Determination of Dynamic Dispersion Coefficient for Solid Particles Flowing in a Fracture With Consideration of Gravity Effect

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Yanan Ding ◽  
Xiaoyan Meng ◽  
Daoyong Yang
Keyword(s):  
Particle Size ◽  
Point Source ◽  
Line Source ◽  
Dispersion Coefficient ◽  
Solid Particles ◽  
Gravity Effect ◽  
Dispersion Coefficients ◽  
Source Condition ◽  
Advection Diffusion Equation ◽  
Gravity Settling

Abstract A robust and pragmatic method has been developed and validated to analytically determine dynamic dispersion coefficients for particles flowing in a parallel-plate fracture, in which gravity settling has been considered due to its significant impact on particle flowing behavior. More specifically, a two-dimensional (2D) advection–diffusion equation together with the initial and boundary conditions has been formulated to describe the flow behavior of finite-sized particles on the basis of coupling the Poiseuille flow with vertical settling. Meanwhile, three types of instantaneous source conditions (i.e., point source, uniform line source, and volumetric line source) have been considered. Explicit expressions, which can directly and time-efficiently calculate dynamic dispersion coefficient, have been derived through the moment analysis and the Green’s function method. By performing the simulation based on the random walk particle tracking (RWPT) algorithm, the newly developed model has been verified to determine particle dispersion coefficients agreeing well with those obtained from the RWPT simulations. It is found that the point source is the most sensitive to gravity effect among different source conditions, while the volumetric line source is affected more than the uniform line source. For particle size larger than its critical value, an increased particle size leads to a decreased asymptotical dispersion coefficient for all the source conditions due to the significant gravity effect, while gravity positively affects the dispersion coefficient at early times for the point source condition. In addition, average flow velocity positively affects the dispersion coefficient for all the source conditions, while the associated gravity effect is influenced only at early times for the point source condition.

Longitudinal dispersion of matter due to the shear effect of steady and oscillatory currents

1984 ◽  
Vol 148 ◽  
pp. 383-403 ◽  
Author(s):  
Hidekazu Yasuda
Keyword(s):  
Line Source ◽  
Dispersion Coefficient ◽  
Longitudinal Dispersion ◽  
Shear Effect ◽  
Two Dimensional ◽  
Clear Definition ◽  
Dispersion Coefficients ◽  
Initial Stage ◽  
Definition Of ◽  
A Current

The longitudinal dispersion due to the shear effect of a current is examined theoretically in the idealized two-dimensional case. This study reveals the process whereby the dispersion reaches a stationary stage after the release of the dispersing substance as an instantaneous line source in steady and in oscillatory currents. In addition, the relation between the stationary dispersion coefficients in steady and oscillatory currents is given analytically. Analysis of the dispersion during the initial stage needs a clear definition of the vertical average of the variance. We can understand the problem of the negative dispersion coefficient, which is obtained by the usual vertical average, through introduction of a new vertical average.

Solid Fluctuations and Dispersion in Liquid-Solid Fluidized Beds With Low Surface Tension Media

2011 ◽  
Author(s):  
H. O. Lim ◽  
M. J. Seo ◽  
Y. Kang ◽  
K. W. Jun
Keyword(s):  
Surface Tension ◽  
Particle Size ◽  
Dispersion Coefficient ◽  
Liquid Velocity ◽  
Stochastic Theory ◽  
Solid Particles ◽  
Liquid Media ◽  
Operating Variables ◽  
Dimensionless Groups ◽  
Fluctuation Frequency

Fluctuations and dispersion of solid particles were investigated in a liquid-solid fluidized bed of which diameter was 0.102 m and 2.5 m in height. Effects of liquid velocity (0.005 ∼ 0.13 m/s), particle size (0.5 ∼ 3.0 × 10−3 m) and surface tension of continuous liquid media (56 ∼ 72 × 10−3 N/m) on the fluctuation frequency and dispersion coefficient of fluidized solid particles were determined. The fluctuating frequency and dispersion coefficient of particles were estimated by means of the relaxation model based on the stochastic theory. Both of fluctuating frequency and dispersion coefficient of particles showed maximum values with a variation of liquid velocity and increased with an increase in the particle size or surface tension of liquid media. The values of fluctuating frequency and dispersion coefficient of fluidized solid particles were well correlated in terms of dimensionless groups as well as operating variables.

Investigation of the different particle size dust releases from rigid filter candles during pulse-jet cleaning

2021 ◽  
pp. 095440622110179
Author(s):  
Xin Luan ◽  
Zhongli Ji ◽  
Longfei Liu ◽  
Ruifeng Wang
Keyword(s):  
Particle Size ◽  
Critical Role ◽  
Operating Conditions ◽  
Solid Particles ◽  
Dust Particles ◽  
Cleaning Efficiency ◽  
Term Operation ◽  
Cleaning Performance ◽  
Experimental Apparatus ◽  
Pulse Jet

Rigid filters made of ceramic or metal are widely used to remove solid particles from hot gases at temperature above 260 °C in the petrochemical and coal industries. Pulse-jet cleaning of fine dust from rigid filter candles plays a critical role in the long-term operation of these filters. In this study, an experimental apparatus was fabricated to investigate the behavior of a 2050 mm filter candle, which included monitoring the variation of pressure dynamic characteristics over time and observing the release of dust layers that allowed an analysis of the cleaning performance of ISO 12103-1 test dusts with different particle size distributions. These results showed the release behavior of these dusts could be divided into five stages: radial expansion, axial crack, flaky release, irregular disruption and secondary deposition. The cleaning performance of smaller sized dust particles was less efficient as compared with larger sized dust particles under the same operating conditions primarily because large, flaky-shaped dust aggregates formed during the first three stages were easily broken into smaller, dispersed fragments during irregular disruption that forced more particles back to the filter surface during secondary deposition. Also, a “low-pressure and long-pulse width” cleaning method improved the cleaning efficiency of the A1 ultrafine test dust from 81.4% to 95.9%.

Penetration Dynamics of Solid Particles into Liquids High-Speed Experimental Results and Modelling

2005 ◽  
Vol 473-474 ◽  
pp. 429-434 ◽  
Author(s):  
Olga Verezub ◽  
György Kaptay ◽  
Tomiharu Matsushita ◽  
Kusuhiro Mukai
Keyword(s):  
Contact Angle ◽  
Particle Size ◽  
Aqueous Solutions ◽  
Particle Velocity ◽  
Weber Number ◽  
High Speed ◽  
Solid Particles ◽  
Bulk Liquid ◽  
Distilled Water ◽  
Critical Weber Number

Penetration of model solid particles (polymer, teflon, nylon, alumina) into transparent model liquids (distilled water and aqueous solutions of KI) were recorded by a high speed (500 frames per second) camera, while the particles were dropped from different heights vertically on the still surface of the liquids. In all cases a cavity has been found to form behind the solid particle, penetrating into the liquid. For each particle/liquid combination the critical dropping height has been measured, above which the particle was able to penetrate into the bulk liquid. Based on this, the critical impact particle velocity, and also the critical Weber number of penetration have been established. The critical Weber number of penetration was modelled as a function of the contact angle, particle size and the ratio of the density of solid particles to the density of the liquid.

Gaseous dispersion in laminar flow through a circular tube

1965 ◽  
Vol 284 (1399) ◽  
pp. 540-550 ◽  
Keyword(s):  
Circular Tube ◽  
Dispersion Coefficient ◽  
Straight Tube ◽  
Laminar Regime ◽  
Thermal Conductivity Detector ◽  
Longitudinal Dispersion Coefficient ◽  
Dispersion Coefficients ◽  
Effective Dispersion ◽  
Flow Through ◽  
Gaseous Dispersion

The dispersion of a pulse of ethylene injected into nitrogen, flowing in the laminar régime through straight and curved tubes, has been investigated at pressures of 1.0 and 4.4 atm. From the study of the concentration profiles with a thermal conductivity detector (katharometer) it is found that the experimental results for gas velocities between 1.00 and 16.00 cm/s agree well with the analytical solution to this problem for a straight tube given by Sir Geoffrey Taylor and extended by Aris. In particular, at low velocities, the effective dispersion coefficients tend to the molecular diffusivities. The presence of a bend slightly reduces the effective longitudinal dispersion coefficient and the introduction of constrictions enhances it. Data are also given on a number of other gas pairs. It is concluded that measurements of dispersion provide an accurate and simple way of studying diffusion in gas mixtures.

A Numerical Model for Simulating Liquid Particles Deposition on Surface

2018 ◽  
Author(s):  
Zhenxia Liu ◽  
Fei Zhang ◽  
Zhengang Liu
Keyword(s):  
Particle Size ◽  
Numerical Model ◽  
Particle Deposition ◽  
Surface Profile ◽  
Leading Edge ◽  
Solid Particles ◽  
Liquid Particle ◽  
Aircraft Icing ◽  
Turbine Vane ◽  
Deposition Thickness

The deposition of liquid particles, which may be converted from solid particles due to high temperature gas heating, makes much more harm on turbine vane blades compared to solid particles, since it may block film-cooling holes, worsen the cooling efficiency and aerodynamic performance of the turbine vane blades. Due to the similarity between the deposition of liquid particles on a surface and the icing on a surface, a numerical model for simulating particles deposition was developed based on the Myers icing model, an extension of the Messinger model, which has been applied in predicting aircraft icing or aero-engine icing. Compared to the conventional liquid particle deposition model, the numerical model in this paper considers the heat transfer and the flow of liquid particles during the particles phase transition from liquid state to solid state. In this model, the change of the surface profile due to the particles deposition was also considered, which was implemented with dynamic mesh technique. To test this model, deposition distribution and thickness obtained from the numerical simulations were compared to the experimental results. Additionally, a numerical simulation was conducted for liquid particle deposition on a flat plate. The result showed that the deposition thickness at the leading edge was much larger than that on the upper surface where the deposition appeared mainly at the middle and rear of the plate. The deposition mass and thickness increased with the increasing in the particle size. The effect of the particle size on the deposition thickness was more notable on the upper surface compared to that at the leading edge.

Improvement in Precision, Accuracy, and Efficiency in Standardizing the Characterization of Granular Materials

2013 ◽  
Author(s):  
J. R. Tucker ◽  
L. J. Shadle ◽  
S. Benyahia ◽  
J. Mei ◽  
C. Guenther ◽  
...  
Keyword(s):  
Particle Size ◽  
Distribution Density ◽  
Particle Density ◽  
Solid Particles ◽  
Minimum Fluidization Velocity ◽  
Void Fractions ◽  
Multiphase Systems ◽  
Precision And Accuracy ◽  
Accuracy And Repeatability

Useful prediction of the kinematics, dynamics, and chemistry of a system relies on precision and accuracy in the quantification of component properties, operating mechanisms, and collected data. In an attempt to emphasize, rather than gloss over, the benefit of proper characterization to fundamental investigations of multiphase systems incorporating solid particles, a set of procedures were developed and implemented for the purpose of providing a revised methodology having the desirable attributes of reduced uncertainty, expanded relevance and detail, and higher throughput. Better, faster, cheaper characterization of multiphase systems result. Methodologies are presented to characterize particle size, shape, size distribution, density (particle, skeletal and bulk), minimum fluidization velocity, void fraction, particle porosity, and assignment within the Geldart Classification. A novel form of the Ergun equation was used to determine the bulk void fractions and particle density. Accuracy of properties-characterization methodology was validated on materials of known properties prior to testing materials of unknown properties. Several of the standard present-day techniques were scrutinized and improved upon where appropriate. Validity, accuracy, and repeatability were assessed for the procedures presented and deemed higher than present-day techniques. A database of over seventy materials has been developed to assist in model validation efforts and future designs.

scholarly journals Effect of soil textural characteristics on longitudinal dispersion in saturated porous media

2021 ◽  
Vol 69 (2) ◽  
pp. 161-170
Author(s):  
Mojtaba G. Mahmoodlu ◽  
Amir Raoof ◽  
Martinus Th. van Genuchten
Keyword(s):  
Particle Size ◽  
Dispersion Coefficient ◽  
Average Particle Size ◽  
Longitudinal Dispersion ◽  
Average Particle ◽  
Sand Sample ◽  
Average Pore ◽  
Advection Dispersion ◽  
Strong Positive Relationship

Abstract This study focuses on the effects of soil textural heterogeneity on longitudinal dispersion under saturation conditions. A series of solute transport experiments were carried out using saturated soil columns packed with two filter sands and two mixtures of these sands, having d50 values of 95, 324, 402, and 480 µm, subjected to four different steady flow rates. Values of the dispersion coefficient (D) were estimated from observed in-situ distributions of calcium chlo-ride, injected as a short nonreactive tracer pulse, at four different locations (11, 18, 25, 36 cm). Analyses of the observed distributions in terms of the standard advection-dispersion equation (ADE) showed that D increased nonlinearly with travel distance and higher Peclet numbers+. The dispersion coefficient of sand sample S1 with its largest average particle size (d 50) was more affected by the average pore-water velocity than sample S4 having the smallest d 50. Results revealed that for a constant velocity, D values of sample S1 were much higher than those of sample S4, which had the smallest d 50. A correlation matrix of parameters controlling the dispersion coefficient showed a relatively strong positive relationship between D and the Peclet number. In contrast, almost no correlation was evident between D and porosity as well as grain size. The results obtained with the four sandy matrices were consistent and proved that the dispersion coefficient depends mainly on the particle size.

Mechanism of Hydrogen Sulfide Drug-Loaded Nanoparticles Promoting the Repair of Spinal Cord Injury in Rats Through Mammalian Target of Rapamycin/Signal Transducer and Activator of Transcription 3 Signaling Pathway

2021 ◽  
Vol 13 (9) ◽  
pp. 1691-1698
Author(s):  
Hongzhe Liu ◽  
Kai Tong ◽  
Ziyi Zhong ◽  
Gang Wang
Keyword(s):  
Spinal Cord ◽  
Spinal Cord Injury ◽  
Particle Size ◽  
Dispersion Coefficient ◽  
Drug Loading ◽  
Average Particle Size ◽  
Mammalian Target Of Rapamycin ◽  
Average Particle ◽  
Recovery Effect ◽  
Cord Injury

To explore the effect of hydrogen sulfide (H2S) drug-loaded nanoparticles (H2S-NPs) on the mTOR/STAT3 signaling pathway in rats and its mechanism on repair of spinal cord injury (SCI), a new H2S-NP (G16MPG-ADT) was prepared and synthesized. The rats were selected as the research objects to explore the mechanism of SCI repair. The G16MPG-ADT NPs were evaluated by average particle size (APS), dispersion coefficient (DC), drug loading content (DLC), drug loading efficacy (DLE), in vitro release (IV-R), and acute toxicity (AT). It was found that G16MPG-ADT nanoparticles had a uniform particle size distribution with a unimodal distribution, with an average particle size of 186.5 nm and a dispersion coefficient of 0.129; within the concentration range of 8~56 μg/L, there was a good linear relationship with the peak area; and the release rate of the nanoparticles within 16 h~32 h was higher than 50%. G16MPG-ADT NP injection treatment was performed on rats with SCI. Western blotting (WB) and immunofluorescence staining were adopted to analyze the expression levels of mammalian target of rapamycin (mTOR) and signal transducers and activators of transcription (STAT3) protein and the growth of neurites. It was found that G16MPG-ADT can increase mTOR and STAT3 protein levels and promote nerve growth after SCI. Finally, the Basso, Beattie and Bresnahan locomotor rating (BBB) score was to evaluate the recovery effect of rats after treatment. It was found that the recovery effect was excellent after G16MPG-ADT treatment. In summary, G16MPG-ADT has a good effect on SCI repair in rats and can be promoted in the clinic.

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