Numerical simulations of a sphere settling in simple shear flows of yield stress fluids

We perform $3$D numerical simulations to investigate the sedimentation of a single sphere in the absence and presence of a simple cross shear flow in a yield stress fluid with weak inertia. In our simulations, the settling flow is considered to be the primary flow, whereas the linear cross shear flow is a secondary flow with amplitude $10\%$ of the primary flow. To study the effects of elasticity and plasticity of the carrying fluid on the sphere drag as well as the flow dynamics, the fluid is modeled using the elastovisco-plastic (EVP) constitutive laws proposed by \cite{saramito2009new}. The extra non-Newtonian stress tensor is fully coupled with the flow equation and the solid particle is represented by an immersed boundary (IB) method. Our results show that the fore-aft asymmetry in the velocity is less pronounced and the negative wake disappears when a linear cross shear flow is applied. We find that the drag on a sphere settling in a sheared yield stress fluid is reduced significantly as compared to an otherwise quiescent fluid. More importantly, the sphere drag in the presence of a secondary cross shear flow cannot be derived from the pure sedimentation drag law owing to the non-linear coupling between the simple shear flow and the uniform flow. Finally, we show that the drag on the sphere settling in a sheared yield-stress fluid is reduced at higher material elasticity mainly due to the form and viscous drag reduction.Comment: 41 pages, 24 figure

Flows of suspensions of particles in yield stress fluids

International audienceWe 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 / in the 0%–50% range. We observe a good agreement between the experimental variations of the consistency with / 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

The interaction of two spherical particles in simple-shear flows of yield stress fluids

International audienceThis study focuses on the interaction of two small freely-moving spheres in a linear flow field of yield stress fluids. We perform a series of experiments over a range of shear rates and different shear histories using an original apparatus and with the aid of conventional rheometry, Particle Image Velocimetry (PIV) and Particle Tracking Velocimetry (PTV). We investigate the flow field around a single sphere as well as two spheres in a simple-shear flow. The flow is Stokesian and the Bingham number is in the range of 0 ≤ B ≤ 2. To explore the limit of zero Bingham number, we use both Newtonian and shear thinning suspending fluids. We use guar gum solutions and Carbopol gels as shear thinning and yield stress test fluids, respectively. We show that the presence of a slight elasticity, which is unavoidable when dealing with polymer solutions, plays an important role in establishing the flow field, e.g., disturbance velocities and stream lines around a single sphere as well as particle trajectories. Therefore, ideal yield stress fluid models cannot provide a full description of flow problems involving particles in practical yield stress fluids. The flow field around a single sphere can be used to understand the two particle interactions. We show how particle-particle contact and non-Newtonian behaviors result in relative trajectories with fore-aft asymmetry. Particularly, the fore-aft asymmetry depends on the Deborah number, Bingham number, shear history, initial offset and roughness of the particles. Finally, we discuss how the relative particle trajectories may affect the microstructure of complex suspensions and consequently the bulk rheology

Rheology of Dense Suspensions of Non-Colloidal Particles in Yield-Stress Fluids

Pressure-imposed rheometry is used to study the rheological properties of suspensions of non-colloidal spheres in yield stress fluids. Accurate measurements for both the shear stress and particle normal stress are obtained in the dense regime. The rheological measurements are favourably compared to a model based on scaling arguments and homogenisation methods

Transport and dispersion of particles in visco-plastic fluids

This thesis focuses on development of a model to predict “spreading” of the solids (i.e. proppant) fraction during the fracturing operation. We develop a 1D model that allows us to estimate dispersion of solid particles along a vertical pipe in a fully turbulent flow of a shear thinning yield stress fluid (i.e., visco-plastic fluid), as well as slip relative to the mean flow. In dimensionless form, this results in a quasilinear advection-diffusion equation. Advection by the mean flow, particle settling relative to the mean, in the direction of gravity, turbulent particle dispersivity and Taylor dispersion are the 4 main transport phenomena modelled in the 1D model. We provide a simple analysis of the 1D model, suitable for spreadsheet-type field design purposes, in which we estimate “mixing lengths” due to both settling and dispersion. Secondly, we provide an accurate numerical algorithm for solution of the 1D model and show how pulses of proppant (i.e. slugs) may or may not interact for typical process parameters.Science, Faculty ofMathematics, Department ofGraduat

Suspensions of non-Brownian Particles in Complex Fluids

This talk aims at introducing our current understanding of the rheology of suspensions of non-Brownian particles in non-Newtonian fluids. These complex suspensions can be found in natural settings such as landslides, mudslides, and submarine avalanches as well as industrial applications such as in mining operations, chemical mechanical, conversion of biomass into fuel, the petroleum industry, etc. The main scientific challenge is to establish a continuum framework and refine it through microstructure investigations. Suspensions may vary on the particle scale from Stokesian behavior to inertial behavior depending on the flow configuration, the type of suspending fluids, etc. We present a tensorial continuum framework based on our recent computational and experimental works and discuss how this framework can be used to study the dispersion of solids in industrial processes and geophysical flows.Non UBCUnreviewedAuthor affiliation: Ohio UniversityFacult

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

Non UBCUnreviewedAuthor affiliation: Ohio UniversityFacult