The University of Warwick is offering fully-funded 3-year PhD Scholarships in nanoscale fluid dynamics. The broad aims are 1) to discover, explore and understand new flow phenomena at the nanoscale, 2) develop and implement new mathematical models (beyond Navier-Stokes) that capture the relevant molecular-scale physics, allowing predictive simulations to be performed.

A range of projects are available in:

• Fluctuating gas dynamics at the nanoscale. As an object in a dilute gas decreases in scale, non-equilibrium behaviour begins to dominate (i.e. the Navier-Stokes model begins to fail). At the same time, thermal fluctuations become critical to its dynamics, and cannot be ignored (as they are usually). In this project, for the first time, you will combine latest advances in extended hydrodynamics (a way of representing the fluid with high-order partial differential equations) with fluctuating hydrodynamics (a stochastic approach to introducing thermal fluctuations in continuum fluid models) to derive a new class of model for fluctuating gas dynamics at the nanoscale.
• Ultrasonic cavitation for therapeutic and industrial applications. The violent collapse of bubbles (inertial cavitation), generated by ultrasound, has myriad applications, including targetted drug delivery in cancer therapy. What is currently not fully understood is how the continual collapse and growth of these bubbles gives rise to an effect known as 'micro streaming': a time-averaged flow that can be used to drive drugs more deeply into tumours. In this research, and in collaboration with biomedical engineers from Oxford, you will derive and test (by comparing with your own simulations, and experiments in Oxford) an accuarate anayltical tool to inform the development of the technology.
• Integrated experimental/numerical investigation of thermally-driven nanoscale flows. Counter-intuitive flow physics are commonplace at the micro and nano scale. For example, in certain conditions, flow can be driven along a surface by a temperature gradient, but in a direction from cold to hot (opposite to what you might expect). This phenomena is known as thermal creep; other, sometimes competing, effects can arise from thermally-generated stresses in the flow (thermal-stress flows). But exactly how thermal-creep and thermal-stress flows combine in nano-flow systems is not at all understood. To shed light on this open question, you will contribute to developing and implementing a highly-accurate Boundary Integral Method (BIM) for solving extended hydrodynamic equations (capable of describing such thermal-creep/stress flows) in tandem and in complementarity to an experimental programme that you will define (co-supervised by Dr Petr Denissenko, Engineering). These experiments will be performed in a vacuum chamber, to emulate the effect of miniaturisation using rarefaction.
• Stability of moving contact lines on complex surfaces. The spreading of liquids over solids is ubiquitous throughout industry and nature. Whilst the motion of a straight liquid-solid-gas contact line is well studied, little is known about a myriad of factors which cause it to deform, either due to the nature of the underlying solid (e.g. nanoscale roughness) or through instabilities (e.g. during drop splashing). Understanding this complex motion, and being able to control it (e.g. by modifying the underlying substrate), is of great interest from both a fundamental and a practical standpoint (e.g. to suppress or enhance splashing). Your project will be to use a combination of mathematical modelling and cutting-edge computational techniques in order to create new understanding of this fascinating phenomenon.

These prestigious opportunities are funded by a flagship £3.4M EPSRC Programme Grant awarded to Professor Duncan Lockerby (Engineering) and Dr James Sprittles (Maths) at the University of Warwick, who will be your co-supervisors.

Environment
Warwick is always in the top ten of all UK League tables and in the latest research assessment (REF2014), over 90% of the the research in Engineering and Mathematics was rated as world leading or internationally excellent. You will be integrated into our large (10+) interdisciplinary research group, existing within an extensive UK network (see www.micronanoflows.ac.uk), and will benefit from strong links with the Fluid Dynamics Research Centre and Centre for Scientific Computing. Your training will give you the opportunity to become a leader in either academia or industry.

Applicant Requirements
A 1st or 2:1 honours degree (or equivalent) in applied maths, computer science, engineering science, physics, or a related subject with a strong mathematical content.

Stipend and Fees
The annual stipend will be £14,254 (tax free), for 3 years, with all university fees paid. The scholarships are for EU/UK students only.

To Apply
Email a full CV, academic transcripts, and cover letter, explaining your interest in pursuing a PhD in this Programme, d swith the names and contact details of two referees to d.lockerby@warwick.ac.uk, with ‘PhD Application’ in the subject line.

We will offer these studentships to the first applicants with the appropriate set of skills.

Start Date
By arrangement, in the period: 01/04/2017 to 31/12/2017