Postgraduate research opportunities

Developing a multiscale description of complex fluids from the molecular to the continuum scales

This ambitious project attempts to build a single, unified description of complex fluids that incorporates molecular-level detail but can be applied on a wide range of length and time scales that extends to the continuum scale.

Number of places



17 February 2020


3 years


The project will suit a student with a background in chemical engineering or related discipline (e.g. physics or applied mathematics). Applicants should already have or be expecting shortly to obtain a first class or upper second class degree in one of the above mentioned disciplines. Candidates trained to masters level are preferred, but exceptional candidates trained to bachelors level can also be considered. Applicants are expected to demonstrate strong mathematical and problem-solving skills, as well as experience and/or interest in statistical mechanics, fluid mechanics, numerical computation, and computer programming.

Project Details

Engineers have traditionally used continuum equations to model processes, such as the Navier-Stokes equation for fluid flow. These methods require constitutive relations that encode the properties of the fluid; these are typically determined empirically and have limited predictive capabilities. While the continuum description is well established and has become commonplace in engineering calculations, their limitations have become apparent with the increasing use of complex materials (e.g., polymer solutions, nanoparticle suspensions etc.), which may possess underlying mesoscopic structures that can impart intricate behaviours.

In principle, these complex materials can be modelled using molecular scale methods, such as molecular dynamics and Monte Carlo simulations. At these very short length scales, the discrete nature of matter becomes important, and the system is typically treated from a "particle" perspective, where the mathematical focus is on the dynamics of particles and their mutual interactions. The tremendous progress of computational power and algorithmic efficiencies have dramatically extended the range of time and length scales where these methods can be practically applied; these are beginning to reach scales where the continuum description becomes reasonable. However, they are nowhere near practical to use in process scale calculations. Coarse graining approaches have been developed to try to extend the scales at which molecular simulations can be applied, however, these still represent the system as a collection of interacting particles, and, consequently, it is unclear how these methods can transition to the continuum description at large scales, thereby limiting their use as engineering tools.

This ambitious project attempts to build a single, unified description of complex fluids that incorporates molecular-level detail but can be applied on a wide range of length and time scales that extends to the continuum scale. The initial phase of the project will focus on the static properties of the fluid (e.g., thermodynamics and structure); later, the dynamics of the fluid will be examined. This approach will be developed and tested against data from large scale event-driven molecular dynamics simulations, as well as direct numerical simulations of the hydrodynamic equations for compressible flow.

In addition to undertaking cutting edge research, students are also registered for the Postgraduate Certificate in Researcher Development (PGCert), which is a supplementary qualification that develops a student’s skills, networks and career prospects.

Key Words: Statistical Mechanics, Thermodynamics, Fluid Dynamics, Molecular Dynamics, Direct Numerical Simulations

Funding Details

This PhD project is initially offered on a self-funding basis. It is open to applicants with their own funding, or those applying to funding sources. However, excellent candidates will be eligible to be considered for a University scholarship.

Contact us

Miss Ewa Kosciuk

+44(0) 141 548 2835

James Weir Building, 75 Montrose Street, Glasgow, G1 1XJ

How to apply

Apply for this project here â€“ please quote the project title in your application.

During the application you'll be asked for the following information and evidence uploaded to the application:

  • your full contact details
  • transcripts and certificates of all degrees
  • proof of English language proficiency if you are not from a majority English-speaking country as recognised by UKVI
  • two references, one of which must be academic. Please see our guidance on referees
  • funding or scholarship information
  • international students must declare any previous UK study

By filling these details out as fully as possible, you'll avoid any delay to your application being processed by the University.

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