Flexible filaments and fibres are essential components of important complex fluids that appear in many biological and industrial settings. Direct simulations of these systems that capture the motion and deformation of many immersed filaments in suspension remain a formidable computational challenge due to the complex, coupled fluid-structure interactions of all filaments, the numerical stiffness associated with filament bending, and the various constraints that must be maintained as the filaments deform. In this paper, we address these challenges by first describing filament kinematics using quaternions to resolve both bending and twisting, applying implicit time-integration to alleviate numerical stiffness, and using quasi-Newton methods to obtain solutions to the resulting system of nonlinear equations. In particular, we employ geometric time integration to ensure that the quaternions remain unit as the filaments move. We also show that our framework can be used with a variety of models and methods, including matrix-free fast methods, that resolve low Reynolds number hydrodynamic interactions. We provide a series of tests and example simulations to demonstrate the performance and possible applications of our method. Finally, we provide a link to a MATLAB/Octave implementation of our framework that can be used to learn more about our approach and as a tool for filament simulation.
We consider the fluid dynamics of the chocolate fountain. Molten chocolate is a mildly shear-thinning non-Newtonian fluid. Dividing the flow into three main domains-the pumped flow up the centre, the film flow over each dome, and the freely falling curtain flow between the domes-we generate a wideranging study of Newtonian and non-Newtonian fluid mechanics. The central pumped flow is a benchmark to elucidate the effects of shear-thinning. The dome flow can be modelled as a thin-film flow with the leading-order effects being a simple balance of gravity and viscosity. Finally, the curtain flow is analytically intractable but is related to the existing theory of water bells (both inviscid and viscous). In pipe flow, Newtonian fluids exhibit a parabolic velocity profile; shear-thinning makes the profile more blunted. In thin-film flow over the dome, gravitational and viscous effects balance and the dome shape is not important beyond the local slope. We find that the chocolate thins and slows down as it travels down the dome. Finally, in the curtain flow, we predict the shape of the falling sheet for an inviscid fluid, and compare this with the literature to predict the shape for a viscous fluid, having shown that viscous forces are too great to ignore. We also find that the primary effect driving the shape of the curtain (which falls inwards towards the axis of the fountain) is surface tension. We find that the three domains provide excellent introductions to non-Newtonian mechanics, the important mathematical technique of scaling, and how to manipulate existing data to make our own predictions. We also find that the topic generates interest among the public in our engagement work.
In Stokesian Dynamics, particles are assumed to interact in two ways: through longrange mobility interactions and through short-range lubrication interactions. To speed up computations, in shear-driven concentrated suspensions, often found in rheometric contexts, it is common to consider only lubrication. We show that, although this approximation may provide acceptable results in shear-driven, periodic suspensions, for bidisperse suspensions where the particles are exposed to an external force, it can produce physically unreasonable results. We suggest that this problem could be mitigated by a careful choice of particle pairs on which lubrication interactions should be included.
BACKGROUND: The rheology of shear thickening fluids is well characterized for many physical applications, however the literature surrounding biologically or cryobiologically compatible shear thickening fluids is less well understood. OBJECTIVE: This study examined fluids consisting of corn-derived hydroxyethyl starch with a variety of sugars and cryoprotectants to characterize their shear-rate viscosity relationship. The objective was to establish if cryobiologically relevant materials could be used to afford biologics protection through shear-thickening. RESULTS: Fluids consisting of 50% hydroxyethyl starch by weight exhibited shear thickening with a variety of cryoprotectants. Lowering the temperature of the fluid both reduced critical shear rates and enhanced thickening magnitude. Starch derived from corn, wheat, and rice all exhibited non-Newtonian shear-dependent viscosity behaviour at 50% by weight in water. Between the starch sources however, the shear-rate viscosity relationship varied widely, with wheat-derived starch shear thinning, and the remaining starches forming shear thickening fluids. Different starch sources had different baseline viscosities, critical shear rates, and rates of viscosity increase. CONCLUSIONS: This study established that shear thickening is compatible with cryobiologically relevant agents, particularly so at lower temperatures. This forms the basis for harnessing these phenomena in biological processes such as cryopreservation.
We study non-Brownian suspensions under steady shear flow. In concentrated suspensions, we are trying to reproduce the shear thickening phenomenon seen in, for example, cornstarch. We investigate the effect of different frictional contact models. When contact acts to impose a fixed minimum separation between particles, there is a strict upper bound to the viscosity predicted by simulations. We deduce that soft or compressible contacts are a critical component of the strong shear thickening seen in experiments.
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