Project title: Multiscale simulations of instabilities in complex (non-Newtonian) fluids

Supervisors: Dr Tamer Zaki, Dr Daniele Dini and Dr Fernando Bresme

Project description:

Instabilities are often associated with high Reynolds number flows, where organized fluid motion gives way to chaotic trajectories, or turbulence. However, in non-Newtonian complex fluids, this transition can take place even at very low flow speeds. While viscous forces normally dominate in this slow flow regime, the inherent microstructure of some visco-elastic fluids can introduce new instability mechanisms. These instabilities dictate many industrial processes that include, for example, polymer extrusions and mixing. Accurate prediction of these instabilities is highly dependent on the ability to describe the energy transport phenomena and constitutive relations that govern visco-elastic fluid mechanics. From this information, then, we should be able to determine the macroscopic flow behaviour. However, the problem is multi-scale in nature: the constitutive relation and microstructural evolution of the visco-elastic fluid cannot be described by continuum theory and so must be modeled using molecular-scale simulations. The flow instabilities, on the other hand, are described at the macroscopic scale and can only be feasibly evaluated (at present times) using continuum theory.

Molecular dynamics models will be developed for complex, visco‚Äźelastic fluids under shear and in inhomogeneous flow conditions (for example near solid walls). These models will be embedded `on-the-fly' to compute constitutive relations for complex fluids within a Navier-Stokes continuum solver. In order to simulate the emergence of instability waves and chaotic flow behaviour in macroscopic flows, the two problems must be solved dynamically and concurrently. Such an approach will mitigate any uncertainty in predicting the required range of strain-rates for a sequential coupling approach - an issue which is made challenging due to the interdependence of the continuum state on the molecular behaviour and vice-versa. In addition, the multi-scale nature of the emerging chaotic motion exacerbates the difficulties in predicting the relevant strain rates a priori.