scholarly journals A Packing Computational Method Relating Fractal Particle Size Distribution and Void Fraction in Granular Media

Author(s):  
Carlos García-Gutiérrez ◽  
Miguel A. Martín ◽  
Francisco Muñoz Ortega ◽  
Miguel Reyes ◽  
Francisco J. Taguas
Author(s):  
Seyyed Mahdi Nemati Mehr ◽  
Salman Sohrabi ◽  
Pedram Falsafi ◽  
Paniz Gorji

In this paper we developed a new mathematical model for the flow inside cascade impactors and via this simplified model, we determined the particle size distribution by a fast and low cost computational method. Using cascade impactors for determining the particle size distribution, one can use comprehensive CFD methods to fully simulate the particle traces. Although the results from those CFD analyses can be very accurate, usually that is not a time and cost efficient routine. In contrast, we showed that by using our proposed calculation we can estimate the particle size distribution very fast and yet with the slight error — comparing to the results from CFD method. Cascade impactors are being used to measure the range of substances moving through an opening and determine the particle size of distributed substances. Air flow containing aerosol entering in each stage, after colliding vertically with a plate will deviate 90 degrees from its original direction. Larger (massive) particles cannot follow the flow because of their larger linear momentum. Hence, they will deviate from the flow and deposit on the plate instead. The mass difference before and after the experiment represents the deposited mass in each stage. By integrating multiple uniquely designed stages into one impactor, we can determine size of particles in the flow. Typical cascade impactors consist of up to ten stages in which different size of aerosols are being separated. This paper presents a simple model for the flow in one single stage of a cascade impactor. Flow inside cascade impactor is approximated by stagnation point potential flow with the stream function of Psi = Axy, and particles are tracked by velocity verlet algorithm. Absorbed particles are associated with unit value; otherwise they are associated with zero. It is assumed that particles in entrance have random size distribution and location. Drag, Saffman and Brownian forces are taken into account in this model for different particle sizes. The results are discussed in detail and compared with data driven from different approaches in the literature.


Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 601 ◽  
Author(s):  
Carlos García-Gutiérrez ◽  
Miguel Ángel Martín ◽  
Yakov Pachepsky

The particle size distribution (PSD) of complex granular media is seen as a mathematical measure supported in the interval of grain sizes. A physical property characterizing granular products used in the Andreasen and Andersen model of 1930 is re-interpreted in Information Entropy terms leading to a differential information equation as a conceptual approach for the PSD. Under this approach, measured data which give a coarse description of the distribution may be seen as initial conditions for the proposed equation. A solution of the equation agrees with a selfsimilar measure directly postulated as a PSD model by Martín and Taguas almost 80 years later, thus both models appear to be linked. A variant of this last model, together with detailed soil PSD data of 70 soils are used to study the information content of limited experimental data formed by triplets and its ability in the PSD reconstruction. Results indicate that the information contained in certain soil triplets is sufficient to rebuild the whole PSD: for each soil sample tested there is always at least a triplet that contains enough information to simulate the whole distribution.


AIP Advances ◽  
2021 ◽  
Vol 11 (9) ◽  
pp. 095113
Author(s):  
Zhiqiang Lai ◽  
Dong Chen ◽  
Enhui Jiang ◽  
Lianjun Zhao ◽  
Luis E. Vallejo ◽  
...  

2002 ◽  
Vol 69 (6) ◽  
pp. 854-856 ◽  
Author(s):  
A. Carpinteri ◽  
N. Pugno

Based on the fractal particle size distribution, a fragmentation theory for quasi-brittle materials is herein developed. The results are three simple and powerful universal laws for the multiscale energy dissipation under impact and explosion fragmentation for one, two, and three-dimensional bodies, respectively. The three-dimensional law unifies the most important and well-known fragmentation theories. As an example, it has been applied to the prediction of the devastated area due to asteroid impacts on earth as a function of the energy released in the collision.


2006 ◽  
Vol 6 (4) ◽  
pp. 125-134 ◽  
Author(s):  
J. Kim ◽  
D.F. Lawler

Granular media filtration is used almost universally as the last particle removal process in conventional water treatment plants, but every particle cannot be removed. Laboratory-scale filtration experiments were performed at a filtration velocity of 5 m/h using spherical glass beads with mean diameter of 0.55 mm as collectors; the 10 cm depth ensured particles would be in the effluent. Particle suspensions (Min-U-Sil 5) with 1.7 μm mean particle size were filtered at pH values of 3.0, 4.0, and 5.0, all above the isoelectric point (near pH 2.0). Zeta potential distribution (ZPD) and particle size distribution (PSD) of influent and effluent particles were measured. More favorable particles, i.e. particles with smaller surface charge, were well attached to the collectors during the early stage of filtration. This selective attachment of the lower charged particles caused the ZPD of the effluent to move to a more negative range. However, the ZPD did not keep moving to a more negative range during later stages of filtration, and this result was thought to be caused by two reasons: ripening effects and detachment of flocs. In the early stages of filtration, particles were captured better at pH 3.0 than at the higher pH values (as expected), but this trend reversed at a cumulative hydraulic loading (CHL) of only 5–10 m3/m2. Particle breakoff apparently occurs as flocs of particles that are initially captured individually, as indicated by the trends for different particle sizes. At pH 3.0, particles in the 3–5 μm range had worse removal after a CHL of 5 m3/m2, whereas removal improved through the entire CHL of 20 m3/m2 for all size particles at pH 4.0. Chemical parameters such as zeta potential can be important during the initial stage of filtration, but their importance can decrease over time depending on the specific chemical conditions. The influent particle size distribution and the removal of certain size particles during the initial stage can significantly influence ripening which, in turn, can influence the overall particle removal efficiency. Better initial particle removal does not necessarily mean better overall particle removal.


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