Postgraduate research opportunities

Direct numerical simulation of polymeric-fluid flows

The purpose of this project is to apply a formulation to polymeric turbulent boundary layer flows and, in this way, to make some first, yet decisive, steps in the physics and algorithmics of fully-coupled polymeric boundary layer turbulence.

Number of places



24 February 2021


3 years


We are looking for an enthusiastic student with strong mathematics skills and aptitude for computing. A first class honours degree (or equivalent) at either Bachelor or Master level is required in any of Mathematics, Physics, Mechanics, Mechanical/Aerospace/Chemical Engineering disciplines.

Project Details

Polymers and turbulence are two of the most difficult problems in statistical physics. In the past, the study of polymeric liquids was divided in two categories: rheological investigations, where coarse- grained molecular models of polymers are interacting with a prescribed velocity field, hence the effects of the polymers on fluid motion are not taken into account, and fluid dynamics investigations, where the polymeric fluid is modeled at large/slow enough scales for the polymers to loose their individuality, hence for the total system (fluid + polymers) to appear as a viscoelastic liquid. A major weakness of the latter approach is its reliance on constitutive laws for (Brownian motion induced) polymer elastic stresses, since these are difficult to formulate for all polymer concentrations, especially in the dense regime where entanglements between chains exert topological constraints on polymer motion. In response to these, the Strathclyde group has recently developed a mesoscopic approach to polymeric liquids, where discrete polymer chains participate in two-way interactions with an incompressible flow field. This formulation is exact, and can model both laminar and turbulence flows, spanning the whole range of polymer concentrations: from dilute via semidilute to dense (entangled), whilst employing the same polymer model.

The purpose of this project is to apply this formulation to polymeric turbulent boundary layer flows and, in this way, to make some first, yet decisive, steps in the physics and algorithmics of fully-coupled polymeric boundary layer turbulence. For example, the two-way interactions between polymer chains and vortical structures in the classical turbulent boundary layer, and their role in polymer turbulent drag reduction phenomena are going to be investigated with advanced, projection, finite-volume and stochastic dynamics solvers. The PhD student will have access to in-house developed, well-tested computational codes for mesoscopic polymeric fluid dynamics that they will need to develop further and adapt to boundary layer turbulence research; there are many opportunities here for uncovering deep and intriguing turbulence physics, that would feature in high impact factor physics journals. For example, previous work has appeared in Chemical Physics and Physical Review journals. The findings are expected to be of great importance to a wide range of industries and government agencies whose business/mission requires a detailed understanding of polymer- fluid interactions. Moreover, the PhD student will acquire a plethora of transferable skills including, Turbulence and Polymer Physics, projection, finite volume and stochastic dynamics numerical methods, and advanced algorithmics, including a great deal of computational geometry. The computations are going to be performed on a new, in-house, multi-processor machine offering ideal opportunities for parallel computing. The student is going to be embedded within the “multi-scale simulation and theory” research division of the Department, thus, having plenty of opportunities to interact with researchers in molecular dynamics, nonequilibrium statistical mechanics, colloidal fluids, superfluids, and reacting and multiphase flows among other.

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.

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 may be considered for a University scholarship.

Contact us

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

How to apply

Apply for this project here – 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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