A formula for the settling velocity of cohesive sediment flocs in water

2019 ◽  
Vol 19 (5) ◽  
pp. 1422-1428
Author(s):  
Zhongfan Zhu
Keyword(s):  
Simple Formula ◽  
Settling Velocity ◽  
Basic Structure ◽  
Cohesive Sediment ◽  
Data Sets ◽  
Floc Size ◽  
Median Size ◽  
Primary Particles ◽  
Fractal Architecture ◽  
Good Agreement

Abstract A simple formula is developed to relate the size and settling velocity of cohesive sediment flocs in both the viscous and inertial settling ranges. This formula maintains the same basic structure as the existing formula but is amended to incorporate the fact that the flocculated sediment has an internal fractal architecture and is composed of different-sized primary particles. The input parameters needed for calculating the settling velocity include the median size and size distribution of the primary particles, the fractal dimension of the floc, the density of the sediment, and two calibrated coefficients that incorporate the effects of floc shape, permeability, and flow separation on drag. The proposed formula is compared with four data sets of settling velocity–floc size collected from the published literature, and a good agreement between the model and these data can be found.

scholarly journals Modeling of Flocculation and Sedimentation Using Population Balance Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Zhipeng Shi ◽  
Genguang Zhang ◽  
Yuzhuo Zhang ◽  
Tingting He ◽  
Guoliang Pei
Keyword(s):  
Settling Velocity ◽  
Population Balance ◽  
Nonlinear Process ◽  
Fine Sediment ◽  
Population Balance Modeling ◽  
Floc Size ◽  
Bed Topography ◽  
Computational Fluid Dynamics Cfd ◽  
Sediment Particles ◽  
Good Agreement

Flocculation is a special phenomenon for fine sediment or silt in reservoirs and estuaries. Flocculation usually results in changes of size, morphology, and settling velocity of sediment particles and finally changes of bed topography of reservoirs and estuaries. The process of flocculation and sedimentation was simulated based on population balance modeling (PBM) and computational fluid dynamics (CFD); the changes of particle or floc size and their settling velocities over time were examined. The results showed that flocculation is a dynamic and nonlinear process containing aggregation, breakage, reaggregation, and rebreakage between particles, microflocs, and macroflocs. Furthermore, the visual process of flocculation and sedimentation was directly created by the simulation results and is in good agreement with the results of the previous experiments.

scholarly journals An Extended Entropic Model for Cohesive Sediment Flocculation in a Piecewise Varied Shear Environment

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1263
Author(s):  
Zhongfan Zhu ◽  
Jie Dou
Keyword(s):  
Steady State ◽  
Shear Rate ◽  
Size Variation ◽  
Cohesive Sediment ◽  
Turbulent Shear ◽  
Data Sets ◽  
Extended Model ◽  
Floc Size ◽  
Probability Methods ◽  
Empirical Coefficients

In this study, an extended model for describing the temporal evolution of a characteristic floc size of cohesive sediment particles when the flocculation system is subject to a piecewise varied turbulent shear rate was derived by the probability methods based on the Shannon entropy theory following Zhu (2018). This model only contained three important parameters: initial and steady-state values of floc size, and a parameter characterizing the maximum capacity for floc size increase (or decay), and it can be adopted to capture well a monotonic pattern in which floc size increases (or decays) with flocculation time. Comparison with 13 literature experimental data sets regarding floc size variation to a varied shear rate showed the validity of the entropic model with a high correlation coefficient and few errors. Furthermore, for the case of tapered shear flocculation, it was found that there was a power decay of the capacity parameter with the shear rate, which is similar to the dependence of the steady-state floc size on the shear rate. The entropic model was further parameterized by introducing these two empirical relations into it, and the finally obtained model was found to be more sensitive to two empirical coefficients that have been incorporated into the capacity parameter than those in the steady-state floc size. The proposed entropic model could have the potential, as an addition to existing flocculation models, to be coupled into present mature hydrodynamic models to model the cohesive sediment transport in estuarine and coastal regions.

Systematic calculations of energy levels and transitions rates in Mo XXVIII

2020 ◽  
Vol 75 (8) ◽  
pp. 739-747
Author(s):  
Feng Hu ◽  
Yan Sun ◽  
Maofei Mei
Keyword(s):  
Energy Levels ◽  
Oscillator Strengths ◽  
Atomic Data ◽  
Data Sets ◽  
Electron Systems ◽  
Excitation Energies ◽  
Experimental Values ◽  
Qed Effects ◽  
Hyperfine Structures ◽  
Good Agreement

AbstractComplete and consistent atomic data, including excitation energies, lifetimes, wavelengths, hyperfine structures, Landé gJ-factors and E1, E2, M1, and M2 line strengths, oscillator strengths, transitions rates are reported for the low-lying 41 levels of Mo XXVIII, belonging to the n = 3 states (1s22s22p6)3s23p3, 3s3p4, and 3s23p23d. High-accuracy calculations have been performed as benchmarks in the request for accurate treatments of relativity, electron correlation, and quantum electrodynamic (QED) effects in multi-valence-electron systems. Comparisons are made between the present two data sets, as well as with the experimental results and the experimentally compiled energy values of the National Institute for Standards and Technology wherever available. The calculated values including core-valence correction are found to be in a good agreement with other theoretical and experimental values. The present results are accurate enough for identification and deblending of emission lines involving the n = 3 levels, and are also useful for modeling and diagnosing plasmas.

A new risk-adjusted Bernoulli cumulative sum chart for monitoring binary health data

2016 ◽  
Vol 25 (6) ◽  
pp. 2704-2713 ◽  
Author(s):  
Giuseppe Rossi ◽  
Simone Del Sarto ◽  
Marco Marchi
Keyword(s):  
Simple Formula ◽  
Efficient Solution ◽  
Real Data ◽  
Health Data ◽  
Data Sets ◽  
Cumulative Sum ◽  
Baseline Incidence ◽  
Health Event ◽  
Control Limits ◽  
Underlying Risk

To monitor a health event in patients with a specific risk of developing the event, a risk-adjusted cumulative sum chart is needed. The risk-adjusted cumulative sum chart proposed in the literature has some limitations. Setting appropriate control limits is not straightforward, there is no simple formula for constructing them, and they remain sensitive to changes in the underlying risk distribution and the baseline incidence rate. To overcome these limits, we propose a new risk-adjusted Bernoulli cumulative sum chart as a simple and efficient solution. Analyses of simulated and real data sets illustrate the performance and usefulness of the proposed procedure.

PWA OF πN SCATTERING WITH FIXED-t DISPERSION RELATIONS

2005 ◽  
Vol 20 (08n09) ◽  
pp. 1810-1813
Author(s):  
PEKKO PIIROLA ◽  
M. E. SAINIO
Keyword(s):  
Data Base ◽  
Forward Direction ◽  
Dispersion Relations ◽  
Data Sets ◽  
Coupling Constant ◽  
Partial Waves ◽  
Scattering Measurements ◽  
Pion Nucleon ◽  
Good Agreement

The πN scattering measurements from last couple of decades are not in very good agreement with each other. In fact, using the different data sets one finds different values for the pion-nucleon coupling constant. An analysis with theoretical constraints is the only way to produce accurate partial waves. In this analysis, the fixed-t dispersion relations are used to ensure analyticity in the invariant amplitudes and to decrease the effects of inaccuracies in the data base. Pietarinen's expansion is the method used to enforce the dispersion constraints. The strength of the analyticity constraints is illustrated with C± amplitudes in the forward direction.

Comparison of Small-Angle Neutron Scattering of δ' Precipitation in an Al–Li Alloy at a High-Flux Reactor and at a Pulsed-Neutron Source

1997 ◽  
Vol 30 (5) ◽  
pp. 602-606 ◽  
Author(s):  
G. Albertini ◽  
F. Carsughi ◽  
R. Coppola ◽  
R. K. Heenan ◽  
M. Stefanon
Keyword(s):  
Neutron Scattering ◽  
Small Angle ◽  
Small Angle Neutron Scattering ◽  
Size Distribution Function ◽  
Data Sets ◽  
Flux Reactor ◽  
Average Size ◽  
Pulsed Neutron ◽  
Pulsed Neutron Source ◽  
Good Agreement

Two different small-angle neutron scattering (SANS) facilities, the D11 camera at the Institut Laue–Langevin (ILL, Grenoble, France) and the LOQ time-of-flight diffractometer at the Rutherford Appleton Laboratory (RAL, Didcot, Oxon, England), were used in the investigations of δ′-Al3Li precipitation at 463 K in Al–Li 3% alloy. The results obtained from the steady-state reactor and from the pulsed source by using two different data-acquisition techniques and two different procedures for data analysis are compared. The SANS curves for the same set of samples investigated using the two different instruments are in good agreement within the experimental uncertainties. A check was also made on the metallurgically relevant quantities, namely the average size and the size-distribution function of the δ′ precipitates at the various stages of the ageing process, obtained from the two sets of SANS curves by applying the same numerical method. Good agreement was found between the results from the two data sets.

An evaluation of fire-plume properties simulated with the Fire Dynamics Simulator (FDS) and the Clark coupled wildfire model

2006 ◽  
Vol 36 (11) ◽  
pp. 2894-2908 ◽  
Author(s):  
Ruiyu Sun ◽  
Mary Ann Jenkins ◽  
Steven K Krueger ◽  
William Mell ◽  
Joseph J Charney
Keyword(s):  
Fluid Dynamics ◽  
Data Sets ◽  
Fire Plume ◽  
Fire Dynamics ◽  
Fire Model ◽  
Fire Dynamics Simulator ◽  
Physically Based ◽  
Vertical Grid ◽  
Simplifying Assumptions ◽  
Good Agreement

Before using a fluid dynamics physically based wildfire model to study wildfire, validation is necessary and model results need to be systematically and objectively analyzed and compared to real fires, which requires suitable data sets. Observational data from the Meteotron experiment are used to evaluate the fire-plume properties simulated by two fluid dynamics numerical wildfire models, the Fire Dynamics Simulator (FDS) and the Clark coupled atmosphere–fire model. Comparisons based on classical plume theory between numerical model and experimental Meteotron results show that plume theory, because of its simplifying assumptions, is a fair but restricted rendition of important plume-averaged properties. The study indicates that the FDS, an explicit and computationally demanding model, produces good agreement with the Meteotron results even at a relatively coarse horizontal grid size of 4 m for the FDS, while the coupled atmosphere–fire model, a less explicit and less computationally demanding model, can produce good agreement, but that the agreement is sensitive to surface vertical-grid sizes and the method by which the energy released from the fire is put into the atmosphere.

scholarly journals Modeling the Peach Sugar Contents in Relation to Fruit Growth

1996 ◽  
Vol 121 (6) ◽  
pp. 1122-1131 ◽  
Author(s):  
Michel Génard ◽  
Michel Souty
Keyword(s):  
Growth Curve ◽  
Prunus Persica ◽  
Transfer Functions ◽  
Dry Weight ◽  
Fruit Growth ◽  
Data Sets ◽  
Weight Growth ◽  
Using Data ◽  
Good Agreement

The edible quality of peaches (Prunus persica L. Batsch) to a great extent depends on their sweetness, which is related to sugar composition. Our objective was to develop a model to predict carbon partitioning within fruit flesh and to predict the sucrose, sorbitol, glucose, and fructose contents. The model is dynamic and deterministic and was designed to be driven by the flesh dry-weight growth curve, flesh water content, and temperature data. It uses differential equations where the state of the system is defined by variables that describe how much carbon is present as each form of sugar and as other compounds (acids and structural carbohydrates). The rates of change of these amounts of carbon depend on the current values of corresponding variables and on the transfer functions between them. These functions are defined by rate constants or by functions of degree-days after full bloom. The model was calibrated and tested using data sets from treatments that covered several leaf: fruit ratios. The predictions of the model were in fairly good agreement with experimental data. A sensitivity analysis was performed to identify the most influential transfer function parameters. Carbon flows between sugar forms were analyzed. Sucrose, which was the most abundant sugar, and fructose, which is the sweetest, contributed most to fruit sweetness. Simulations were performed to study the effects of changes in fruit growth-curve parameters on sugar contents and concentrations.

scholarly journals Flocculation of Clay Suspensions by Anionic and Cationic Polyelectrolytes: A Systematic Analysis

Minerals ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. 999
Author(s):  
Ahmad Shakeel ◽  
Zeinab Safar ◽  
Maria Ibanez ◽  
Leon van Paassen ◽  
Claire Chassagne
Keyword(s):  
Light Scattering ◽  
Shear Rate ◽  
Settling Velocity ◽  
Rheological Analysis ◽  
Floc Size ◽  
Clay Concentration ◽  
History Of ◽  
Settling Column ◽  
Cationic Polyelectrolytes ◽  
Shear History

The characteristics of clayey suspensions, majorly composed of quartz microparticles, in the presence of anionic and cationic polyelectrolytes were investigated using different techniques. A wide range of clay concentrations was used, i.e., from 0.07 to 1000 g/L for different experimental techniques, based on the fact that the clay concentration possible to analyze with selected experimental methods was significantly different. The optimum flocculant to clay ratio was defined as the ratio that gives the fastest initial floc growth by static light scattering or fastest initial settling velocity by settling column experiments. In case of anionic polyelectrolyte, it was observed that the optimum flocculant dose depends on the amount of cations present in the system. For suspensions made with demi-water, a lower optimum flocculant dose (<1 mg/g) than for suspensions prepared in tap water (2.28 mg/g) was observed. At these lower salinities, the supernatant remained turbid in all the experiments and was, therefore, not a good measure for optimal anionic based flocculation. The equilibrium floc size at a given shear rate was found to be independent on the shear history of the floc and only dependent on the current applied shear. This was confirmed by both light scattering and rheological analysis. In case of cationic polyelectrolyte, the optimum flocculant ratio (5–6 mg/g) corresponded to the ratio that gives the lowest electrophoretic mobility for each clay concentration and to the ratio that gives the fastest settling velocity for the highest clay concentrations (12–15 g/L), where static light scattering measurements were not possible. All investigation techniques, therefore, proved to be good indicators for predicting the optimum flocculant to clay ratio. For the lowest concentrations (1.75–8.7 g/L) studied by settling column measurements, the optimum flocculant ratio was observed to increase with decreasing clay concentration, for fixed mixing conditions. The optimum flocculant to clay ratio was not always corresponding to the clearest supernatant and the size of flocs at optimum dosage was dependent on the mixing efficiency. The equilibrium floc size at a given shear rate was found to be dependent on the shear history of the floc and the current applied shear. This was confirmed by both light scattering and rheological analysis.

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