I’ve been interested in non-Newtonian and viscoelastic fluids since my MSc degree at the University of Wales Aberystwyth. More recently, I’ve been considering lattice Boltzmann implementations of the Fokker-Planck equation. Based on the work of Amine Ammar (2010) I’ve begun to investigate the LBM for polymer kinetic theory.
Initial results for planar extensional and start-up shear flow (both with imposed velocity fields) are encouraging, showing the expected behaviour and convergence to the solutions. The above plot shows the steady state solution of the Fokker-Planck equation in extensional flow computed by the LBM. The Weissenberg number, We, is unity in the left plot, and 5 in the right. A FENE connector force with extensibility parameter b=50. The results converge to the analytical solution with second order accuracy.
The plots above show the the viscosity and first normal stress difference in start-up shear when We=10. This work was first presented in the mini symposium on the Mathematics of Complex Fluids at the 2016 British Applied Mathematics Colloquium (BAMC 2016).
While a postdoc under the guidance of Helen Wilson at UCL I worked on instabilities in polymer processing. This built on the work of Mehmet Sahin and formed part of the second Microscopic Polymer Processing project (MuPP2). To help understand the physics of elastic instabilities of entangled polymer melts we performed a numerical linear stability study of a molecular based constitutive model. We studied two constriction flows (one shear dominated, the other extension dominated) and detected two distinct instabilities. In both cases, chain relaxation and orientation were found to play a crucial role.
This plot shows tangential stress (left) the contours and streamlines (right) for one of “bumpy wall” geometry that we used as part of our study. Take from Reis and Wilson (2013).
Dr Tim Reis 