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We generate a wide range of models of proppant-packed fractures using discrete element simulations, and measure fracture conductivity using finite element flow simulations. This allows for a controlled computational study of proppant structure and its relationship to fracture conductivity and stress in the proppant pack. For homogeneous multi-layered packings, we observe the expected increase in fracture conductivity with increasing fracture aperture, while the stress on the proppant pack remains nearly constant. This is consistent with the expected behavior in conventional proppant-packed fractures, but the present work offers a novel quantitative analysis with an explicit geometric representation of the proppant particles. In single-layered packings (i.e. proppant monolayers), there is a drastic increase in fracture conductivity as the proppant volume fraction decreases and open flow channels form. However, this also corresponds to a sharp increase in the mechanical stress on the proppant pack, as measured by the maximum normal stress relative to the side crushing strength of typical proppant particles. We also generate a variety of computational geometries that resemble highly heterogeneous proppant packings hypothesized to form during channel fracturing. In some cases, these heterogeneous packings show drastic improvements in conductivity with only moderate increase in the stress on the proppant particles, suggesting that in certain applications these structures are indeed optimal. We also compare our computer-generated structures to micro computed tomography imaging of a manually fractured laboratory-scale shale specimen, and find reasonable agreement in the geometric characteristics. [ABSTRACT FROM AUTHOR]

Abstract: Continuous jets of non-Newtonian fluids impinging on a fluid surface exhibit instabilities from jet buckling and coiling at low Reynolds numbers to delayed die swell, mounding, and air entrainment at higher Reynolds numbers. Filling containers with complex fluids is an important process for many industries, where the need for high throughput requires operating at high Reynolds numbers. In this regime, air entrainment can produce a visually unappealing product, causing a major quality control issue. Just prior to the onset of air entrainment, however, there exists an ideal filling regime which we term “planar filling,” as it is characterized by a relatively flat free surface that maintains its shape over time. In this paper, we create a steady-state, 2-D axisymmetric finite element model to study the transition from planar filling to the onset of air entrainment in a container filling process with generalized-Newtonian fluids. We use this model to explore the operating window for Newtonian and shear-thinning (or, more generally, deformation-rate-thinning) fluids, demonstrating that the flow behavior is characterized by a balance between inertial, viscous, and gravitational forces, as characterized by the Reynolds and Froude numbers. A scaling analysis suggests that the relevant parameters for calculating these dimensionless numbers are located where the jet impacts the liquid surface, and simulations show that the transition from planar filling to air entrainment often occurs when . We found that the bottom and side surfaces of the container drastically influence this transition to entrainment, stabilizing the flow. [Copyright &y& Elsevier]

The practical implementation of several thixotropic rheological models has been evaluated for a prototypical industrial application. We have studied the ability of the models to predict both steady and transient rheology of a suspension of alumina particles and the suitability of those models for full transient finite element calculations. The constitutive models for thixotropic materials examined include the Carreau-Yasuda model and first and second-order indirect structure models. While all of these models were able to predict the shear-thinning behavior of the steady viscosity, the first and second-order structure models were also able to capture some aspects of the transient structure formation and fluid history. However, they were not able to predict some more complex transient behavior observed in step shear experiments. For most thixotropic suspensions, the time constant required to form structure is longer than the time constant to break it down. For this suspension, the time constant at a given shear rate was also dependent on the previous shear rate. If the previous shear rate was high, the time required to reach equilibrium was longer than if the previous shear rate was lower. This behavior was not captured by the simple initial structure dependence in the previous models. By adding an additional dependence on the initial suspension structure, the prediction of the transient rheology was substantially improved while maintaining an excellent agreement with the steady shear viscosity. Finite element results are presented for extrusion of a suspension to form a fiber. This model two-dimensional problem contains many of the same complexities as practical three-dimensional mold filling simulations (i.e., nonviscometric and mobile free surface). Our results show that these direct structure models exhibit oscillations near the stick-slip point in finite element calculations similar to many polymeric constitutive equations, but are otherwise suitable for implementation in complex industrial modeling applications. [ABSTRACT FROM AUTHOR]

Shear-induced migration of particles is studied during the slow flow of suspensions of neutrally buoyant spheres, at 50% particle volume fraction, in an inelastic but shear-thinning, suspending fluid. The suspension is flowing in between a rotating inner cylinder and a stationary outer cylinder. The conditions are such that nonhydrodynamic effects are negligible. Nuclear magnetic resonance (NMR) imaging demonstrates that the movement of particles away from the high shear rate region is more pronounced than for a Newtonian suspending liquid. We test a continuum constitutive model for the evolution of particle concentration in a flowing suspension proposed by Phillips et al., but extended to shear-thinning, suspending fluids. The fluid constitutive equation is Carreau-like in its shear-thinning behavior but also varies with the local particle concentration. The model captures many of the trends found in the experimental data, but does not yet agree quantitatively. In fact, quantitative agreement with a diffusive flux constitutive equation would be impossible without the addition of another fitting parameter that may depend on the shear-thinning nature of the suspending fluid. Because of this, we feel that the Phillips model may be fundamentally inadequate for simulating flows of particles innon-Newtonian suspending fluids without the introduction of a normal stress correction or other augmenting terms. [ABSTRACT FROM AUTHOR]

Liquid-liquid extraction (LLE) is a widely used separation method for an extensive range of metals including actinides. The Gibbs energy minimization (GEM) method is used to compute the complex chemical equilibria for the LLE system HNO3–H2O–UO2(NO3)2–TBP plus diluent at 25°C. The nonelectrolyte phase is treated as an ideal mixture defined by eight tri-n-butyl phosphate (TBP) complexes plus the inert diluent. The Pitzer method is used to capture nonidealities in the concentrated electrolyte phase. The generated extraction isotherms are in very good agreement with reported experimental data for various TBP loadings and electrolyte concentrations demonstrating the adequacy of this approach to analyze complex multiphase multicomponent systems. The model is robust and yet flexible allowing for expansion to other LLE systems and coupling with computational tools for parameter analysis and optimization. [ABSTRACT FROM AUTHOR]

Many important engineering and scientific applications such as cement slurries, foams, crude oil, and granular avalanches involve the concept of yield stress. Therefore, modeling yield stress fluids in different flow configurations, including the accurate prediction of the yield surface, is important. In this paper, we present a computational model based on the finite element method to study the flow of yield stress fluids in a thin mold and compare the results with data from flow visualization experiments. We use the level set method to describe the interface between the filling fluid and air. We use polypropylene glycol as a model Newtonian fluid and Carbopol for the model yield stress fluid, as the Carbopol solution demonstrates yielding without thixotropy. To describe the yielding and shear-thinning behavior, we use a generalized Newtonian constitutive equation with a Bingham–Carreau–Yasuda form. We compare the results obtained from the mold filling experiments with the results from the three-dimensional (3D) model and from a reduced-order Hele-Shaw (HS) model that is two-dimensional, including the effect of shear-thinning along the thin direction only approximately. We show that both the 3D and the HS model can capture the experimental meniscus shape reasonably well for all the fluids considered at three different flow rates. This indicates that the shape evolution is insensitive to the dimensionality of the model. However, the viscosity and yield surfaces predicted by the 3D and HS models are different. The HS model underestimates the high viscosity and unyielded regions compared to the estimation by the 3D model. • Computational model of yield stress fluids using Bingham–Carreau–Yasuda equation. • Mold filling between thin plates is studied for a Newtonian fluid and two Carbopols. • Comparison between a full 3D and a Hele-Shaw model with validation data. • Finite element/level method is used for the discretization. • Accuracy of 3D is superior to Hele-Shaw but both match experiments well. [ABSTRACT FROM AUTHOR]

Materials which exhibit elastic and yielding behavior are present in many industrial processes including thin-film coating, oil extraction, manufacturing of consumer products, and food processing. Numerical simulation is a powerful tool for gaining insights into the flow behavior of complex fluids and can facilitate the design of commercially relevant processes, such as mold filling and coating flows. In this study, we perform numerical simulations of an elastoviscoplastic fluid expanding into a thin, rectangular mold. We use a Saramito model to describe the rheology of the fluid (Saramito, 2007) as well as the Bingham–Carreau–Yasuda generalized Newtonian model. The Saramito model used describes the material as an Oldroyd-B fluid above yield and an elastic solid below yield; the yield criterion is based on the von Mises stress. Conservation equations for momentum and mass and the Saramito constitutive equations for stress are solved using the finite element method coupled to a free surface moving mesh algorithm. We assess our Saramito model implementation by comparing computations to benchmarks in the literature, including flow past a cylindrical obstacle and channel flow. We compare results from two and three-dimensional mold filling simulations to flow visualization experiments where fluid fills a thin gap between transparent plates. For both two and three-dimensional, the Saramito model is generally more predictive of the shape of the growing fluid droplet than the Bingham–Carreau–Yasuda model. Saramito model results for 2D computations match experimental droplet shapes well with the addition of a model for the drag terms to capture the effects of the unresolved third dimension. For fully 3D computations, the Saramito model is able to reproduce experimentally-observed droplet shapes for the smallest (5 mL/min) and largest (20 mL/min) flow rates, but struggles to accurately reproduce experimental observations at an intermediate flow rate (10 mL/min). This discrepancy is probably due to the over prediction of slip from the wetting model. • Growing droplet simulated using elastoviscoplastic and generalized-Newtonian models. • EVP model reproduced droplet shapes more accurately than the GN model. • Generalized-Newtonian model typically less accurate than elastoviscoplastic model. • Accuracy of 2D predictions improved by a drag model accounting for unresolved walls. [ABSTRACT FROM AUTHOR]

Abstract: Highly conductive polymers are difficult to process utilizing standard polymer approaches. This report describes a polymer composite loaded with a eutectic metal that is molten during melt processing along with a more traditional Nickel particulate filler. Conductivities over 300 S/cm were achieved, and 60 vol% metals loading was processable with a single screw extruder. The addition of the Nickel particulate was critical for maintaining eutectic dispersion. We anticipate that this approach will facilitate the implementation of conductive polymers into a broader variety of practical applications, due to the enhanced compatibility with standard polymer processing techniques such as extrusion, melt mixing, and resin transfer-molding operations. [Copyright &y& Elsevier]

Blood flowing through microvascular bifurcations has been an active research topic for many decades, while the partitioning pattern of nanoscale solutes in the blood remains relatively unexplored. Here we demonstrate a multiscale computational framework for direct numerical simulation of the nanoparticle (NP) partitioning through physiologically relevant vascular bifurcations in the presence of red blood cells (RBCs). The computational framework is established by embedding a particulate suspension inflow-outflow boundary condition into a multiscale blood flow solver. The computational framework is verified by recovering a tubular blood flow without a bifurcation and validated against the experimental measurement of an intravital bifurcation flow. The classic Zweifach-Fung (ZF) effect is shown to be well captured by the method. Moreover, we observe that NPs exhibit a ZF-like heterogeneous partition in response to the heterogeneous partition of the RBC phase. The NP partitioning prioritizes the high-flow-rate daughter branch except for extreme (large or small) suspension flow partition ratios under which the complete phase separation tends to occur. By analyzing the flow field and the particle trajectories, we show that the ZF-like heterogeneity in the NP partition can be explained by the RBC-entrainment effect caused by the deviation of the flow separatrix preceded by the tank treading of RBCs near the bifurcation junction. The recovery of homogeneity in the NP partition under extreme flow partition ratios is due to the plasma skimming of NPs in the cell-free layer. These findings, based on the multiscale computational framework, provide biophysical insights to the heterogeneous distribution of NPs in microvascular beds that are observed pathophysiologically. [ABSTRACT FROM AUTHOR]

A theory is presented for the transition between the coflowing and the drop-generation regimes observed in microfluidic channels with a rectangular cross section. This transition is characterized by a critical ratio of the dispersed- to continuous-phase volume flow rates. At flow-rate ratios higher than this critical value, drop generation is suppressed. The critical ratio corresponds to the fluid cross section where the dispersed-phase fluid is just tangent to the channel walls. The transition criterion is a function of the ratio of the fluid viscosities, the three-phase contact angle formed between the fluid phases and the channel walls, and the aspect ratio of the channel cross section; the transition is independent of interfacial tension. Hysteretic behavior of drop generation with respect to the flow-rate ratio is predicted for partially wetting dispersed-phase fluids. Experimental data are consistent with this theory. [ABSTRACT FROM AUTHOR]