Townsend, AK; (2017) The mechanics of suspensions. Doctoral thesis , UCL (University College London).

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Abstract

Suspension mechanics—the flow of a fluid with small fragments of solid material suspended in it—is an area of wide applicability in both industry and nature. Examples include the transport of silt in rivers, the manufacture of toothpaste, and inkjet printing where pigments remain solid within the ink. One widespread method to simulate these flows is Stokesian Dynamics, a truncated multipole expansion of the Stokes equations. It is computationally efficient while making a reasonable approximation to the hydrodynamic interactions between particles; however, all particles are identical spheres and the background matrix must be Newtonian. This project extends Stokesian Dynamics to include differently-sized spheres. This allows us to study a variety of previously inaccessible suspension problems. In many suspensions, e.g. toothpaste, the suspending fluid itself is non-Newtonian and exhibits viscoelastic properties. We have extended Stokesian Dynamics to incorporate a simple model of viscoelasticity by using the small spheres as 'beads' in bead--spring dumbbells. Different spring laws are then tested in shear, and their rheological behaviour is compared to continuum constitutive models. Next, we replicate experiments in which a large sphere is dropped through a suspension of neutrally buoyant smaller spheres undergoing oscillatory shear flow. We qualitatively replicate the principal experimental observation—that at the moment of shear reversal, the suspension microstructure hinders the falling; while at the instant of fastest shear, it enhances the falling. We propose a physical mechanism explaining the observations. Finally, we extend Stokesian Dynamics to properly implement interparticle frictional contact. Contact forces are a critical component of shear thickening in suspensions such as cornflour, yet are usually implemented in an ad hoc way, resulting in inaccurate predictions or high computational cost. The new method allows us to investigate contact models quickly and efficiently, and suggests an important factor in models of strongly shear-thickening fluids.

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