# Laboratoire de Mécanique des Fluides et d’Acoustique - UMR 5509

LMFA - UMR 5509
Laboratoire de Mécanique des Fluides et d’Acoustique
Lyon
France

## Nos partenaires

Article dans J. Fluid Mech. (2015)

## Non-isothermal droplet spreading/dewetting and its reversal

Yi Sui & Peter D. M. Spelt

Axisymmetric non-isothermal spreading/dewetting of droplets on a substrate is studied, wherein the surface tension is a function of temperature, resulting in Marangoni stresses. A lubrication theory is first extended to determine the drop shape for spreading/dewetting limited by slip. It is demonstrated that an apparent angle inferred from a fitted spherical cap shape does not relate to the contact-line speed as it would under isothermal conditions. Also, a power law for the thermocapillary spreading rate versus time is derived. Results obtained with direct numerical simulations (DNS), using a slip length down to $O(10^{−4})$ times the drop diameter, confirm predictions from lubrication theory. The DNS results further show that the behaviour predicted by the lubrication theory – that a cold wall promotes spreading, and a hot wall promotes dewetting – is reversed at sufficiently large contact angles and/or viscosity of the surrounding fluid. This behaviour is summarized in a phase diagram, and a simple model that supports this finding is presented. Although the key results are found to be robust when accounting for heat conduction in the substrate, a critical thickness of the substrate is identified above which wall conduction significantly modifies wetting behaviour.