Funding: T.-S.L. acknowledges support from the National Science and Technology Council, Taiwan, under research grants 111-2628-M-A49-008-MY4, and support from the National Center for Theoretical Sciences, Taiwan.
Uncontrolled Keywords:	thin films,condensed matter physics,mechanics of materials,mechanical engineering,applied mathematics ,/dk/atira/pure/subjectarea/asjc/3100/3104
Faculty \ School:	Faculty of Science > School of Mathematics
UEA Research Groups:	Faculty of Science > Research Groups > Fluid and Solid Mechanics
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	LivePure Connector
Date Deposited:	27 Jan 2023 16:30
Last Modified:	22 Mar 2023 09:30
URI:	https://ueaeprints.uea.ac.uk/id/eprint/90845
DOI:	10.1017/jfm.2023.115

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