Sarah Hormozi

Flows of suspensions of particles in yield stress fluids

We study the rheological behavior of suspensions of noncolloidal spheres in yield stress fluids (concentrated emulsions). These are good model systems for understanding, e.g., the rheology of fresh concrete or debris flows, and more generally, the behavior of particles dispersed in any nonlinear material. We use magnetic resonance imaging techniques to investigate the flows of these yield stress suspensions in a concentric-cylinder Couette geometry. We extend the theoretical approach of Chateau et al. [J. Rheol. 52, 489–506 (2008)], valid for isotropic suspensions, to describe suspensions in simple shear flows, in which an anisotropic spatial distribution of particles is induced by flow. Theory and experiments show that the suspensions can be modeled by a Herschel–Bulkley behavior of same index as their interstitial fluid. We characterize the increase of their consistency and their yield stress with the particle volume fraction ϕ in the 0%–50% range. We observe a good agreement between the experimental variations of the consistency with ϕ and the theoretical prediction. This shows that the average apparent viscosity of the sheared interstitial material is correctly estimated and taken into account. We also observe shear-induced migration with similar properties as in a Newtonian fluid, which we predict theoretically, suggesting that particle normal stresses are proportional to the shear stress. However, the yield stress at flow stoppage increases much less than predicted. We also show that new features emerge in the rheology of the yield stress fluid when adding particles. We predict and observe the emergence of a nonzero normal stress difference at the yielding transition. We observe that the yield stress at flow start can differ from the yield stress at flow stoppage, and depends on flow history. It is likely a signature of a shear-dependent microstructure, due to the nonlinear behavior of the interstitial fluid, which makes these materials different from suspensions in Newtonian media. This is confirmed by direct characterization of shear-rate-dependent pair distribution functions using X-ray microtomography. This last observation explains why the theory predictions for the consistency can be correct while failing to model the yield stress at flow stoppage: a unique microstructure was indeed assumed as a first approximation. More sophisticated theories accounting for a shear-dependent microstructure are thus needed.We study the rheological behavior of suspensions of noncolloidal spheres in yield stress fluids (concentrated emulsions). These are good model systems for understanding, e.g., the rheology of fresh concrete or debris flows, and more generally, the behavior of particles dispersed in any nonlinear material. We use magnetic resonance imaging techniques to investigate the flows of these yield stress suspensions in a concentric-cylinder Couette geometry. We extend the theoretical approach of Chateau et al. [J. Rheol. 52, 489–506 (2008)], valid for isotropic suspensions, to describe suspensions in simple shear flows, in which an anisotropic spatial distribution of particles is induced by flow. Theory and experiments show that the suspensions can be modeled by a Herschel–Bulkley behavior of same index as their interstitial fluid. We characterize the increase of their consistency and their yield stress with the particle volume fraction ϕ in the 0%–50% range. We observe a good agreement between the experimental v...

Time-resolved 2D concentration maps in flowing suspensions using X-ray

In this paper, we introduce a new technique based on X-ray radiography with high temporal (O(0.1 s)) and spatial (O(10 μm)) resolutions to study fast suspension flows regardless of optical access. We benefit from the axial symmetry of our flow configuration, a wide gap Couette setup, to extract a 3D solid volume fraction field from a single X-ray projection image. We propose a mathematical algorithm based on the inversion of Abel transform in conjunction with H1 regularization and data denoising to measure the solid volume fraction field in suspensions in a fraction of a second. We show that the results are in excellent agreement with those obtained from micro Computed Tomography (CT scan) in one hour. This significant reduction in the data acquisition time opens a new avenue in the field of suspensions. As a proof of concept, we study the kinetics of shear-induced migration for suspensions of particles in both Newtonian and yield stress suspending fluids. The latter experiments include two different conditions: With and without a plug region. In both cases, we are able to capture in detail the kinetics of migration. In the presence of a plug region, we manage to accurately describe the particle accumulation at the interface between the sheared and the static regions. Remarkably, even in the absence of sedimentation, the concentration profiles show a complex 2D structure, with no z-invariant region, which illustrates the strong impact of top and bottom boundary effects on migration. We also show the importance of boundary effects on the shear induced migration of particles in a Newtonian suspending fluid. This further shows the necessity of developing techniques that give access to the full spatial concentration field, as the one we present here.In this paper, we introduce a new technique based on X-ray radiography with high temporal (O(0.1 s)) and spatial (O(10 μm)) resolutions to study fast suspension flows regardless of optical access. We benefit from the axial symmetry of our flow configuration, a wide gap Couette setup, to extract a 3D solid volume fraction field from a single X-ray projection image. We propose a mathematical algorithm based on the inversion of Abel transform in conjunction with H1 regularization and data denoising to measure the solid volume fraction field in suspensions in a fraction of a second. We show that the results are in excellent agreement with those obtained from micro Computed Tomography (CT scan) in one hour. This significant reduction in the data acquisition time opens a new avenue in the field of suspensions. As a proof of concept, we study the kinetics of shear-induced migration for suspensions of particles in both Newtonian and yield stress suspending fluids. The latter experiments include two different co...

Computational modeling of multiphase viscoelastic and elastoviscoplastic flows: Computational modeling of multiphase elastoviscoplastic flows

In this paper, a three-dimensional numerical solver is developed for suspensions of rigid and soft particles and droplets in viscoelastic and elastoviscoplastic (EVP) fluids. The presented algorithm is designed to allow for the first time three-dimensional simulations of inertial and turbulent EVP fluids with a large number particles and droplets. This is achieved by combining fast and highly scalable methods such as an FFT-based pressure solver, with the evolution equation for non-Newtonian (including elastoviscoplastic) stresses. In this flexible computational framework, the fluid can be modelled by either Oldroyd-B, neo-Hookean, FENE-P, and Saramito EVP models, and the additional equations for the non-Newtonian stresses are fully coupled with the flow. The rigid particles are discretized on a moving Lagrangian grid while the flow equations are solved on a fixed Eulerian grid. The solid particles are represented by an Immersed Boundary method (IBM) with a computationally efficient direct forcing method allowing simulations of a large numbers of particles. The immersed boundary force is computed at the particle surface and then included in the momentum equations as a body force. The droplets and soft particles on the other hand are simulated in a fully Eulerian framework, the former with a level-set method to capture the moving interface and the latter with an indicator function. The solver is first validated for various benchmark single-phase and two-phase elastoviscoplastic flow problems through comparison with data from the literature. Finally, we present new results on the dynamics of a buoyancy-driven drop in an elastoviscoplastic fluid.

Interface-resolved simulations of particle suspensions in Newtonian, shear thinning and shear thickening carrier fluids

We present a numerical study of noncolloidal spherical and rigid particles suspended in Newtonian, shear thinning and shear thickening fluids employing an Immersed Boundary Method. We consider a linear Couette configuration to explore a wide range of solid volume fractions (

Experimental Studies of Visco-Elastic Flow Using Visco-Plastic Lubricant

0.1\le \Phi \le 0.4

Numerical Approach to Nonlinear Temporal Stability of Visco-Plastic Lubrication

) and particle Reynolds Numbers (

Rheology of dense suspensions of non-colloidal spheres in yield-stress fluids

0.1\le Re_p \le 10

Entry, start up and stability effects in visco-plastically lubricated pipe flows

). We report the distribution of solid and fluid phase velocity and solid volume fraction and show that close to the boundaries inertial effects result in a significant slip velocity between the solid and fluid phase. The local solid volume fraction profiles indicate particle layering close to the walls, which increases with the nominal

Two–dimensional viscoplastic dambreaks

\Phi

Nonlinear stability of a visco-plastically lubricated viscoelastic fluid flow

. This feature is associated with the confinement effects. We calculate the probability density function of local strain rates and compare their mean value with the values estimated from the homogenization theory of \cite{Chateau08}, indicating a reasonable agreement in the Stokesian regimes. Both the mean value and standard deviation of the local strain rates increase primarily with the solid volume fraction and secondarily with the