Bubble population phenomena in sonochemical reactor: I Estimation of bubble size distribution and its number density with pulsed sonication – Laser diffraction method

In addition to bubble number density, bubble size distribution is an important population parameter governing the activity of acoustic cavitation bubbles. In the present paper, an iterative numerical method for equilibrium size distribution is proposed and combined to a model for bubble counting, in order to approach the number density within a population of acoustic cavitation bubbles of inhomogeneous sizing, hence the sonochemical activity of the inhomogeneous population based on discretization into homogenous groups. The composition of the inhomogeneous population is analyzed based on cavitation dynamics and shape stability at 300 kHz and 0.761 W/cm2 within the ambient radii interval ranging from 1 to 5 µm. Unstable oscillation is observed starting from a radius of 2.5 µm. Results are presented in terms of number probability, number density, and volume probability within the population of acoustic cavitation bubbles. The most probable group having an equilibrium radius of 3 µm demonstrated a probability in terms of number density of 27%. In terms of contribution to the void, the sub-population of 4 µm plays a major role with a fraction of 24%. Comparisons are also performed with the homogenous population case both in terms of number density of bubbles and sonochemical production of HO●, HO2●, and H● under an oxygen atmosphere.

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Measurement of soil dry aggregate size distribution using the laser diffraction method

Soil and Tillage Research ◽

10.1016/j.still.2021.105023 ◽

2021 ◽

Vol 211 ◽

pp. 105023

Author(s):

C. Polakowski ◽

A. Sochan ◽

M. Ryżak ◽

M. Beczek ◽

R. Mazur ◽

...

Keyword(s):

Size Distribution ◽

Diffraction Method ◽

Aggregate Size ◽

Laser Diffraction ◽

Aggregate Size Distribution

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Particle Size Distribution of Various Soil Materials Measured by Laser Diffraction—The Problem of Reproducibility

Minerals ◽

10.3390/min11050465 ◽

2021 ◽

Vol 11 (5) ◽

pp. 465

Author(s):

Cezary Polakowski ◽

Magdalena Ryżak ◽

Agata Sochan ◽

Michał Beczek ◽

Rafał Mazur ◽

...

Keyword(s):

Particle Size ◽

Particle Size Distribution ◽

Normal Distribution ◽

Size Distribution ◽

Precise Measurement ◽

Soil Analysis ◽

Statistical Tests ◽

Diffraction Method ◽

Laser Diffraction ◽

Method Analysis

Particle size distribution is an important soil parameter—therefore precise measurement of this characteristic is essential. The application of the widely used laser diffraction method for soil analysis continues to be a subject of debate. The precision of this method, proven on homogeneous samples, has been implicitly extended to soil analyses, but this has not been sufficiently well confirmed in the literature thus far. The aim of this study is to supplement the information available on the precision of the method in terms of reproducibility of soil measurement and whether the reproducibility of soil measurement is characterized by a normal distribution. To estimate the reproducibility of the laser diffraction method, thirteen various soil samples were characterized, and results were analysed statistically. The coefficient of variation acquired was lowest (3.44%) for silt and highest for sand (23.28%). Five of the thirteen tested samples were characterized by a normal distribution. The fraction content of eight samples was not characterized by normal distribution, but the extent of this phenomenon varied between soils. Although the laser diffraction method is repeatable, the measurement of soil particle size distribution can have limited reproducibility. The main cause seems to be small amounts of sand particles. The error can be amplified by the construction of the dispersion unit. Non-parametric statistical tests should be used by default for soil laser diffraction method analysis.

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Bubble size distribution in surface wave breaking entraining process

Science in China Series D Earth Sciences ◽

10.1007/s11430-007-0116-7 ◽

2007 ◽

Vol 50 (11) ◽

pp. 1754-1760 ◽

Cited By ~ 3

Author(s):

Lei Han ◽

YeLi Yuan

Keyword(s):

Surface Wave ◽

Size Distribution ◽

Bubble Size ◽

Wave Breaking ◽

Bubble Size Distribution

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Physiochemical properties and reproducibility of air-based sodium tetradecyl sulphate foam using the Tessari method

Phlebology The Journal of Venous Disease ◽

10.1177/0268355516655078 ◽

2016 ◽

Vol 32 (6) ◽

pp. 390-396 ◽

Cited By ~ 2

Author(s):

Mike R Watkins ◽

Richard J Oliver

Keyword(s):

Size Distribution ◽

Bubble Size ◽

Bubble Size Distribution ◽

Foam Density ◽

Physiochemical Properties ◽

Significant Difference ◽

Experienced Operator ◽

Sodium Tetradecyl Sulphate ◽

Foam Production ◽

Made In

Objectives The objectives were to examine the density, bubble size distribution and durability of sodium tetradecyl sulphate foam and the consistency of production of foam by a number of different operators using the Tessari method. Methods 1% and 3% sodium tetradecyl sulphate sclerosant foam was produced by an experienced operator and a group of inexperienced operators using either a 1:3 or 1:4 liquid:air ratio and the Tessari method. The foam density, bubble size distribution and foam durability were measured on freshly prepared foam from each operator. Results The foam density measurements were similar for each of the 1:3 preparations and for each of the 1:4 preparations but not affected by the sclerosant concentration. The bubble size for all preparations were very small immediately after preparation but progressively coalesced to become a micro-foam (<250 µm) after the first 30 s up until 2 min. Both the 1% and 3% solution foams developed liquid more rapidly when made in a 1:3 ratio (37 s) than in a 1:4 ratio (45 s) but all combinations took similar times to reach 0.4 ml liquid formation. For all the experiments, there was no statistical significant difference between operators. Conclusions The Tessari method of foam production for sodium tetradecyl sulphate sclerosant is consistent and reproducible even when made by inexperienced operators. The best quality foam with micro bubbles should be used within the first minute after production.

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Development of Bubble Characteristics on Chute Spillway Bottom

Water ◽

10.3390/w10091129 ◽

2018 ◽

Vol 10 (9) ◽

pp. 1129

Author(s):

Ruidi Bai ◽

Chang Liu ◽

Bingyang Feng ◽

Shanjun Liu ◽

Faxing Zhang

Keyword(s):

Size Distribution ◽

Bubble Size ◽

Dissipation Rate ◽

Bubble Diameter ◽

Bubble Size Distribution ◽

Impact Zone ◽

Air Bubble ◽

Air Supply ◽

Bubble Characteristics ◽

The Impact

Chute aerators introduce a large air discharge through air supply ducts to prevent cavitation erosion on spillways. There is not much information on the microcosmic air bubble characteristics near the chute bottom. This study was focused on examining the bottom air-water flow properties by performing a series of model tests that eliminated the upper aeration and illustrated the potential for bubble variation processes on the chute bottom. In comparison with the strong air detrainment in the impact zone, the bottom air bubble frequency decreased slightly. Observations showed that range of probability of the bubble chord length tended to decrease sharply in the impact zone and by a lesser extent in the equilibrium zone. A distinct mechanism to control the bubble size distribution, depending on bubble diameter, was proposed. For bubbles larger than about 1–2 mm, the bubble size distribution followed a—5/3 power-law scaling with diameter. Using the relationship between the local dissipation rate and bubble size, the bottom dissipation rate was found to increase along the chute bottom, and the corresponding Hinze scale showed a good agreement with the observations.

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