Rheology and flow properties of a deformable droplet suspension
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Concentrated suspensions of colloidal particles in a liquid solvent are often found in nature and industry. Familiar examples include ice cream, mayonnaise, paints and biological fluids such as blood. It is well known that the flow properties of colloidal suspensions can be distinctly non-trivial, for instance presenting shear thinning or shear thickening behaviour under different circumstances. Often, in such colloidal fluids, the dispersed particles are not hard but soft and deformable. For instance, we can think about fat droplets floating in milk or eukaryotic cells: all these can deform under flow or when subjected to a mechanical stress. While hard-spheres fluids have been extensively studied and provide the basis for our understanding of the glass transition and soft glassy rheology, comparatively less is known about the flow response of a suspension of deformable particles. Nonetheless, there is evidence suggesting that the physics of soft suspensions is both highly interesting and important in applications. Indeed, particle deformability is important to determine the rheology of a material; for example, emulsions and foam do not normally display shear thickening, unlike hard-spheres colloidal fluids. In this thesis, we use two-dimensional lattice Boltzmann simulations to investigate the dynamics and the rheological properties of a suspension of soft, non-coalescing deformable droplets. In particular, in the first results chapter, we analysed the rheology of a deformable suspension when subjected to a pressure driven flow, regulated by the external application of an homogeneous body-force on the underlying fluid. Here, we provide evidence of a discontinuous shear thinning behaviour, occurring at a concentration dependent value of the forcing. We further show that this response is associated with a non-equilibrium transition between a “hard” (or less deformable) phase, which is nearly jammed and flows very slowly, and a “soft” (or mode deformable) one, which flows much more easily. The observed hard-soft transition is further analysed in the second results chapter, where we provide a detailed study of the role of the droplet surface tension in the overall suspension rheology. After confirming the discontinuous shear thinning behaviour for a range of imposed droplet surface tension, we determine and discuss how the property of deformability affects the forcing threshold leading to the discontinuity. Moreover, we find that the effective viscosity of the suspension is mainly determined by its Capillary number. In the last results chapter we aim to understand the reversibility properties of our deformable droplet suspension, shedding light on the onset of irreversibility and loss of predictability. To this end we use two different sets of simulations which represent two distinct ways of imposing a deformation on our system and therefore testing its reversibility properties. In the first part, a droplet in our suspension is periodically inflated and deflated, therefore causing an overall rearrangement of the neighbouring droplets. On the other hand, in the second part an oscillatory shear is imposed on the walls which constrain our suspension. In both cases, the droplets position is carefully tracked, enabling us to verify if, after each period of the imposed deformation, all the droplets come back to their original positions, and therefore our suspension shows reversible behaviour. As we will see, a transition between a reversible and an irreversible phase is detected and found to depend on the amount of imposed deformation.