Using maximum entropy approach for prediction of drop size distribution in a pilot plant multi-impeller extraction contactor

RSC Advances ◽  
2015 ◽  
Vol 5 (116) ◽  
pp. 95967-95980 ◽  
Author(s):  
Mehdi Asadollahzadeh ◽  
Meisam Torab-Mostaedi ◽  
Shahrokh Shahhosseini ◽  
Ahad Ghaemi
Keyword(s):  
Maximum Entropy ◽  
Size Distribution ◽  
Pilot Plant ◽  
Drop Size ◽  
Maximum Entropy Principle ◽  
Drop Size Distribution ◽  
Size Distributions ◽  
Entropy Principle ◽  
Drop Size Distributions ◽  
Column Extractor

In this study, the maximum entropy principle is used to predict the drop size distributions in a multi-impeller column extractor.

scholarly journals Size Distributions of Hydrometeors: Analysis with the Maximum Entropy Principle

2015 ◽  
Vol 73 (1) ◽  
pp. 95-108 ◽  
Author(s):  
Jun-Ichi Yano ◽  
Andrew J. Heymsfield ◽  
Vaughan T. J. Phillips
Keyword(s):  
Maximum Entropy ◽  
Size Distribution ◽  
Mass Flux ◽  
Drop Size ◽  
Maximum Entropy Principle ◽  
Drop Size Distribution ◽  
Homogeneous Distribution ◽  
Bulk Mass ◽  
Drop Mass ◽  
Entropy Principle

Abstract This paper proposes that the maximum entropy principle can be used for determining the drop size distribution of hydrometeors. The maximum entropy principle can be applied to any physical systems with many degrees of freedom in order to determine a distribution of a variable when the following are known: 1) the restriction variable that leads to a homogeneous distribution without constraint and 2) a set of integrals weighted by the distribution, such as mean and variance, that constrain the system. The principle simply seeks a distribution that gives the maximum possible number of partitions among all the possible states. A continuous limit can be taken by assuming a constant bin size for the restriction variable. This paper suggests that the drop mass is the most likely restriction variable, and the laws of conservation of total bulk mass and of total vertical drop mass flux are two of the most likely physical constraints to a hydrometeor drop size distribution. Under this consideration, the distribution is most likely constrained by the total bulk mass when an ensemble of drops under the coalescence–breakup process is confined inside a closed box. Alternatively, for an artificial rain produced from the top of a high ceiling under a constant mass flux of water fall, the total drop mass flux is the most likely constraint to the drop size distribution. Preliminary analysis of already-published data is not inconsistent with the above hypotheses, although the results are rather inconclusive. Data in the large drop size limit are required in order to reach a more definite conclusion.

Drop Size Distributions in Oil Water Mixtures

1973 ◽  
Vol 1973 (1) ◽  
pp. 457-465 ◽  
Author(s):  
Vijay K. Stokes ◽  
Andrew C. Harvey
Keyword(s):  
Size Distribution ◽  
Drop Size ◽  
Standard Procedure ◽  
Drop Size Distribution ◽  
Coulter Counter ◽  
Size Distributions ◽  
Oil Water ◽  
Drop Size Distributions

ABSTRACT The oil drop size distribution in oil water mixtures is of importance in the design of separators that make use of settling or enhanced settling as in centrifuges. This paper describes an attempt to identify the parameters that affect the size distribution of drops in mechanically generated emulsions. Oil/water mixtures were made by three different methods. On the basis of the results of these tests, a standard procedure for making mixtures was adopted. This paper presents the results of an extensive series of tests, with three different oils, in which the drop size distributions were measured by a Coulter Counter.

scholarly journals Drop Size Distribution Measurements in Outer Rainbands of Hurricane Dorian at the NASA Wallops Precipitation-Research Facility

Atmosphere ◽  
2020 ◽  
Vol 11 (6) ◽  
pp. 578 ◽  
Author(s):  
Merhala Thurai ◽  
Viswanathan N. Bringi ◽  
David B. Wolff ◽  
David A. Marks ◽  
Charanjit S. Pabla
Keyword(s):  
Size Distribution ◽  
Drop Size ◽  
Drop Size Distribution ◽  
Size Distributions ◽  
Research Facility ◽  
Bright Band ◽  
Wet Snow ◽  
Double Moment ◽  
Dominant Process ◽  
Drop Size Distributions

Hurricane rainbands are very efficient rain producers, but details on drop size distributions are still lacking. This study focuses on the rainbands of hurricane Dorian as they traversed the densely instrumented NASA precipitation-research facility at Wallops Island, VA, over a period of 8 h. Drop size distribution (DSD) was measured using a high-resolution meteorological particle spectrometer (MPS) and 2D video disdrometer, both located inside a double-fence wind shield. The shape of the DSD was examined using double-moment normalization, and compared with similar shapes from semiarid and subtropical sites. Dorian rainbands had a superexponential shape at small normalized diameter values similar to those of the other sites. NASA’s S-band polarimetric radar performed range height-indicator (RHI) scans over the disdrometer site, showing some remarkable signatures in the melting layer (bright-band reflectivity peaks of 55 dBZ, a dip in the copolar correlation to 0.85 indicative of 12–15 mm wet snow, and a staggering reflectivity gradient above the 0 °C level of −10 dB/km, indicative of heavy aggregation). In the rain layer at heights < 2.5 km, polarimetric signatures indicated drop break-up as the dominant process, but drops as large as 5 mm were detected during the intense bright-band period.

Controls on the space-time variability of raindrop size distributions

2021 ◽  
Author(s):  
Remko Uijlenhoet
Keyword(s):  
Size Distribution ◽  
Drop Size ◽  
Space Time ◽  
Drop Size Distribution ◽  
Time Variability ◽  
Statistical Interpretation ◽  
Size Distributions ◽  
Scaling Exponents ◽  
Raindrop Size ◽  
Drop Size Distributions

&lt;p&gt;It has been stated that &quot;the study of drop-size distributions, with its roots in both land-surface processes [e.g. interception, erosion, infiltration and surface runoff] and atmospheric remote sensing [e.g. radar meteorology], provides an important element to an integrated program of hydrometeorological research&quot; (Smith, 1993). Although raindrop size distributions have been studied from a scientific perspective since the early 20th century, it was not until the mid-1990s that researchers realized that all parameterizations for the drop size distribution published until then could be summarized in the form of a scaling law, which provided &quot;a general phenomenological formulation for drop size distribution&quot; (Sempere Torres et al., 1994). The main implication of the proposed expression is that the integral rainfall variables (such as rain rate and radar reflectivity) are related by power laws, in agreement with experimental evidence. The proposed formulation naturally leads to a general methodology for scaling all raindrop size data in a unique plot, which yields more robust fits of the drop size distribution. Here, we provide a statistical interpretation of the law&amp;#8217;s scaling exponents in terms of different modes of control on the space-time variability of drop size distributions, namely size-control vs. number-control, inspired by the work of Smith and De Veaux (1994). Also, an attempt will be made toward interpreting the values of the scaling exponents and the shape of the scaled drop size distribution in terms of the underlying (micro)physical processes.&lt;/p&gt;&lt;p&gt;REFERENCES&lt;/p&gt;&lt;p&gt;Smith, J. A., 1993: Precipitation. In Maidment, D. R., editor, Handbook of Hydrology, pages 3.1&amp;#8211;3.47. McGraw-Hill, New York.&lt;/p&gt;&lt;p&gt;Sempere Torres, D., J.M. Porr&amp;#224;, and J.-D. Creutin, 1994: A general formulation for raindrop size distribution. J. Appl. Meteor., 33, 1494&amp;#8211;1502.&lt;/p&gt;&lt;p&gt;Smith, J.A. and R.D. De Veaux, 1994: A stochastic model relating rainfall intensity to raindrop processes. Water Resour. Res., 30, 651&amp;#8211;664.&lt;/p&gt;

MEASUREMENTS OF CLOUD DROP-SIZE DISTRIBUTIONS

1957 ◽  
Vol 14 (1) ◽  
pp. 55-59 ◽  
Author(s):  
Ralph G. Eldridge
Keyword(s):  
Size Distribution ◽  
Drop Size ◽  
Drop Size Distribution ◽  
Size Distributions ◽  
Cloud Drop ◽  
Infrared Transmittance ◽  
Drop Size Distributions ◽  
Visual Range ◽  
Mount Washington

Abstract Through the analysis of infrared transmittance of a natural cloud, its drop-size distribution can be inferred. This technique has been used to measure and analyze ten cloud situations on Mount Washington. These clouds show drop-size distributions that are bimodal in character. In all the distributions, a large number of small droplets is inferred. To test the synthesized distributions in another region of the spectrum, the visual range was computed. This determination of the visual range is in agreement with the observed visibilities.

scholarly journals The breakup of levitating water drops observed with a high speed camera

2011 ◽  
Vol 11 (19) ◽  
pp. 10205-10218 ◽  
Author(s):  
C. Emersic ◽  
P. J. Connolly
Keyword(s):  
Size Distribution ◽  
High Speed ◽  
Drop Size ◽  
Initial Conditions ◽  
Water Drop ◽  
Liquid Water Content ◽  
Drop Size Distribution ◽  
High Speed Camera ◽  
Size Distributions ◽  
Drop Size Distributions

Abstract. Collision-induced water drop breakup in a vertical wind tunnel was observed using a high speed camera for interactions between larger drop sizes (up to 7 mm diameter) than have previously been experimentally observed. Three distinct collisional breakup types were observed and the drop size distributions from each were analysed for comparison with predictions of fragment distributions from larger drops by two sets of established breakup parameterisations. The observations showed some similarities with both parameterisations but also some marked differences for the breakup types that could be compared, particularly for fragments 1 mm and smaller. Modifications to the parameterisations are suggested and examined. Presented is also currently the largest dataset of bag breakup distributions observed. Differences between this and other experimental research studies and modelling parameterisations, and the associated implications for interpreting results are discussed. Additionally, the stochastic coalescence and breakup equation was solved computationally using a breakup parameterisation, and the evolving drop-size distribution for a range of initial conditions was examined. Initial cloud liquid water content was found to have the greatest influence on the resulting distribution, whereas initial drop number was found to have relatively little influence. This may have implications when considering the effect of aerosol on cloud evolution, raindrop formation and resulting drop size distributions. Calculations presented show that, using an ideal initial cloud drop-size distribution, ~1–3% of the total fragments are contributed from collisional breakup between drops of 4 and 6 mm.

Drop size distributions by power functions of breakage and coalescence

1982 ◽  
Vol 47 (9) ◽  
pp. 2393-2402 ◽  
Author(s):  
Helena Sovová
Keyword(s):  
Size Distribution ◽  
Drop Size ◽  
Direct Determination ◽  
Drop Size Distribution ◽  
Size Distributions ◽  
Power Functions ◽  
Drop Size Distributions ◽  
Drop Breakage ◽  
Batch Mixer

The frequencies of drop breakage and coalescence in a batch mixer are described by power functions of drop sizes. The shape of a steady state drop size distribution corresponding to the power functions is correlated with their exponents. The use of this correlation for direct determination of linear combination of power functions exponents from an experimental drop size distribution is demonstrated.

Drop-Size Distribution Measurements in Orographic Rain

1948 ◽  
Vol 29 (7) ◽  
pp. 362-366 ◽  
Author(s):  
Lloyd J. Anderson
Keyword(s):  
Size Distribution ◽  
Drop Size ◽  
Rainfall Intensity ◽  
Drop Size Distribution ◽  
Similar Data ◽  
Size Distributions ◽  
Similarities And Differences ◽  
Drop Size Distributions

Measurements on rainfall near Hilo, Hawaii are described. Quartile deviations of drop-size distributions are plotted versus rainfall intensity. Comparison is made with similar data of Laws and Parsons, and certain similarities and differences are pointed out.

Drop-Size Distributions of Bingham Liquid (PAINT) Sprays Produced by Fan-Jet Pressure Nozzles

1979 ◽  
Vol 101 (4) ◽  
pp. 449-455
Author(s):  
W. S. Janna ◽  
J. E. A. John
Keyword(s):  
Shear Stress ◽  
Size Distribution ◽  
Drop Size ◽  
Drop Size Distribution ◽  
Size Distributions ◽  
Collection Device ◽  
Median Diameter ◽  
Drop Size Distributions ◽  
Liquid Paint ◽  
Microscope Slides

The drop-size distribution of Bingham liquid sprays was determined by experimentation. Three different highly viscous paints were sprayed with fan-jet airless spray nozzles at pressure ranging from 5 170 to 18 200 kPa. A collection device was constructed to capture a spray sample on microscope slides. Measurement of flattened droplet diameters with a microscope yielded drop-size distribution curves of accumulated volume per cent versus volume median diameter. It was postulated that the wall shear stress existing at the exit plane of the nozzle initiated liquid atomization. A logarithmic correlation was found between shear stress and volume median diameter.

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