MSE12: Modelling the contact line dynamics of an evaporating drop

Background

The evaporation of a liquid drop on a substrate is of practical importance in numerous geophysical, biomedical and industrial applications including the water cycle, DNA mapping and gene-expression analysis, the manufacturing of semiconductor and micro-fluidic devices, cooling, coating and patterning. The free boundary problem is complicated because of the need to consider the transport of mass and momentum and/or energy within and between the substrate, the liquid drop and the atmosphere around the drop. If the drop is partially wetting (i.e. the contact angle and contact set between the drop and the substrate are both finite), the problem is compounded by the singularities that may arise in the state variables at the contact line. Theoretical efforts have focussed on numerical simulations in the thin-film regime in which it is possible to derive tractable models that incorporate many of the pertinent thermo- and hydro-dynamical effects. However, as stated in [1], the simplifications and physical insight afforded by a systematic asymptotic analysis are largely lacking in the literature.

Techniques and Challenges

We shall apply systematic asymptotic methods, using the same structure as that in [2], to analyse the effect of evaporation on the motion of a contact-line in both the thin- and thick-drop regimes.This will allow us to gain insight into the role of the singularities in the liquid stress and in the evaporation flux at the contact line in systems that are of practical importance.

The Future

The validity and accuracy of the asymptotic solutions will be assessed by comparison with numerical simulations and with data obtained from our experimental collaborators at KAUST and Nottingham.

References

[1] Murisic N., Kondic L.: On evaporation of sessile drops with moving contact lines, J. Fluid Mech, 679: 219-246, (2011)

[2] Hocking L.M., Rivers A.D.: The spreading of a drop by capillary action, J. Fluid Mech, 121: 425-442, (1982)