Finite Volume Simulations of Particle-laden Viscoelastic Fluid Flows: Application To Hydraulic Fracture Processes

Accurately resolving the coupled momentum transfer between the liquid and solid phases of complex fluids is a fundamental problem in multiphase transport processes, such as hydraulic fracture operations. Specifically we need to characterize the dependence of the normalized average fluid-particle force < F > on the volume fraction of the dispersed solid phase and on the rheology of the complex fluid matrix, parameterized through the Weissenberg number Wi measuring the relative magnitude of elastic to viscous stresses in the fluid. Here we use direct numerical simulations (DNS) to study the creeping flow (Re << 1) of viscoelastic fluids through static random arrays of monodisperse spherical particles using a finite volume Navier-Stokes/Cauchy momentum solver. The numerical study consists of N = 150 different systems, in which the normalized average fluid-particle force <F> is obtained as a function of the volume fraction φ (0 < φ ≤ 0.2) of the dispersed solid phase and the Weissenberg number Wi (0 ≤ Wi ≤ 4). From these predictions a closure law < F >( Wi,φ ) for the drag force is derived for the quasi-linear Oldroyd-B viscoelastic fluid model (with fixed retardation ratio β = 0.5) which is, on average, within 5.7% of the DNS results. Additionally, a flow solver able to couple Eulerian and Lagrangian phases (in which the particulate phase is modeled by the discrete particle method (DPM)) is developed, which incorporates the viscoelastic nature of the continuum phase and the closed-form drag law. Two case studies were simulated using this solver, in order to assess the accuracy and robustness of the newly-developed approach for handling particle-laden viscoelastic flow configurations with O (10 5 − 10 6 ) rigid spheres that are representative of hydraulic fracture operations. Three-dimensional settling processes in a Newtonian fluid and in a quasi-linear Oldroyd-B viscoelastic fluid are both investigated using a rectangular channel and an annular pipe domain. Good agreement is obtained for the particle distribution measured in a Newtonian fluid, when comparing numerical results with experimental data. For the cases in which the continuous fluid phase is viscoelastic we compute the evolution in the velocity fields and predicted particle distributions are presented at different elasticity numbers 0 ≤ El ≤ 30 (where El = Wi/Re ) and for different suspension particle volume fractions.

Particle entrapment in elliptical, elastohydrodynamic, rough contacts and the influence of intermolecular (van der Waals) forces

The entrapment/rejection process of spherical, rigid microparticles in elliptical, rough elastohydrodynamic contacts is modelled. An earlier model of the author is extended to include van der Waals intermolecular forces, in addition to mechanical (reaction and friction) and fluid–particle forces. Surface roughness effects are also introduced in terms of the intermolecular force formulation and in the microscale friction (particle–asperity) sub-model. Possibilities related to particle entry into a contact are quantified by weight factors and performance indices. A total entrapment index is defined and linked to the probability of particle entrapment. A parametric analysis investigates the effect of the intermolecular particle force on the entrapment probability by varying the contact load, lubricant viscosity, elastic modulus of the contacting solids, contact velocity and the macroscopic (Coulomb) coefficient of friction.

Failure mode transitions of unconfined granular media from dry to unsaturated to “quasi-fully” saturated states

Recent research has shown discrepancies between the prevailing mathematical representations of near-surface shear strength and the observed shear strengths. This investigation focuses on three granular materials, i.e., 1) poorly-graded, medium-fine silica-quartz sand, 2) an engineered silica-quartz mix of 3.38-mm and 0.638-mm sub-angular particles, and 3) an angular fused quartz sand. Specimens were tested under load-controlled conditions at variable saturations in order to identify and quantify the influence of suction on the granular structures and failure modes. All three materials exhibited localized radial particle force chain buckling failures in unconfined drained dry (UDκ) conditions and classical shear failures in the unconfined drained unsaturated shear (UDP) conditions. In unconfined drained suction failures (UDS) conditions, the poorly-graded, medium-fine silica-quartz sand exhibited a bulging and sloughing failure without weeping, while the other two materials wept and then held loads before failure. Thus, it is suggested that the pore fluid had a predominate lubrication (strength weakening) effect, and the assumption of structure stiffening (strength increase) from matric suction may not be valid at near-surface conditions for sub-angular silica-quartz materials but is valid for the angular fused quartz.

Optical binding of nanoparticles

Optical binding is a laser-induced inter-particle force that exists between two or more particles subjected to off-resonant light. It is one of the key tools in optical manipulation of particles. Distinct from the single-particle forces which operate in optical trapping and tweezing, it enables the light-induced self-assembly of non-contact multi-particle arrays and structures. Whilst optical binding at the microscale between microparticles is well-established, it is only within the last few years that the experimental difficulties of observing nanoscale optical binding between nanoparticles have been overcome. This hurdle surmounted, there has been a sudden proliferation in observations of nanoscale optical binding, where the corresponding theoretical understanding and predictions of the underlying nanophotonics have become ever more important. This article covers these new developments, giving an overview of the emergent field of nanoscale optical binding.

Comparison of Surface Tension Models in Smoothed Particles Hydrodynamics Method

We compare two surface tension models to solve two-phase fluid interaction problems in the context of the mesh-free Smoothed Particles Hydrodynamics (SPH) method. The Continuum Surface Force (CSF) model (later extended to Continuum Surface Stress, CSS), originally derived from grid-based numerical methods, requires an accurate estimation of the interface curvature to express the surface tension. Unlike CSF, the Inter-Particle Force (IPF) model is more robust in this regard as it draws on a molecular dynamics foundation by considering how the pairwise interaction forces between particles within a cutoff distance act in relation to producing the surface tension. Herein, we rely on second-order consistent gradient and Laplacian operators to improve the accuracy of SPH formulations as well as on a particle shifting technique to “disorder” particles from non-differentiable interface geometries. A 3D liquid droplet deformation test is used to compare CSF and IPF in terms of their pressure field and kinetic energy dissipation accuracy.