arXiv subjects

Theodore A. Marschall

Publications and source records attributed to Theodore A. Marschall.

5 recordsLinked to original sources

arXiv2021

Athermal shearing of frictionless cross-shaped particles of varying aspect ratio

We use numerical simulations to study the shear-driven steady-state flow of athermal, frictionless, overdamped, two dimensional cross-shaped particles of varying aspect ratios, and make comparison with the behavior of rod-shaped and staple-shaped particles. We find that the extent of non-convexity of the particle shape plays an important role in determining both the value of the jamming packing fraction as well as the rotational motion and orientational ordering of the particles.

cond-mat.soft↗

arXiv2020

Depletion Forces in Athermally Sheared Mixtures of Frictionless Disks and Rods in Two Dimensions

We carry out numerical simulations to study the behavior of an athermal mixture of frictionless circular disks and elongated rods in two dimensions, under three different types of global linear deformation at a finite strain rate: (i) simple shearing, (ii) pure shearing, and (iii) isotropic compression. We find that the fluctuations induced by such deformations lead to depletion forces that cause rods to group in parallel oriented clusters for the cases of simple and pure shear, but not for isotropic compression. For simple shearing, we find that as the fraction of rods increases, this clustering increases, leading to an increase in the average rate of rotation of the rods, and a decrease in the magnitude of their nematic ordering.

cond-mat.soft↗

arXiv2020

Shear-Driven Flow of Athermal, Frictionless, Spherocylinder Suspensions in Two Dimensions: Spatial Structure and Correlations

We use numerical simulations to study the flow of athermal, frictionless, soft-core two dimensional spherocylinders driven by a uniform steady-state simple shear applied at a fixed volume and a fixed finite strain rate $\dotγ$. Energy dissipation is via a viscous drag with respect to a uniformly sheared host fluid, giving a simple model for flow in a non-Brownian suspension with Newtonian rheology. We study the resulting spatial structure of the sheared system, and compute correlation functions of the velocity, the particle density, the nematic order parameter, and the particle angular velocity. Correlations of density, nematic order, and angular velocity are shown to be short ranged both below and above jamming. We compare a system of size-bidisperse particles with a system of size-monodisperse particles, and argue how differences in spatial order as the packing increases leads to differences in the global nematic order parameter. We consider the effect of shearing on initially well ordered configurations, and show that in many cases the shearing acts to destroy the order, leading to the same steady-state ensemble as found when starting from random initial configurations.

cond-mat.soft↗

arXiv2020

Shear-Driven Flow of Athermal, Frictionless, Spherocylinder Suspensions in Two Dimensions: Particle Rotations and Orientational Ordering

We use numerical simulations to study the flow of a bidisperse mixture of athermal, frictionless, soft-core two dimensional spherocylinders driven by a uniform steady-state simple shear applied at a fixed volume and a fixed finite strain rate $\dotγ$. Energy dissipation is via a viscous drag with respect to a uniformly sheared host fluid, giving a simple model for flow in a non-Brownian suspension with Newtonian rheology. Considering a range of packing fractions $ϕ$ and particle asphericities $α$ at small $\dotγ$, we study the angular rotation $\dotθ_i$ and the nematic orientational ordering $\mathbf{S}_2$ of the particles induced by the shear flow, finding a non-monotonic behavior as the packing $ϕ$ is varied. We interpret this non-monotonic behavior as a crossover from a small $ϕ$ region where single-particle-like behavior occurs, to a large $ϕ$ region where the geometry of the dense packing dominates, the reduced free volume inhibits motion, and a random Poisson-like process for particle rotations results. We also argue that the finite nematic ordering $\mathbf{S}_2$ is a consequence of the shearing serving as an ordering field, rather than a result of long-ranged cooperative behavior among the particles. We arrive at these conclusions by consideration of (i) the distribution of waiting times for a particle to rotate by $π$, (ii) the behavior of the system under pure, as compared to simple, shearing, (iii) the relaxation of the nematic order parameter $\mathbf{S}_2$ when perturbed away from the steady state, and (iv) by construction a numerical mean-field model for the rotational motion of a particle. Our results also help to explain the singular behavior observed when taking the $α\to 0$ limit approaching circular disks.

cond-mat.soft↗

arXiv2019

Shear-Driven Flow of Athermal, Frictionless, Spherocylinder Suspensions in Two Dimensions: Stress, Jamming, and Contacts

We use numerical simulations to study the flow of a bidisperse mixture of athermal, frictionless, soft-core two dimensional spherocylinders driven in uniform steady state shear. Energy dissipation is via a viscous drag with respect to a uniformly sheared host fluid, giving a model for a non-Brownian suspension with a Newtonian rheology. We study pressure $p$ and deviatoric shear stress $σ$ as a function of packing fraction $ϕ$, strain rate $\dotγ$, and a parameter $α$ that measures the asphericity of the particles. We consider the anisotropy of the stress tensor, the macroscopic friction $μ=σ/p$, and the divergence of the transport coefficient $η_p=p/\dotγ$ as $ϕ$ is increased to the jamming $ϕ_J$. From an analysis of Herschel-Bulkley rheology above jamming, we estimate $ϕ_J$ as a function of $α$ and show that the variation of $ϕ_J$ with $α$ is the main cause for differences in rheology as $α$ is varied. However a detailed scaling analysis of the divergence of $η_p$ for our most elongated particles suggests that the jamming transition of spherocylinders may be in a different universality class than that of circular disks. We compute the number of contacts per particle $Z$ in the system and show that at jamming $Z_J$ is a non-monotonic function of $α$ that is always smaller than the isostatic value. We measure the probability distribution of contacts per unit surface length $\mathcal{P}(\vartheta)$ at polar angle $\vartheta$ with respect to the spherocylinder spine, and find that as $α\to 0$ this distribution seems to diverge at $\vartheta=π/2$, giving a finite limiting probability for contacts on the vanishingly small flat sides of the spherocylinder. Finally we consider the variation of the average contact force as a function of location on the particle surface.

cond-mat.soft↗