Mathematical Modelling and Analysis of Droplet Evaporation

Lead Research Organisation: University of Strathclyde
Department Name: Mathematics and Statistics

Abstract

In the last decade the proposed supervisor (Wilson) has established an international reputation for his work on evaporating droplets, including several highly cited papers in leading international journals (e.g. [1-3]), and has been asked to give several invited lectures on the topic at international meetings, notably at Droplets 2015 in Twente in October 2015 and two conferences in China in July 2017.

The present project is directly motivated by the ongoing interest of industrial partners Merck in the printing and drying of droplets of complex fluids on non-homogenous substrates. In particular, Merck are very interested in the dynamics of droplets of liquid crystal on the kind of periodic substrates which arise in the manufacture of flat screen displays (in which individual pixels or small groups of pixels have to be individually filled with liquid crystal). In addition to fundamental scientific questions about the rather subtle the influence of substrate topology on the evolution and lifetime of a drying droplet, Merck are also very interested in how the complex rheology of a nematic liquid crystal influences the drying process. In this regard we are perfectly placed to undertake this work as, in addition to our previous work on during droplets, the Continuum Mechanics and Industrial Mathematics (CMIM) research group within the Department of Mathematics and Statistics has a long-standing international reputation in this area dating back to the pioneering work of the late Professor Frank Leslie FRS on the mathematical modelling of liquid crystals.

The proposed project will build on both the proposed supervisor's previous work (e.g. [1-3]) and the expertise of new lecturer Dr Alex Wray (e.g [4]) to develop and analyse new mathematical models for the evolution and lifetimes of droplets of both simple and complex fluids on non-homogenous substrates

[1] G.J. Dunn, S.K. Wilson, B.R. Duffy, S. David, K. Sefiane,
The strong influence of substrate conductivity on droplet evaporation,
J. Fluid Mech. 623 329-351 (2009)

[2] J.M. Stauber, S.K. Wilson, B.R. Duffy, K. Sefiane,
On the lifetimes of evaporating droplets,
J. Fluid Mech. 744 R2 (2014)

[3] J.M. Stauber, S.K. Wilson, B.R. Duffy, B.R., K. Sefiane,
On the lifetimes of evaporating droplets with related initial and receding contact angles,
Phys. Fluids 27 122101 (2015)

[4] A.W. Wray , Z. Che , O. K. Matar, P. Valluri , J. Kim , K. Sefiane,
Dynamics and universal scaling law in geometrically-controlled sessile drop evaporation,
Nature Communications 8 14783 (2017)

Publications

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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/R512205/1 01/10/2017 31/03/2022
1969724 Studentship EP/R512205/1 01/10/2017 30/11/2021 Hannah May D'Ambrosio