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Contact line motion in axial thermocapillary outward flow

Published online by Cambridge University Press:  01 April 2020

A. Dominguez Torres ,
J. R. Mac Intyre Open the ORCID record for J. R. Mac Intyre [Opens in a new window] ,
J. M. Gomba Open the ORCID record for J. M. Gomba [Opens in a new window] ,
C. A. Perazzo ,
P. G. Correa ,
A. Lopez-Villa  and
A. Medina
A. Dominguez Torres
Affiliation:
SEPI ESIME Azcapotzalco, Instituto Politécnico Nacional, Av. de las Granjas 682, Col. Santa Catarina, 02250, Azcapotzalco DF, México
J. R. Mac Intyre
Affiliation:
Instituto de Física Arroyo Seco IFAS (UNCPBA) and CIFICEN (UNCPBA-CICPBA-CONICET), Pinto 399, 7000, Tandil, Argentina
J. M. Gomba*
Affiliation:
Instituto de Física Arroyo Seco IFAS (UNCPBA) and CIFICEN (UNCPBA-CICPBA-CONICET), Pinto 399, 7000, Tandil, Argentina
C. A. Perazzo
Affiliation:
IMeTTyB, Universidad Favaloro-CONICET, Solís 453, C1078AAIBuenos Aires, Argentina Departamento de Física y Química, FICEN, Universidad Favaloro, Sarmiento 1853, C1198AAGBuenos Aires, Argentina
P. G. Correa
Affiliation:
Instituto de Física Arroyo Seco IFAS (UNCPBA) and CIFICEN (UNCPBA-CICPBA-CONICET), Pinto 399, 7000, Tandil, Argentina
A. Lopez-Villa
Affiliation:
SEPI ESIME Azcapotzalco, Instituto Politécnico Nacional, Av. de las Granjas 682, Col. Santa Catarina, 02250, Azcapotzalco DF, México
A. Medina
Affiliation:
ETSI Aeronáutica y del Espacio UPM, Plaza Cardenal Cisneros 3, 28040Madrid, Spain
*
† Email address for correspondence: [email protected]
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Abstract

We study the contact line dynamics of a viscous droplet deposited at the centre of a substrate subject to an axial thermal gradient. The temperature of the substrate decreases with distance from the centre, so the Marangoni stress induced at the liquid–air interface displaces the liquid radially outward. The flow experiences two stages. In the first stage, the droplet evolves towards an axially symmetric ring whose radius increases with time as $t^{1/3}$. Using the lubrication approximation, we perform numerical simulations that confirm this law for the motion of the front and show that the maximum thickness of the profile decreases as $t^{-0.374}$. We explain the evolution law of the contact line by balancing Marangoni and viscous stresses. In the second stage, the contact line becomes unstable and develops smooth corrugations whose amplitude increases with time and that eventually become long fingers. The temporal evolution of the Fourier spectra of the contour shows a shift of the most unstable mode from smaller to larger azimuthal wavenumbers.

JFM classification

Drops and Bubbles: Thermocapillarity Low-Reynolds-number flows: Lubrication theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 892 , 10 June 2020 , A8
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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