Function Of Solid Volume Fraction Research Articles

Energy release rate for cracks in hydrogels undergoing finite deformations

The rupture of hydrogels and swellable elastomers involves large deformations, and there exists a large literature devoted to their experimental characterization including methods for measuring and enhancing fracture toughness. Analytical investigations of the fracture of hydrogels have recognized the importance of large deformations and the contributions of liquid flow, but they have largely been restricted to plane-strain formulations that ignore through-thickness effects. In this paper, boundary–initial value problems for cracked specimens are solved in plane-strain and three dimensions for both permeable and impermeable boundary conditions and various rates of loading. The transient stress, strain and chemical potential fields near the crack tip/front are found to be notably different than the asymptotic solutions of linear poroelasticity and large deformation plane-strain formulations. The energy release rate is computed using a poroelastic path-independent integral ( J ∗ ), and generally that also is a function of the liquid flow. It is shown for moderately thin three-dimensional specimens that liquid flow is largely in the out-of-plane direction under permeable boundaries and largely in-plane for impermeable boundaries; thus, liquid flow makes larger contributions to the energy release in the latter. In agreement with experiments, the energy release rate tends to be larger at higher loading rates due to the contributions of liquid flow. Finally, criteria for crack growth based on the critical stretch ahead of the crack are adopted to predict the critical energy release rate as a function of solid volume fraction, and the possibility of a non-monotone dependence of energy release on solid volume fraction is uncovered. The methods presented in this paper can be utilized to analyze a wide variety of problems in the rupture of hydrogels including applications to soft tissues and fibrous gels.

Macroscopic rheology of non-Brownian suspensions at high shear rates: the influence of solid volume fraction and non-Newtonian behaviour of the liquid phase

Modelling the macroscopic rheology of non-Brownian suspensions is complicated by the non-linear behaviour that originates from the interaction between solid particles and the liquid phase. In this contribution, a model is presented that describes suspension rheology as a function of solid volume fraction and shear rate dependency of both the liquid phase, as well as the suspension as a whole. It is experimentally validated using rotational rheometry (varphi ≤ 0.40) and capillary rheometry (0.55 ≤ varphi ≤ 0.60) at shear rates > 50 s−1. A modified Krieger-Dougherty relation was used to describe the influence of solid volume fraction on the consistency coefficient, K, and was fitted to suspensions with a shear thinning liquid phase, i.e. having a flow index, n, of 0.50. With the calculated fit parameters, it was possible to predict the consistency coefficients of suspensions with a large variation in the shear rate dependency of the liquid phase (n = 0.20–1.00). With increasing solid volume fraction, the flow indices of the suspensions were found to decrease for Newtonian and mildly shear thinning liquid phases (n ≥0.50), whereas they were found to increase for strongly shear thinning liquid phases (n ≤0.27). It is hypothesized that this is related to interparticle friction and the relative contribution of friction forces to the viscosity of the suspension. The proposed model is a step towards the prediction of the flow curves of concentrated suspensions with non-Newtonian liquid phases at high shear rates.

Permeability of Monodisperse Solid Foams

Fluid permeability of solid foams is a crucial parameter to control transport phenomena in numerous engineering applications, such as heat exchangers or filters for example. Open-cell foams with monodisperse pore diameter ranging from 200 to 1000 µm and solid volume fraction ranging from 0.1 to 0.38 are produced and Darcy permeability is measured. The permeability divided by the square of the pore size shows an exponential decay as a function of solid volume fraction. Surprisingly, existing models do not capture this exponential decay and actually they predict permeability values significantly larger than the measured values. The observed exponential decay is then successfully described by using models based on the viscous dissipation occurring through the apertures that connect the foam pores and by accounting for both the mean size of the apertures and the mean number of apertures per pore.

Effect of stem-generated turbulence on sediment resuspension within rigid vegetation canopies in waves

浅水湖泊沉积物再悬浮过程促进了沉积物内源性物质的释放，造成湖泊水体内源污染，加剧湖泊水质污染与生态恶化.开展刚性植被不同分布格局下的沉积物再悬浮水槽试验，能为浅水草型湖泊、滨海湿地等水环境治理与生态修复提供理论参考.本研究通过开展实验室波浪水槽试验，检验了3种直径12种密度的刚性模型植被对波浪扰动白洋淀沉积物再悬浮的影响，通过测定不同植被情景不同波浪条件下的瞬时速度和沉积物再悬浮浓度，详细阐述了植被产生的紊动能对沉积物再悬浮临界状态的影响，构建并验证了沉积物再悬浮植被紊流模型，预测了沉积物再悬浮的临界速度，为湿地生态恢复与保护提供参考.结果表明：1）植被的存在能有效增加近床面的紊动能；2）紊动能是控制沉积物再悬浮的关键性因素；3）沉积物再悬浮的临界波速与植被的固相体积分数相关.;Sediment resuspension in shallow lakes promotes the nutrients release, which leads to the internal pollution, degrading the water quality and lake ecology. This research aims to study the impact of rigid vegetation on wave-driven sediment resuspension through wave flume experiments. It could provide a theoretical reference for environmental management and ecological restoration of shallow lakes and coastal wetlands. Vegetation canopies were constructed by rigid cylinders considering three diameters and 12 vegetation densities. The near-bed instantaneous velocity was measured within vegetation canopies and under different wave conditions by a Nortek Vectrino at sampling rate of 200 Hz. Suspended sediment concentrations were measured using an optical backscatter with frequency of 20 Hz. The vegetation-generated turbulence was positively linear with the root mean square of wave velocity. This vegetated turbulence increased with an increasing ratio (A_w/S) of wave excursion (A_w) to stem spacing (S) when A_w/S>1, and was similar with bare bed case when A_w/S<1. The concentration of sediment resuspension increased with growing solid volume fraction. The critical state of resuspension was initiated when the suspended sediment concentration exceeded the background level. Higher solid volume fraction generated higher turbulence, which promoted a small critical wave velocity. A vegetation-generated turbulence model for sediment resuspension was proposed and validated using the measured turbulence in the model canopy. Therefore, we confirmed that the magnitude of stem-generated turbulence is a function of solid volume fraction. This model proved the key role of turbulent kinetic energy to control the initial sediment resuspension. Based on this, a threshold model of critical velocity for sediment resuspension was proposed and validated. It could predict the critical near-bed wave velocity for sediment resuspension within rigid vegetation canopy or sheath with diameters of 0.32 cm to 1.2 cm. The applicable particle size was limited to 85-280 μm.

Impact of Vegetation‐Generated Turbulence on the Critical, Near‐Bed, Wave‐Velocity for Sediment Resuspension

AbstractLaboratory experiments examined the impact of model vegetation on wave‐driven resuspension. Model canopies were constructed from cylinders with three diameters (d = 0.32, 0.64, and 1.26 cm) and 12 densities (cylinders/m2) up to a solid volume fraction (ϕ) of 10%. The sediment bed consisted of spherical grains with d50 = 85 μm. For each experiment, the wave velocity was gradually adjusted by increasing the amplitude of 2‐s waves in a stepwise fashion. A Nortek Vectrino sampled the velocity at z = 1.3 cm above the bed. The critical wave orbital velocity for resuspension was inferred from records of suspended sediment concentration (measured with optical backscatter) as a function of wave velocity. The critical wave velocity decreased with increasing solid volume fraction. The reduction in critical wave velocity was linked to stem‐generated turbulence, which, for the same wave velocity, increased with increasing solid volume fraction. The measured turbulence was consistent with a wave‐modified version of a stem‐turbulence model. The measurements suggested that a critical value of turbulent kinetic energy was needed to initiate resuspension, and this was used to define the critical wave velocity as a function of solid volume fraction. The model predicted the measured critical wave velocity for stem diameters d = 0.64 to 2 cm. Combining the critical wave velocity with an existing model for wave damping defined the meadow size for which wave damping would be sufficient to suppress wave‐induced sediment suspension within the interior of the meadow.

A fully analytical model for virtual mass force in mixture flows

Virtual mass force plays important role in the dynamics of the mixture mass flow composed of viscous fluid and the solid particles. Often in practice, calibrated numerical values of the virtual mass force are used to validate the simulation results but largely without any further physical basis. Such values are limited to some lower limit of the solid volume fraction. This has restricted its applicability both in small scale and in large scale natural flow simulations where the virtual mass force should be automatically determined and controlled by the mechanical parameters and the flow dynamical variables involved in the mass movements. This requires a full analytical description of the virtual mass force in application that covers the whole domain of particle concentration distribution, from the vanishing limit to any upper limit that is needed. Based on a two-phase general mixture mass flow model (Pudasaini, 2012), here, we present a first-ever, fully analytical, smooth and well bounded model for the virtual mass force that overcomes these deficiencies, and thus the model is more appropriate for application in real flow simulations. The novel virtual mass force is general, evolves automatically as a function of solid volume fraction, is much more realistic and covers the whole spectrum of the flow as governed by the physical parameters, mechanics and dynamics of the mixture flow, including the concentration distribution, material densities and the mass fluxes. So, the new virtual mass force presents the most advanced model that exists for mixture mass flows. The strikingly novel observation and understanding is that the virtual mass force is maximum somewhere between dilute to dense distribution of the solid particles, or the dispersed phase, but not at the maximum solid volume fraction.

Using artificial neural network for investigating of concurrent effects of multi-walled carbon nanotubes and alumina nanoparticles on the viscosity of 10W-40 engine oil

The present study used artificial neural networks (ANNs) and experimental data to model the viscosity of the MWCNT (50%)–Al2O3 (50%)/10W40 hybrid nanofluid at different temperatures from 5 to 55 °C and for nanoparticle volume fractions of 0.05% to 1%. An ANN and a new correlation as function of solid volume fraction, temperature and shear rate. The multidimensional MLP-ANN was employed and investigated as the learning algorithm. The R-squared values for the proposed correlation and ANN were obtained to be 0.9973 and 0.9944, respectively. In order to analyze the importance of each term of correlation, p-value of parameters is determined. Also one factor and two factor analysis of viscosity are presented in this study. According to one and two factor analysis results, temperature changes has the highest effect on viscosity. Shear rate and solid volume fraction effects on viscosity are in next level of importance.

Direct numerical simulation of non-isothermal flow through dense bidisperse random arrays of spheres

Extensive direct numerical simulations were performed to obtain the heat transfer coefficients (HTC) of bidisperse random arrays of spheres. We have calculated the HTC for a range of compositions and solids volume fractions for mixtures of spheres with a size ratio of 1:2. The Reynolds numbers are in the range of 30–100. It was found that the correlation of the monodisperse HTC can estimate the average HTC of bidisperse systems well if the Reynolds and Nusselt numbers are based on the Sauter mean diameter. We report the difference between the HTC for each particle type and the average HTC of the bed in the bidisperse system as function of solids volume fraction, Sauter mean diameter of the mixture, Reynolds number and investigate the heterogeneity of the individual particle HTCs.

Simulations of flow behavior of particles in a liquid-solid fluidized bed using a second-order moments model

Flow behavior of liquid and particles is simulated using an Eulerian-Eulerian two-fluid model based on the theory of granular flow in a liquid-solid fluidized bed. The kinetic interaction of particle collisions is modeled using a second-order moments method. Comparing to simulated results from the kinetic theory of granular flow, the simulated results from the second-order moments method are in agreement with the experimental data of Razzak et al. [25] in a riser. Simulated results indicate that the component of second-order moments in the axial direction is higher than that in the radial direction. The distribution of velocity and volume fraction is predicted at the different inlet liquid velocities. Simulations indicate that axial velocities of particles increase with increasing inlet liquid velocity. The granular temperature is computed from simulations as a function of solid volume fraction. Roughly, the granular temperature increases, reach a maximum, and then decreases with the increase of solid volume fraction. To verify the numerical model further, the liquid-solid flow in the downcomer is simulated, and the simulated results are agreement with the experimental results from Lan et al. [33]. As well as, the liquid-solid circulation fluidized bed loop is investigated, and comparisons with Roy et al. simulations [12] are conducted.

Computational high-throughput screening of fluid permeability in heterogeneous fiber materials.

We explore computational high-throughput screening as a design strategy for heterogeneous, isotropic fiber materials. Fluid permeability, a key property in the design of soft porous materials, is systematically studied using a multi-scale lattice Boltzmann framework. After characterizing microscopic permeability as a function of solid volume fraction in the microstructure, we perform high-throughput computational screening of in excess of 35 000 macrostructures consisting of a continuous bulk interrupted by spherical/elliptical domains with either lower or higher microscopic permeability (hence with two distinct microscopic solid volume fractions and therefore two distinct microscopic permeabilities) to assess which parameters determine macroscopic permeability for a fixed average solid volume fraction. We conclude that the fractions of bulk and domains and the distribution of solid volume fraction between them are the primary determinants of macroscopic permeability, and that a substantial increase in permeability compared to the corresponding homogenous material is attainable.

A new model for the viscosity of highly concentrated multi-sized particulate Bingham slurries

ABSTRACTBench scale tests were carried out to investigate the rheological properties of multi-sized particulate Bingham slurries at high solid concentrations ranging from 50% to 70% by weight. In addition, rheological data from Biswas et al. (2000) and Chandel et al. (2009, 2010) have also been considered. Based on these extensive amount of rheological data, an empirical model is proposed for viscosity as a function of solid volume fraction (ɸ), maximum solid volume fraction (ɸm), median particle diameter (d50), and coefficient of uniformity (Cu) using optimization and nonlinear least-square curve-fitting technique. The proposed model shows good agreement with the experimental data considered in the present study and is found to be much better than the previously developed models in predicting the viscosity of multi-sized particulate Bingham slurries at high solid concentrations.

Experimental study on the rheological behaviour of coal ash slurries

Abstract Extensive experimental investigations were carried out to evaluate the rheological behaviour of fly ash (FA) slurry without and with the addition of bottom ash (BA) and BA slurry without and with the addition of FA. The FA slurries exhibited Bingham behaviour at solid mass concentrations ranging from 60–65% and mixing proportions from 10– 40%. A substantial reduction in yield stress was observed except for mixing proportion of 40% on which the yield stress and viscosity were increased drastically for all solid concentrations. Hence, it can be concluded that the yield stress and viscosity of FA slurry were very much influenced by adding BA up to the mixing proportion of 30%. The rheological behaviour of BA slurries with and without the addition of FA in proportions of 10–50% was investigated and exhibited Newtonian behaviours for solid mass concentrations ranging from 30–50% without and with the addition of FA. The viscosity increases with increasing the solid concentrations and proportion of FA. Based on these experimental data, a correlation was developed to predict the relative viscosity of BA slurries as a function of solid volume fraction and FA mass proportion of 0–50% and the RMSE and R2 values showed good agreement between the experimental and the predicted data.

Pseudo-turbulent gas-phase velocity fluctuations in homogeneous gas–solid flow: fixed particle assemblies and freely evolving suspensions

Gas-phase velocity fluctuations due to mean slip velocity between the gas and solid phases are quantified using particle-resolved direct numerical simulation. These fluctuations are termed pseudo-turbulent because they arise from the interaction of particles with the mean slip even in ‘laminar’ gas–solid flows. The contribution of turbulent and pseudo-turbulent fluctuations to the level of gas-phase velocity fluctuations is quantified in initially ‘laminar’ and turbulent flow past fixed random particle assemblies of monodisperse spheres. The pseudo-turbulent kinetic energy $k^{(f)}$ in steady flow is then characterized as a function of solid volume fraction ${\it\phi}$ and the Reynolds number based on the mean slip velocity $\mathit{Re}_{m}$. Anisotropy in the Reynolds stress is quantified by decomposing it into isotropic and deviatoric parts, and its dependence on ${\it\phi}$ and $Re_{m}$ is explained. An algebraic stress model is proposed that captures the dependence of the Reynolds stress on ${\it\phi}$ and $Re_{m}$. Gas-phase velocity fluctuations in freely evolving suspensions undergoing elastic and inelastic particle collisions are also quantified. The flow corresponds to homogeneous gas–solid systems, with high solid-to-gas density ratio and particle diameter greater than dissipative length scales. It is found that for the parameter values considered here, the level of pseudo-turbulence differs by only 15 % from the values for equivalent fixed beds. The principle of conservation of interphase turbulent kinetic energy transfer is validated by quantifying the interphase transfer terms in the evolution equations of kinetic energy for the gas-phase and solid-phase fluctuating velocity. It is found that the collisional dissipation is negligible compared with the viscous dissipation for the cases considered in this study where the freely evolving suspensions attain a steady state starting from an initial condition where the particles are at rest.

Suspension of solid particles in a density stratified fluid

Widespread implications of settling particles in stratified fluids call for accurate assessment of a suspension of particles at pycnoclines. We perform direct numerical simulations of the motion of particles based on a distributed Lagrange multiplier technique to quantify the effect of density stratification on the settling velocity and microstructure of a suspension of rigid particles. The flow field around particles is fully resolved, and a statistically steady-state condition is obtained after a transient acceleration of particles. Based on the simulation results, we propose a correlation for the mean settling velocity of the suspension as a function of solid volume fraction and background density gradient in a fluid column. The correlation follows a power-law dependence on the solid volume fraction of the suspension. The effect of the stratification on the microstructure of the suspension is also investigated by direct comparison of the pair correlation function between homogeneous and stratified fluids. It is shown that the presence of the background density gradient enhances the formation of horizontally aligned clusters in the fluid column.

Effect of carrier and particle concentration on ultrasound properties of magnetic nanofluids

Ultrasound wave propagation in nanofluids and its rheological behavior has been studied as a function of solid volume fraction, temperature and magnetic field for magnetic nanofluids synthesized in kerosene and transformer oil. Ultrasonic velocity decreases while viscosity increases with increasing volume fraction. The attenuation of ultrasonic wave is explained using dipolar coupling co-efficient which favors oligomer structures with increasing number density of particles. The structure formation increases further with increase in magnetic field which is prominent in transformer oil compared to kerosene. This difference can be due to the structural difference between these two carriers.

Structure-dependent drag in gas–solid flows studied with direct numerical simulation

Quantification of drag F is critical to the simulation of gas–solid flows in both discrete particle models and two-fluid models. It is commonly accepted that for homogeneous flow the drag is a function of solid volume fraction ϕ and particle Reynolds number Rep (based on the mean slip velocity and particle radius). However, its adequacy for heterogeneous flows encountered more frequently is in debate yet. In this work, we reveal the strong structural dependence of the drag in both a simple case of two particles and a typical case with stepwise heterogeneity, demonstrating the necessity for a structure-dependent drag description. To quantify such dependence, flow past idealized static suspensions with linear heterogeneity is studied first, which confirms a general form F(Rep,ϕ,|∇ϕ|,θ) suggested previously, where θ is the angle between the gradient ∇ϕ and the mean slip velocity. In the studied range of 5<Rep<30, F depends linearly on Rep for a given static particle configuration. However, the concrete expressions are yet to be found. Then for dynamic gas–solid suspension, large-scale simulations enabled by supercomputing systems reveal a much more complicated dependence: on one hand, the drag coefficients on individual particles scatter even in the absence of distinct heterogeneity; and on the other hand, with the presence of distinct heterogeneity, the drag predicted by Wen and Yu (1966) deviates significantly from the simulation value in both direction and magnitude. A purely bottom-up statistical approach to establish a drag correlation in this case seems difficult and a theoretical elucidation is needed.

Olive Paste Rheological Analysis

In this article, experimental data are reported concerning viscosity measurements carried out on olive paste at different phases of the extraction process. Using these data, a rheological analysis of experimental samples was carried out. The analysis showed that the actual olive paste rheological behavior is correctly described by a non-Newtonian model expressed by a power law model, well known in the literature. Numerical values for the power law parameters were determined at each step of the olive milling process. Moreover, a deeper analysis was carried out to investigate the capability of three different analytical models to predict the relative viscosity of olive paste as a function of solids volume fraction at different phases of the extraction process. Model predictions are compared to experimental data and discussed.

Apparent stiffness tensors for porous solids using symmetric Galerkin boundary elements

Representative volume elements (RVEs) from porous or cellular solids can often be too large for numerical or experimental determination of effective elastic constants. Volume elements which are smaller than the RVE can be useful in extracting apparent elastic stiffness tensors which provide bounds on the homogenized elastic stiffness tensor. Here, we make efficient use of boundary element analysis to compute the volume averages of stress and strain needed for such an analysis. For boundary conditions which satisfy the Hill criterion, we demonstrate the extraction of apparent elastic stiffness tensors using a symmetric Galerkin boundary element method. We apply the analysis method to two examples of a porous ceramic. Finally, we extract the eigenvalues of the fabric tensor for the example problem and provide predictions on the apparent elastic stiffnesses as a function of solid volume fraction.

Drag law for monodisperse gas–solid systems using particle-resolved direct numerical simulation of flow past fixed assemblies of spheres

Gas–solid momentum transfer is a fundamental problem that is characterized by the dependence of normalized average fluid–particle force F on solid volume fraction ϕ and the Reynolds number based on the mean slip velocity Re m . In this work we report particle-resolved direct numerical simulation (DNS) results of interphase momentum transfer in flow past fixed random assemblies of monodisperse spheres with finite fluid inertia using a continuum Navier–Stokes solver. This solver is based on a new formulation we refer to as the Particle-resolved Uncontaminated-fluid Reconcilable Immersed Boundary Method (PUReIBM). The principal advantage of this formulation is that the fluid stress at the particle surface is calculated directly from the flow solution (velocity and pressure fields), which when integrated over the surfaces of all particles yields the average fluid–particle force. We demonstrate that PUReIBM is a consistent numerical method to study gas–solid flow because it results in a force density on particle surfaces that is reconcilable with the averaged two-fluid theory. The numerical convergence and accuracy of PUReIBM are established through a comprehensive suite of validation tests. The normalized average fluid–particle force F is obtained as a function of solid volume fraction ϕ (0.1 ⩽ ϕ ⩽ 0.5) and mean flow Reynolds number Re m (0.01 ⩽ Re m ⩽ 300) for random assemblies of monodisperse spheres. These results extend previously reported results of Hill et al. (2001a,b) to a wider range of ϕ, Re m , and are more accurate than those reported by Beetstra et al. (2007). Differences between the drag values obtained from PUReIBM and the drag correlation of Beetstra et al. (2007) are as high as 30% for Re m in the range 100–300. We take advantage of PUReIBM’s ability to directly calculate the relative contributions of pressure and viscous stress to the total fluid–particle force, which is useful in developing drag correlations. Using a scaling argument, Hill et al. (2001b) proposed that the viscous contribution is independent of Re m but the pressure contribution is linear in Re m (for Re m > 50). However, from PUReIBM simulations we find that the viscous contribution is not independent of the mean flow Reynolds number, although the pressure contribution does indeed vary linearly with Re m in accord with the analysis of Hill et al. (2001b). An improved correlation for F in terms of ϕ and Re m is proposed that corrects the existing correlations in Re m range 100–300. Since this drag correlation has been inferred from simulations of fixed particle assemblies, it does not include the effect of mobility of the particles. However, the fixed-bed simulation approach is a good approximation for high Stokes number particles, which are encountered in most gas–solid flows. This improved drag correlation can be used in CFD simulations of fluidized beds that solve the average two-fluid equations where the accuracy of the drag law affects the prediction of overall flow behavior.

Dynamic Dielectric Response of Concentrated Colloidal Dispersions: Comparison between Theory and Experiment

The cell-model electrokinetic theory of Ahualli et al. Langmuir 2006, 22, 7041; Ahualli et al. J. Colloid Interface Sci. 2007, 309, 342; and Bradshaw-Hajek et al. Langmuir 2008, 24, 4512 is applied to a dense suspension of charged spherical particles, to exhibit the system's dielectric response to an applied electric field as a function of solids volume fraction. The model's predictions of effective permittivity and complex conductivity are favorably compared with published theoretical calculations and experimental measurements on dense colloidal systems. Physical factors governing the volume fraction dependence of the dielectric response are discussed.