YIELD STRESS OF FRACTAL AGGREGATES

Fractals ◽  
2015 ◽  
Vol 23 (03) ◽  
pp. 1550028 ◽  
Author(s):  
YUE XI ◽  
JINJIAN CHEN ◽  
YONGFU XU ◽  
FEIFEI CHU ◽  
CHUANXIN LIU
Keyword(s):  
Fractal Dimension ◽  
Yield Stress ◽  
Power Law ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Published Data ◽  
Proposed Model ◽  
Wide Range ◽  
The Relationship ◽  
Theory And Experiments

A model for the yield stress of aggregates is presented that incorporates fractal dimension taking into account the solid volume fraction and the aggregate diameter. The model shows the yield stress (σy) of aggregates increases with the solid volume fraction (ϕs) as a power law, and is given by [Formula: see text], where the exponent (m) is related to fractal dimension (D), and σy0 is a referenced parameter. The relationship between exponent (m) and fractal dimension is validated by published data of aggregates and represents the measured data very well, over a wide range of the solid volume fractions. The referenced parameter (σy0) is calibrated from experiments of yield stress using power law fittings. The agreement between theory and experiments supports the idea that yielding is ultimately caused by the rupture of a few interparticle bonds within aggregates. In addition, the proposed model for the yield stress of aggregates is found to match better with experiments by comparing with all models in literature.

Dispersion of solids in fracturing flows of yield stress fluids

2017 ◽  
Vol 830 ◽  
pp. 93-137 ◽  
Author(s):  
S. Hormozi ◽  
I. A. Frigaard
Keyword(s):  
Yield Stress ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Three Dimensional ◽  
Process Variations ◽  
Model Framework ◽  
Shear Rates ◽  
Low Viscosity ◽  
High Shear Rates ◽  
Solids Concentration

Solids dispersion is an important part of hydraulic fracturing, both in helping to understand phenomena such as tip screen-out and spreading of the pad, and in new process variations such as cyclic pumping of proppant. Whereas many frac fluids have low viscosity, e.g. slickwater, others transport proppant through increased viscosity. In this context, one method for influencing both dispersion and solids-carrying capacity is to use a yield stress fluid as the frac fluid. We propose a model framework for this scenario and analyse one of the simplifications. A key effect of including a yield stress is to focus high shear rates near the fracture walls. In typical fracturing flows this results in a large variation in shear rates across the fracture. In using shear-thinning viscous frac fluids, flows may vary significantly on the particle scale, from Stokesian behaviour to inertial behaviour across the width of the fracture. Equally, according to the flow rates, Hele-Shaw style models give way at higher Reynolds number to those in which inertia must be considered. We develop a model framework able to include this range of flows, while still representing a significant simplification over fully three-dimensional computations. In relatively straight fractures and for fluids of moderate rheology, this simplifies into a one-dimensional model that predicts the solids concentration along a streamline within the fracture. We use this model to make estimates of the streamwise dispersion in various relevant scenarios. This model framework also predicts the transverse distributions of the solid volume fraction and velocity profiles as well as their evolutions along the flow part.

scholarly journals Thermal conductivity of textile reinforcements for composites

2018 ◽  
Vol 1 ◽  
pp. 251522111775115 ◽  
Author(s):  
Yue El-Hage ◽  
Simon Hind ◽  
François Robitaille
Keyword(s):  
Thermal Conductivity ◽  
Carbon Fibre ◽  
Volume Fraction ◽  
Fibre Volume Fraction ◽  
Three Dimensional ◽  
Fibre Volume ◽  
Published Data ◽  
Manufacturing Processes ◽  
Composites Manufacturing ◽  
The Relationship

Thermal conductivity data for dry carbon fibre fabrics are required for modelling heat transfer during composites manufacturing processes; however, very few published data are available. This article reports in-plane and through-thickness thermal conductivities measured as a function of fibre volume fraction ( Vf) for non-crimp and twill carbon reinforcement fabrics, three-dimensional weaves and reinforcement stacks assembled with one-sided carbon stitch. Composites made from these reinforcements and glass fibre fabrics are also measured. Clear trends are observed and the effects of Vf, de-bulking and vacuum are quantified along with orthotropy ratios. Limited differences between the conductivity of dry glass and carbon fibre fabrics in the through-thickness direction are reported. An unexpected trend in the relationship between that quantity and Vf is explained summarily through simple simulations.

scholarly journals Sampling for Plant Disease Incidence

1999 ◽  
Vol 89 (11) ◽  
pp. 1088-1103 ◽  
Author(s):  
L. V. Madden ◽  
G. Hughes
Keyword(s):  
Power Law ◽  
Binomial Distribution ◽  
Disease Incidence ◽  
Sequential Sampling ◽  
Cluster Sampling ◽  
Diseased Plant ◽  
Ratio Test ◽  
Wide Range ◽  
Sequential Probability ◽  
The Relationship

Knowledge of the distribution of diseased plant units (such as leaves, plants, or roots) or of the relationship between the variance and mean incidence is essential to efficiently sample for diseased plant units. Cluster sampling, consisting of N sampling units of n individuals each, is needed to determine whether the binomial or beta-binomial distribution describes the data or to estimate parameters of the binary power law for disease incidence. The precision of estimated disease incidence can then be evaluated under a wide range of settings including the hierarchical sampling of groups of individuals, the various levels of spatial heterogeneity of disease, and the situation when all individuals are disease free. Precision, quantified with the standard error or the width of the confidence interval for incidence, is directly related to N and inversely related to the degree of heterogeneity (characterized by the intracluster correlation, ρ). Based on direct estimates of ρ (determined from the θ parameter of the beta-binomial distribution or from the observed variance) or a model predicting ρ as a function of incidence (derived from the binary power law), one can calculate, before a sampling bout, the value of N needed to achieve a desired level of precision. The value of N can also be determined during a sampling bout using sequential sampling methods, either to estimate incidence with desired precision or to test a hypothesis about true disease incidence. In the latter case, the sequential probability ratio test is shown here to be useful for classifying incidence relative to a hypothesized threshold when the data follows the beta-binomial distribution with either a fixed ρ or a ρ that depends on incidence.

A Sharp Interface Direct Forcing Immersed Boundary Approach for Fully Resolved Simulations of Particulate Flows

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Jianming Yang ◽  
Frederick Stern
Keyword(s):  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Density Ratio ◽  
Sharp Interface ◽  
Immersed Boundary ◽  
Particulate Flows ◽  
Order Accuracy ◽  
Wide Range ◽  
Direct Forcing ◽  
Coarse Grids

In recent years, the immersed boundary method has been well received as an effective approach for the fully resolved simulations of particulate flows. Most immersed boundary approaches for numerical studies of particulate flows in the literature were based on various discrete delta functions for information transfer between the Lagrangian elements of an immersed object and the underlying Eulerian grid. These approaches have some inherent limitations that restrict their wider applications. In this paper, a sharp interface direct forcing immersed boundary approach based on the method proposed by Yang and Stern (Yang and Stern, 2012, “A Simple and Efficient Direct Forcing Immersed Boundary Framework for Fluid-Structure Interactions,” J. Comput. Phys., 231(15), pp. 5029–5061) is given for the fully resolved simulations of particulate flows. This method uses a discrete forcing approach and maintains a sharp profile of the fluid-solid interface. It is not limited to low Reynolds number flows and the immersed boundary discretization can be arbitrary or totally eliminated for particles with analytical shapes. In addition, it is not required to calculate the solid volume fraction in low density ratio problems. A strong coupling scheme is employed for the fluid-solid interaction without including the fluid solver in the predictor-corrector iterative loop. The overall algorithm is highly efficient and very attractive for simulating particulate flows with a wide range of density ratios on relatively coarse grids. Several cases are examined and the results are compared with reference data to demonstrate the simplicity and robustness of our method in particulate flow simulations. These cases include settling and buoyant particles and the interaction of two settling particles showing the kissing-drafting-tumbling phenomenon. Systematic verification studies show that our method is of second-order accuracy on very coarse grids and approaches fourth-order accuracy on finer grids.

scholarly journals Seismo Electric Transfer Function Fractal Dimension for Characterizing Shajara Reservoirs Of The Permo-Carboniferous Shajara Formation, Saudi Arabia

2018 ◽  
Vol 1 (1) ◽  
Keyword(s):  
Fractal Dimension ◽  
Transfer Function ◽  
Capillary Pressure ◽  
Fractal Dimensions ◽  
Pressure Profile ◽  
Wide Range ◽  
Phase Saturation ◽  
Second Procedure ◽  
Bottom To Top ◽  
The Relationship

The quality of a reservoir can be described in details by the application of seismo electric transfer function fractal dimension. The objective of this research is to calculate fractal dimension from the relationship among seismo electric transfer fuction, maximum seismo electric transfer function and wetting phase saturation and to confirm it by the fractal dimension derived from the relationship among capillary pressure and wetting phase saturation. In this research, porosity was measured on real collected sandstone samples and permeability was calculated theoretically from capillary pressure profile measured by mercury intrusion techniques. Two equations for calculating the fractal dimensions have been employed. The first one describes the functional relationship between wetting phase saturation, seismo electric transfer function, maximum seismo electric transfer function and fractal dimension. The second equation implies to the wetting phase saturation as a function of capillary pressure and the fractal dimension. Two procedures for obtaining the fractal dimension have been developed. The first procedure was done by plotting the logarithm of the ratio between seismo electric transfer function and maximum seismo electric transfer function versus logarithm wetting phase saturation. The slope of the first procedure = 3- Df (fractal dimension). The second procedure for obtaining the fractal dimension was completed by plotting the logarithm of capillary pressure versus the logarithm of wetting phase saturation. The slope of the second procedure = Df -3. On the basis of the obtained results of the constructed stratigraphic column and the acquired values of the fractal dimension, the sandstones of the Shajara reservoirs of the Shajara Formation were divided here into three units. The gained units from bottom to top are: Lower Shajara Seismo Electric Transfer Function Fractal Dimension Unit, Middle Shajara Seismo Electric Tranfser Function Fractal dimension Unit, and Upper Shajara Seismo Electric Transfer Function Fractal Dimension Unit. The results show similarity between seismo electric transfer tunction fractal dimension and capillary pressure fractal dimension. It was also noted that samples with wide range of pore radius were characterized by high values of fractal dimension due to an increase in their connectivity and seismo electric transfer function. In our case , and as conclusions the higher the fractal dimension, the higher the permeability, the better the shajara reservoir characteristics.

scholarly journals An Efficient Approach of Predicting the Elastic Property of Hydrating Cement Paste

2021 ◽  
Vol 8 ◽  
Author(s):  
Baoyu Ma ◽  
Guansuo Dui ◽  
Zhenglin Jia ◽  
Bo Yang ◽  
Chunyan Yang ◽  
...  
Keyword(s):  
Elastic Properties ◽  
Cement Paste ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Empirical Method ◽  
Elastic Behavior ◽  
Engineering Practice ◽  
Proposed Model ◽  
Hydration Model ◽  
Semi Empirical

Although elastic properties of hydrating cement paste are crucial in concrete engineering practice, there are only a few widely available models for engineers to predict the elastic behavior of hydrating cement paste. Therefore, in this paper, we derive an analytical model to efficiently predict the elastic properties (e.g., Young’s modulus) of hydrating cement paste. Notably, the proposed model provides the prediction of hydration, percolation, and homogenization of the cement paste, enabling the study of the early age elasticity evolution in cement paste. A hydration model considering the mineral composition and the initial w/c ratio was used, while the percolation threshold was calculated adopting a phenomenological semi-empirical method describing the effects of the solid volume fraction and the w/c ratio. An efficient mixing rule based on the degree of solid connectivity was then adopted to calculate the elastic properties of the hydrating cement paste. Moreover, for ordinary Portland cement, a simplified model was built using Powers’ hydration model. The obtained modeling results are following experimental data and other numerical results available in the literature.

scholarly journals Flexible and consistent quantile estimation for intensity–duration–frequency curves

2021 ◽  
Vol 25 (12) ◽  
pp. 6479-6494
Author(s):  
Felix S. Fauer ◽  
Jana Ulrich ◽  
Oscar E. Jurado ◽  
Henning W. Rust
Keyword(s):  
Power Law ◽  
Skill Score ◽  
Observation Time ◽  
Performance Model ◽  
Wide Range ◽  
Intensity Duration Frequency ◽  
The Individual ◽  
The Relationship ◽  
Flexible Model

Abstract. Assessing the relationship between the intensity, duration, and frequency (IDF) of extreme precipitation is required for the design of water management systems. However, when modeling sub-daily precipitation extremes, there are commonly only short observation time series available. This problem can be overcome by applying the duration-dependent formulation of the generalized extreme value (GEV) distribution which fits an IDF model with a range of durations simultaneously. The originally proposed duration-dependent GEV model exhibits a power-law-like behavior of the quantiles and takes care of a deviation from this scaling relation (curvature) for sub-hourly durations (Koutsoyiannis et al., 1998). We suggest that a more flexible model might be required to model a wide range of durations (1 min to 5 d). Therefore, we extend the model with the following two features: (i) different slopes for different quantiles (multiscaling) and (ii) the deviation from the power law for large durations (flattening), which is newly introduced in this study. Based on the quantile skill score, we investigate the performance of the resulting flexible model with respect to the benefit of the individual features (curvature, multiscaling, and flattening) with simulated and empirical data. We provide detailed information on the duration and probability ranges for which specific features or a systematic combination of features leads to improvements for stations in a case study area in the Wupper catchment (Germany). Our results show that allowing curvature or multiscaling improves the model only for very short or long durations, respectively, but leads to disadvantages in modeling the other duration ranges. In contrast, allowing flattening on average leads to an improvement for medium durations between 1 h and 1 d, without affecting other duration regimes. Overall, the new parametric form offers a flexible and enhanced performance model for consistently describing IDF relations over a wide range of durations, which has not been done before as most existing studies focus on durations longer than 1 h or day and do not address the deviation from the power law for very long durations (2–5 d).

Use of χ As a Function of Volume Fraction of Rubber to Determine Crosslink Density by Swelling

2003 ◽  
Vol 76 (4) ◽  
pp. 832-845 ◽  
Author(s):  
William L. Hergenrother ◽  
Ashley S. Hilton
Keyword(s):  
Carbon Black ◽  
Metal Oxides ◽  
13C Nmr ◽  
Crosslink Density ◽  
Volume Fraction ◽  
Good Measure ◽  
Noticeable Effect ◽  
Wide Range ◽  
The Relationship

Abstract A technique is described allowing a relatively simple determination of χ as a function of vr from swelling in heptane. A good measure of the true νe of the cured elastomer at all values of vr was demonstrated by substituting this relationship for χ in the Flory-Rehner (F-R) equation. The relationship was established over a wide range of vr values by using samples that had the νe of the cured elastomer determined by tensile retraction (TR). Applying this function to samples treated using the thiol probe method of Campbell gave an improved measure of the types of crosslinks present in sulfur-cured stocks. An identical equation describing χ as a function of vr in heptane was obtained with NR, EPDM and SBR containing up to a 0.31 volume fraction of carbon black (CB) and other fillers. The presence of up to 10 % of clay, talc, silica, resins or metal oxides in the CB had no noticeable effect on the relationship measured. However, when the filler contained about 50% silica a distinctly different slope in the relationship was found. The percent S1, S2 and Sx distribution measured was contrasted between measurements made by 13C NMR, swelling with χ = constant or χ as a function of vr.

Modelling levitated 2-lobed droplets in rotation using Cassinian oval curves

2018 ◽  
Vol 846 ◽  
pp. 1088-1113 ◽  
Author(s):  
Haruki Ishikawa ◽  
Katsuhiro Nishinari
Keyword(s):  
Deformation Behaviour ◽  
Stationary Solutions ◽  
Suitable Model ◽  
Maximum Deformation ◽  
Proposed Model ◽  
Wide Range ◽  
Deformation Length ◽  
Central Cross Section ◽  
The Stability ◽  
The Relationship

A simple model of rotating 2-lobed droplets is proposed by setting the outline shape of the droplet to the Cassinian oval, a mathematical curve that closely resembles in shape. By deriving the governing equation of the proposed model and obtaining its stationary solutions, the relationship between the angular velocity of rotation and the maximum deformation length is explicitly and precisely calculated. The linear stability analysis is performed for the stationary solutions, and it is demonstrated that the stability of the solutions depends only on the ratio of the deformation length to the radius of the central cross-section of the droplet, which is independent of the physical properties of the droplet. Via comparison with an experimental study, it is observed that the calculated result is consistent with the deformation behaviour of actual 2-lobed droplets in the range where the stationary solution of the proposed model is linearly stable. Therefore, the proposed model is a suitable model for reproducing the steady deformation behaviour of 2-lobed droplets in a wide range of viscosities, surface tensions, densities and initial radii of the droplet, and especially if the viscosity of the droplet is low, the entire process of deformation of the 2-lobed droplet, including the unsteady breakup process, can be very well reproduced by the proposed model.

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