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Register a new userImplementation note on a minimal hybrid lubrication/granular dynamics model for dense suspensions
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We describe and summarize a class of minimal numerical models emerged from recent development of simulation methods for dense particle suspensions in overdamped linear flows. The main ingredients include (i) a frame-invariant, short-range lubrication model for spherical particles, and (ii) a soft-core, stick/slide frictional contact model activated when particles overlap. We implement a version of the model using a modified velocity-Verlet algorithm that explicitly solves the $N$-body dynamical system in $mathcal{O}(cN)$ operations, where $c$ is a kernel constant depending on the cutoff of particle interactions. The implementation is validated against literature results on jamming transition and shear thickening suspensions from 40% to 64% volume fractions. Potential strategies to extend the present methodology to non-spherical particles are also suggested for very concentrated suspensions.
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We experimentally investigate the rheology and stress fluctuations of granules densely suspended in silicone oil. We find that both thickening strength and stress fluctuations significantly weaken with oil viscosity $eta_0$. Comparison of our rheological results to the Wyart-Cates model for describing different dynamic jamming states suggests a transition from frictional contacts to lubrication interactions as $eta_0$ increases. To clarify the contribution from viscous interactions to the rheology, we systematically measure stress fluctuations in various flow states. Reduction of stress fluctuations with $eta_0$ indicates that a strong lubrication layer greatly inhibits force correlations among particles. Measuring stress fluctuations in the strong shear thickening regime, we observe a crossover from asymmetric Gamma to symmetric Gaussian distributions and associated with it a decrease of lateral (radial) correlation length $xi$ with increasing shear rate.
Dense suspensions have previously been shown to produce a range of anomalous and gravity-defying behaviors when subjected to strong vibrations in the direction of gravity. These behaviors have previously been interpreted in terms of rigid body phenomena and shear-thickening, but here we examine discontinuous shear thickening (DST) as the cause of a negative viscosity effect, i.e. the average shear rate being opposite to the direction of the average shear stress. Using ideas from the Wyart and Cates modeling framework, we show that such a negative viscosity can be achieved in shear flows driven by oscillating stress with both square and sinusoidal wave forms. We extend this same modeling approach to study falling films in a vibrating gravitational field, where we similarly find it is possible to attain an overall flow opposite to the direction of gravity. Preliminary experimental findings are also provided in support of the modeling work.
Near field hydrodynamic interactions are essential to determine many important emergent behaviors observed in active suspensions, but have not been successfully modeled so far. In this work we propose an effective model capable of efficiently capturing the essence of the near field hydrodynamic interactions, validated numerically by a pedagogic model system consisting of an E. coli and a spherical tracer. The proposed model effectively captures all the details of near field hydrodynamics through only a tensorial coefficient of resistance, which is fundamentally different from, and thus cannot be replaced by, an effective interaction of conservative nature. In a critical test case that studies the scattering angle of the bacterium-tracer pair dynamics, calculations based on the proposed model reveals a region in parameter space where the bacterium is trapped by the spherical tracer, a phenomenon that is regularly observed in experiments but cannot be explained by any existing model.
Granular fronts are a common yet unexplained phenomenon emerging during the gravity driven free-surface flow of concentrated suspensions. They are usually believed to be the result of fluid convection in combination with particle size segregation. However, suspensions composed of uniformly sized particles also develop a granular front. Within a large rotating drum, a stationary recirculating avalanche is generated. The flowing material is a mixture of a visco-plastic fluid obtained from a kaolin-water dispersion, with spherical ceramic particles denser than the fluid. The goal is to mimic the composition of many common granular-fluid materials, like fresh concrete or debris flow. In these materials, granular and fluid phases have the natural tendency to segregate due to particle settling. However, through the shearing caused by the rotation of the drum, a reorganization of the phases is induced, leading to the formation of a granular front. By tuning the material properties and the drum velocity, it is possible to control this phenomenon. The setting is reproduced in a numerical environment, where the fluid is solved by a Lattice-Boltzmann Method, and the particles are explicitly represented using the Discrete Element Method. The simulations confirm the findings of the experiments, and provide insight into the internal mechanisms. Comparing the time-scale of particle settling with the one of particle recirculation, a non-dimensional number is defined, and is found to be effective in predicting the formation of a granular front.
Particle-based simulations of discontinuous shear thickening (DST) and shear jamming (SJ) suspensions are used to study the role of stress-activated constraints, with an emphasis on resistance to gear-like rolling. Rolling friction decreases the volume fraction required for DST and SJ, in quantitative agreement with real-life suspensions with adhesive surface chemistries and rough particle shapes. It sets a distinct structure of the frictional force network compared to only sliding friction, and from a dynamical perspective leads to an increase in the velocity correlation length, in part responsible for the increased viscosity. The physics of rolling friction is thus a key element in achieving a comprehensive understanding of strongly shear-thickening materials.
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