





Our group's research concerns the theoretical and computational rheology (deformation and flow properties) of complex fluids such as polymers, surfactants, liquid crystals, colloids and emulsions. A particular focus concerns the understanding from a fundamental viewpoint of the onset of flow instabilities, which routinely hinder the experimental measurement of rheological properties, and also hamper the processing and use of these materials in a commercial context  or indeed in some situations can also be very useful, for example in enhancing mixing.
The work forms several distinct yet related strands:
Complex fluids such as surfactant solutions, polymers and liquid
crystals commonly show flow instabilities when subject to shear. Often
these instabilities lead to the formation of macroscopic "shear bands"
of differing viscosity and internal structure.
This effect can be viewed as a nonequilibrium (flowinduced) phase transition. Indeed, much of the phenomenology mirrors that of conventional (equilibrium) phase transitions, and I have pursued this analogy to study the kinetics of band formation, as well as to construct flow phase diagrams for the ultimate banded state. At the same time, there are fundamental differences from the equilibrium case, for example in the way the coexistence state is selected in the absence of a free energy minimisation principle. Particularly exciting developments have concerned the chaotic dynamics of shear banded flows, studying both the possibility of a bulk instability of one band, as shown in this shear rate greyscale: and of an instability of the interface between the bands:
Collaborations/links:
Edge fracture is a free surface instability that arises almost ubiquitously when a viscoelastic material is sheared in an open flow cell. It has been cited as the most significant limiting factor in experimental shear rheometry. The aim of this work is to elucidate a full mechanistic understanding of this phenomenon in a combined theory/simulation study, and to suggest a way experimentalists might mitigate it, potentially enabling them to achieve and measure faster flows than hitherto.
Collaborations/links
Besides shear flows, complex fluids are also widely subject to
extensional deformations. In an industrial context these form the
basis of spinning polymeric materials into fibres for textiles, for
example. In fluid dynamical terms, extensional flows cause material
elements to separate exponentially quickly and so subject the
underlying macromolecules to greater stretching and reorientation than
shear. Indeed extensional flow response is very sensitive to
underlying molecular details (linear vs. branched polymer chains, for
example), and many nonlinear flow effects manifest themselves only in
extension.
When an initially homogeneous mixture of two fluids (A and B) undergoes a deep temperature quench into the spinodal regime, it phase separates into well defined domains of Arich and Brich fluid. These then slowly coarsen in time through the action of the surface tension in the interfaces that separate them, such that the excess interfacial energy of the system progressively relaxes towards its minimal equilibrium value. This coarsening process proceeds through three distinct regimes that are successively dominated by diffusive, viscous and inertial dynamics. In the limit of an infinite system size, the typical domain size perpetually increases without bound: the system never globally equilibrates, even in the limit of infinite time. Here, we consider systems that are both undergoing phase separation and simultaneously subject to an applied shear flow. The main question that we address is whether shear interrupts domain coarsening to give a nonequilibrium steady state with a typical domain size set by the inverse of the applied shear rate; or whether coarsening persists indefinitely, up to the system size, as in zero shear. For systems with inertia we have reproduced the nonequilibrium steady states reported in a recent lattice Boltzmann study by the group of Cates. The domain coarsening that would occur in zero shear is arrested by the applied shear flow, which restores a finite domain size set by the inverse shear rate. For inertialess systems, in contrast, we have found no evidence of nonequilibrium steady states free of finite size effects: coarsening persists indefinitely until the typical domain size attains the system size, as in zero shear. In simple fluids, hydrodynamic instabilities and turbulent flows have long been known to arise at high Reynolds number, due to the nonlinearity inherent in the Navier Stokes equation. In the viscoelastic fluids and flow regimes of interest here, the Reynolds number is negligible. Despite this, the inherent nonlinearity of a polymeric material's constitutive response can cause purely viscoelastic instabilities. In curved flow devices, these include an inertialess TaylorCouette instability. In plateplate flow, a pathway through to fully developed viscoelastic turbulence has recently been demonstrated experimentally by the group of Larson.
Laminar viscoelastic flows with parallel streamlines are known to be
linearly stable: that is, able to resist perturbations of tiny
amplitude. Despite this, a nonlinear instability with respect to
perturbations of a finite amplitude was recently predicted by Morozov
et al. My work has focused on testing this prediction numerically
within a popular model of polymeric flows.
This work brings a unifying approach to the rheological (deformation and flow) behaviour of a broad class of soft materials, including:
The essential hypothesis is that all these materials share the basic features of disorder and metastability, which result in an underlying glassiness in the rheological response. This approach has successfully explained a broad class of existing rheological data. Furthermore it has led to new predictions of rheological ageing (slow progression towards a more elastic state), now widely being studied experimentally. Collaborations/links In addition to fluids that are taken far from equilibrium by external driving (shearing applied at the boundaries, as in the above example), another even more challenging class of complex fluids concerns those that are driven out of equilibrium by an activity inherent within their own bulk. Examples include swarms of selfpropelled bacteria or protozoa; and the viscoelastic matrix of the biological cell, in which molecular motors at crosslinks between polymeric strands render the network as a whole capable of mechanical motion (in cell division or amoebic crawling). Here each mesoscopic substructure (bacterium/motor) itself individually consumes energy, and so can actively propel itself: ``swimming'' through the suspending fluid, or ``marching'' along a neighbouring cytoskeletal filament. Their collective dynamics is thus inherently far from equilibrium, even without boundary driving. Indeed in this new class of fluids the driving away from equilibrium occurs from within the volume of the fluid itself. Emergent phenomena include hydrodynamic instabilities in which an initially quiescent fluid gives way to shear banded (establishing a link to (i) above) or turbulently swirling patterns, as seen experimentally and reproduced in my simulations below.
Collaborations/links

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Last updated:
4th September 2017
