Mathematical Modelling and Analysis of Sessile Droplets
Lead Research Organisation:
University of Strathclyde
Department Name: Mathematics and Statistics
Abstract
Background
The evaporation of sessile droplets is an area of very active international research, with new publications appearing on a daily basis and entire conferences (such as "Droplets 2019" held in Durham in 2019) now dedicated to the topic. Over the last decade, the lead supervisor (Professor Stephen Wilson) has collaborated very successfully with Professor Khellil Sefiane from the School of Engineering at the University of Edinburgh (and a Visiting Professor at the University of Strathclyde) on a variety of practically important fluid-dynamical problems, including evaporating droplets, bubble dynamics, self-rewetting fluids, and anti-surfactants. In particular, over that period they have jointly supervised four previous PhD students, namely Gavin Dunn, Jutta Stauber, Justin Conn and Feargus Schofield, with whom they have published more than 10 joint papers in top journals, including Dunn et al. ["The strong influence of substrate conductivity on droplet evaporation" J. Fluid Mech. 623 329-351 (2009)] (over 250 citations) and Stauber et al. ["On the lifetimes of evaporating droplets" J. Fluid Mech. 744 R2 (2014)] (over 125 citations). Tangible evidence for the value Edinburgh see in this collaboration is provided by the significant cash contribution they made towards the present studentship.
The Present Project
The aim of the proposed project is to build on the supervisors' previous work on evaporating droplets to explore two exciting new aspects of this scientifically and practically important problem.
(1) Mathematical Modelling of Desiccant Droplets
Recent work by Sefiane and his collaborators ["Water vapor uptake into hygroscopic lithium bromide desiccant droplets: mechanisms of droplet growth and spreading", Soft Matter (2018)] has provided the first comprehensive experimental investigation of the drying of droplets of a desiccant liquid (i.e. one which draws moisture from the air rather than evaporating vapour into the air). The mathematical modelling and analysis of such systems is an entirely open problem which we are uniquely well placed to tackle.
(2) Collective Behaviour of Large Arrays of Small Droplets
In practice, droplets almost never occur singly, but, due to the inherent complexity of the multiple-droplet problem, so far very little work has been done on the interactions between multiple droplets. A rare exception is the recent work by Carrier et al. ["Evaporation of water: evaporation rate and collective effects" J. Fluid Mech. 798 774-786 (2016)] and the lead supervisor's ongoing work with Feargus Schofield and Dr David Pritchard on the interactions between two droplets in two dimensions, and with the second supervisor (Dr Alexander Wray) and Dr Brian Duffy ["Competitive evaporation of multiple sessile droplets" J. Fluid Mech (2020)] on the interactions between widely-separated droplets in three dimensions. The aim of the present project work is to build on this work to investigate the fascinating but virtually unexplored subject of the collective behaviour of large arrays of small droplets. Interactions between the droplets (in particular, so-called "shielding" effects) are expected to lead to very different collective behaviour compared to that of isolated droplets. In addition to its intrinsic scientific value, recent discussions with industrial collaborator Merck Chemicals Ltd have indicated that this problem is of considerable practical interest to them.
The student will join a lively and mutually supportive cohort of fellow PhD students within the Continuum Mechanics and Industrial Mathematics (CMIM) research group.
The evaporation of sessile droplets is an area of very active international research, with new publications appearing on a daily basis and entire conferences (such as "Droplets 2019" held in Durham in 2019) now dedicated to the topic. Over the last decade, the lead supervisor (Professor Stephen Wilson) has collaborated very successfully with Professor Khellil Sefiane from the School of Engineering at the University of Edinburgh (and a Visiting Professor at the University of Strathclyde) on a variety of practically important fluid-dynamical problems, including evaporating droplets, bubble dynamics, self-rewetting fluids, and anti-surfactants. In particular, over that period they have jointly supervised four previous PhD students, namely Gavin Dunn, Jutta Stauber, Justin Conn and Feargus Schofield, with whom they have published more than 10 joint papers in top journals, including Dunn et al. ["The strong influence of substrate conductivity on droplet evaporation" J. Fluid Mech. 623 329-351 (2009)] (over 250 citations) and Stauber et al. ["On the lifetimes of evaporating droplets" J. Fluid Mech. 744 R2 (2014)] (over 125 citations). Tangible evidence for the value Edinburgh see in this collaboration is provided by the significant cash contribution they made towards the present studentship.
The Present Project
The aim of the proposed project is to build on the supervisors' previous work on evaporating droplets to explore two exciting new aspects of this scientifically and practically important problem.
(1) Mathematical Modelling of Desiccant Droplets
Recent work by Sefiane and his collaborators ["Water vapor uptake into hygroscopic lithium bromide desiccant droplets: mechanisms of droplet growth and spreading", Soft Matter (2018)] has provided the first comprehensive experimental investigation of the drying of droplets of a desiccant liquid (i.e. one which draws moisture from the air rather than evaporating vapour into the air). The mathematical modelling and analysis of such systems is an entirely open problem which we are uniquely well placed to tackle.
(2) Collective Behaviour of Large Arrays of Small Droplets
In practice, droplets almost never occur singly, but, due to the inherent complexity of the multiple-droplet problem, so far very little work has been done on the interactions between multiple droplets. A rare exception is the recent work by Carrier et al. ["Evaporation of water: evaporation rate and collective effects" J. Fluid Mech. 798 774-786 (2016)] and the lead supervisor's ongoing work with Feargus Schofield and Dr David Pritchard on the interactions between two droplets in two dimensions, and with the second supervisor (Dr Alexander Wray) and Dr Brian Duffy ["Competitive evaporation of multiple sessile droplets" J. Fluid Mech (2020)] on the interactions between widely-separated droplets in three dimensions. The aim of the present project work is to build on this work to investigate the fascinating but virtually unexplored subject of the collective behaviour of large arrays of small droplets. Interactions between the droplets (in particular, so-called "shielding" effects) are expected to lead to very different collective behaviour compared to that of isolated droplets. In addition to its intrinsic scientific value, recent discussions with industrial collaborator Merck Chemicals Ltd have indicated that this problem is of considerable practical interest to them.
The student will join a lively and mutually supportive cohort of fellow PhD students within the Continuum Mechanics and Industrial Mathematics (CMIM) research group.
Organisations
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/R513349/1 | 01/10/2018 | 30/09/2023 | |||
| 2426093 | Studentship | EP/R513349/1 | 01/08/2020 | 31/01/2024 | Laura Mills |