Richard Graham

Associate Professor in Applied Mathematics

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Dr Richard Graham,
School of Mathematical Sciences,
University of Nottingham,
NG7 2RD, UK.

Tel: (+44) (115) 951 3850
Fax: (+44) (115) 951 4951

Researcher ID: C-9196-2011


Some of the pictures link to a related movie.

Areas of research

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Equations of state for Carbon Capture and Storage

Carbon capture and storage is a crucial technology in the international efforts to meet carbon dioxide emission targets. Capturing carbon dioxide from industrial sources can lead to a 90% reduction in emissions. However, no gas separation process is 100% efficient, and as a result the carbon dioxide generated contains a number of different impurities, depending on its source. These impurities can, depending on their composition and concentration, greatly influence the physical properties of the fluid compared to pure CO2. They have important design, safety and cost implications for the compression and transport of carbon dioxide and its storage location, for example geological sequestration. A descriptive sentence
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My research is designed to tackle one of the key technical challenges facing the development of commercially viable CO2 transport networks: modelling phase behaviour of impure carbon dioxide, under the conditions typically found in carbon capture from power stations, and in high-pressure (liquid phase) and low-pressure (gas phase) pipelines. Accurate modelling of the physical properties of CO2 mixtures is essential for the design and operation of compression and transport systems for CO2. I use a range of techniques, from empirical parametric and non-parameter methods, through to ab initio molecular simulation.

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Flow induced crystallization in polymer melts

Using theories of molecular motion to understand and predict the effect of flow on crystallisation of polymeric materials. I have been developing a series of computational models for anisotropic crystal nucleation and growth in polymer melts and the effect of flow on these processes. I am tackling this problem with a range of techniques, including analytic calculations, numerical solution of closed-form PDEs and kinetic Monte-Carlo simulations.

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Electrophoresis of DNA molecules

Developing models and Brownian dynamics simulation algorithms for the motion of DNA molecules under the influence of strong electric fields. Applying these models to understand and improve processes involved in separating and sequencing DNA molecules.

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Dynamics of entangled polymers

Developing quantitative models of polymer dynamics under flow. Using statistical mechanical theories of polymer motion I derive detailed fundamental models for concentrated fluids of branched and linear polymer undergoing rapid flows. In particular, I have constructed a family of coarse-grained models for linear polymers, which allows the level of detail and computation expense to be selected according to the desired application.

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Neutron scattering from polymers under strong flow

Neutron scattering provides a very detailed picture of the dynamics of a polymer chain under flow, and is a very good testing ground for polymer theories. I use molecular models to predict and interpret the results of small angle neutron scattering measurements from polymers subjected to flow and I have shown some successful quantitative predictions of neutron scattering measurements from polymer melts under rapid flows.


Click the link to see the journal version of these articles

  • Graham RS, Henry EP and Olmsted PD, Comment on “New Experiments for Improved Theoretical Description of Nonlinear Rheology of Entangled Polymers”, Macromolecules, Published online (2014).
  • Demetriades TA, Drage TC and Graham RS, Developing a new equation of state for CCS pipeline transport, Journal of Process Mechanical Engineering 227 117 (2013); Invited article in a special issue on Process and Mechanical Engineering for Carbon Capture and Transport.

  • Jolley K and Graham RS, Flow-induced nucleation in polymer melts: A study of the GO model for pure and bimodal blends, under shear and extensional flow, Rheological Acta. 52 (3) 271 (2013); invited article for a special issue devoted to novel trends in rheology.

  • Shakeel M, Matthews PC, Graham RS, Waters SL, A continuum model of cell proliferation and nutrient transport in a perfusion bioreactor, Mathematical Medicine and Biology 30 (3) 21-44, (2013)

  • Hamer MJ, Wattis JAD, Graham RS, A method to project the rate kinetics of high dimensional barrier crossing problems onto a tractable 1D system, Soft Matter 8 (44)11396-11408 (2012).

  • Jolley K and Graham RS, A fast algorithm for simulating flow-induced nucleation in polymers, Journal of Chemical Physics 134, 164901 (2011); featured as a research highlight and made free to access.

  • Mykhaylyk OO, Fernyhough CM, Okura M, Fairclough JPA, Ryan AJ, Graham R, Monodisperse macromolecules - A stepping stone to understanding industrial polymers, European Polymer Journal 47(4), 447 (2011); invited article for a special issue dedicated to Professor Nikos Hadjichristidis in recognition of his contribution to polymer science.

  • Graham RS, Molecular modelling of flow-induced crystallisation in polymers, Journal of Engineering Mathematics 71 (3) 237-251 (2011); invited article in a special issue on ‘Complex Flows of Complex Fluids’ .

  • Graham RS and Larson RG, Coarse-grained simulations of stretching entangled DNA using oscillating electric fields, Chemical Communications 47(1) 337-339 (2011); invited article in a special issue on ‘Emerging Investigators’.

  • Hamer MJ, Wattis JAD, Graham RS, Analytic calculation of nucleation rates from a kinetic Monte Carlo simulation of flow-induced crystallization in polymers, Journal of Non-Newtonian Fluid Mechanics 165 1294 (2010).

  • Clarke N, De Luca E, Buxton G, Hutchings L, Gough T, Grillo I, Graham RS, Jagannathan K, Klein D, McLeish TCB, Chain Deformation in Entangled Polymer Melts at Re-entrant Corners, Macromolecules 43(3) 1539-1542 (2010).

  • Graham RS, Olmsted PD, Kinetic Monte Carlo simulations of flow-induced nucleation in polymer melts, Faraday Discussions 144(1), 1-22 (2010). Article Click here for a movie related to this paper.

  • McLeish TCB, Clarke N, de Luca E, Hutchings LR, Graham RS, Gough T, Grillo I, Fernyhough CM, Chambon P, Neutron Flow Mapping: Multiscale Modelling Opens a New Experimental Window, Soft Matter, 5(22), 4426-44324 (2009).

  • Graham RS, Olmsted PD, Coarse-grained simulations of flow-induced nucleation in semi-crystalline polymers, Physical Review Letters 103, 115702 (2009). Click here for a movie related to this paper.

  • Tezel AK, Oberhauser JP, Graham RS, Jagannathan K, McLeish TCB, Leal LG, The nonlinear response of entangled star polymers to startup of shear flow, Journal of Rheology 53(5) 1193-1214 (2009).

  • Scelsi L, Mackley MR, Klein H, Olmsted PD, Graham RS, Harlen OG, McLeish TCB, Experimental observations and matching viscoelastic specific work predictions of flow-induced crystallization for molten polyethylene within two flow geometries, Journal of Rheology 53(4) 859-876 (2009).

  • Graham RS, Bent J, Clarke N, Hutchings LR, Richards RW, Gough T, Hoyle DM, Harlen OG, Grillo I, Auhl D, McLeish TCB, The long chain dynamics in a model homopolymer blend under strong flow: small angle neutron scattering and theory, Soft Matter 5 2383-2389 (2009); invited article in a Soft Matter special issue highlighting outstanding young interdisciplinary scientists.

  • Mykhaylyk OO, Chambon P, Graham RS, Fairclough JPA, Olmsted PD, Ryan AJ, The specific work of flow as a criterion for orientation in polymer crystallisation, Macromolecules 41(6) 1901-1904 (2008).

  • Graham RS and McLeish TCB, Emerging applications for models of molecular rheology, Journal of Non-Newtonian Fluid Mechanics 150(1) 11-18 (2008).

  • Chen Z, Graham RS, Burns MA, Larson RG, Modelling ssDNA electrophoretic migration with band broadening in an entangled or cross-linked network, Electrophoresis 28(16) 2783-2800 (2007).

  • Graham RS and Larson RG, Coarse-grained Brownian dynamics simulations of electrophoresis of DNA molecules, Macromolecules 40(2), 366-378 (2007) Click here for a movie related to this paper.

  • Embery J, Graham RS, Duckett RA, Groves DJ, Collis M, Mackley MR, McLeish TCB, A tearing energy study of “oriented and relaxed” polystyrene in the glassy state , Journal of Polymer Science B 45(4), 377-394 (2007).

  • Heeley EL, Fernyhough CM, Graham RS, Olmsted PD, Inkson NJ, Embery J, Groves DJ, Morgovan A, Meneau F, Bras W, Ryan AJ, Shear induced crystallization in model blends of linear and long chain branched hydrogenated polybutadienes, Macromolecules 39(15), 5058- 5071 (2006).

  • Inkson NJ, Graham RS, McLeish TCB, Groves DJ, Fernyhough CM, Viscoelasticity of monodisperse comb polymer melts, Macromolecules 39(12), 4217-4227 (2006).

  • Graham RS, Bent J, Hutchings LR, Richards RW, Gough T, Spares R, Coates PD, Grillo I, Harlen OG, Read DJ, Likhtman AE, Groves DJ, Embery J, Nicholson TM, McLeish TCB, Measuring and predicting the dynamics of linear monodisperse entangled polymers in rapid flow through an abrupt contraction: a small angle neutron scattering study, Macromolecules 39(7), 2700-2709 (2006).

  • Blanchard A, Graham RS, Heinrich M, Pyckhout-Hintzen W, Richter D, Likhtman AE, McLeish TCB, Read DJ, Straube E, Kohlbrecher J, SANS observation of chain retraction after a large step deformation , Physical Review Letters 95 166001 (2005).

  • Collis MW, Lele AK, Mackley MR, Graham RS, Groves DJ, Likhtman AE, Nicholson TM, Harlen OG, McLeish TCB, Hutchins L, Fernyhough C, Young RN, Constriction flows of monodisperse linear entangled polymers: flow visualization and molecular modeling, Journal of Rheology 49(2) 505-522 (2005).

  • Bent J, Hutchings LR, Richards RW, Gough T, Spares R, Coates PD, Grillo I, Harlen OG, Read DJ, Graham RS, Likhtman AE, Groves DJ, Nicholson TM, McLeish TCB, Neutron Mapping Polymer Flow: Scattering, Flow-Visualization and Molecular Theory, Science 301 1691-1695 (2003). Click here for a movie related to this paper.

  • Likhtman AE, Graham RS, A simple constitutive equation for linear polymer melts derived from molecular theory: the Rolie-Poly model , Journal of Non-Newtonian Fluid Mechanics 114(1) 1-12 (2003).

  • Graham RS, Likhtman AE, McLeish TCB, Milner ST, Microscopic theory of linear, entangled polymers under rapid deformation including chain stretch and convective constraint release, Journal of Rheology 47(5) 1171-1200 (2003).

  • Suneel, Graham RS, McLeish TCB, Characterization of an industrial polymer melt through either uniaxial extension or exponential shear data: an application of the pom-pom model, Applied Rheology 13(1) 19-25 (2003).

  • Graham RS, McLeish TCB, Harlen OG, Using the pom-pom equations to analyze polymer melts in exponential shear, Journal of Rheology 45(1) 275-290 (2001).


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Graham RS, Molecular and continuum modelling of polymer melt flows, Department of Applied Mathematics and School of Physics and Astronomy, University of Leeds (2002).
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My thesis was awarded the the Vernon Harrison Annual Doctoral prize for “excellence, creativity and novelty in research” by the British Society of Rheology in 2003.