Final Report Summary - RHEOACTIVE (Geometry, instability and activity in complex and biological fluids) This ERC starting grant has concerned the rheology (deformation and flow properties) of complex fluids and soft materials, including biologically active materials, studied using a combination of analytical theory and numerical simulation.A particularly important achievement has been the forging of a new and unified understanding of the way in which these complex materials yield and start to flow, during the process whereby a steady flowing state is established out of an initial rest state. In particular, we have demonstrated theoretically that such a process is very often accompanied by the onset of flow heterogeneity, in which part of the material bears a disproportionate fraction of the total deformation applied.Fundamentally, two different classes of deformation and flow are possible: shear and extension (and, more generally, a superposition of these).In the context of shear flows, we derived fluid-universal criteria suggesting that many - and indeed perhaps most - complex fluids will, at least transiently, form a heterogeneous shear banded state as they yield and start to flow. Although technically transient, in disordered glassy systems with slow relaxation timescales, this effect is likely to persist long enough to be judged the ultimate flow response of the material for practical purposes. In other important work on shear rheology, we provided the first proper understanding of a free surface instability known as edge fracture, which arises almost ubiquitously when complex fluids are subject to shear, and which is widely cited as the major limiting factor in experimental rotational rheology. Most importantly, we suggested a way in which experimentalists might seek to mitigate the effect in practice.In the context of extensional flows, a widely used protocol is that of filament stretching (a close analogue of which arises in the spinning of fibres in an industrial context). Here we developed a new and unified understanding of the onset of the so-called necking instability, in which part of the filament thins disproportionately quickly, eventually causing the filament to fail altogether (snap).In other work, have developed a new model for the rheology of glassy polymers, and studied its response in shear and extension, showing it to explain hitherto puzzling data in these materials, and also to capture the heterogeneous flow phenomena just described. We also provided a new understanding of the limitations of fabric tensor approaches to modelling the rheology of non-Brownian suspensions; contributed to our understanding of thickening in viscoelastic flow through a porous medium; and to our understanding of the so-called moving contact line problem in fluid dynamics.Another important theme of the project has concerned biologically active suspensions, such as collections of swimming bacteria or protozoa. Here we developed a new continuum model of collective activity that takes place in the backdrop of a complex, viscoelastic environment, thereby rectifying a major shortcoming in the existing literature, much of which had assumed the backdrop of a simple fluid. We furthermore showed that motility induced phase separation, predicted to arise generically in active fluids, is likely to be suppressed if hydrodynamic interactions, which are very often present, are properly accounted for.
