Drop Size Distribution

Complete modeling of a new ultrasonic atomizer, the Spray On Demand (SOD) printhead, was carried out to enable its optimization. The modeling was focused on various factors, including nozzle vibrations and a theoretical prediction of the SOD drop-size distribution. Assuming that the spray is generated based on Faraday instability, a prediction of the drop-size distribution within the framework of a specific and general Maximum Entropy Formalism (MEF) was developed. This prediction was formulated using the conservation laws of energy and mass, as well as the three-parameter generalized Gamma distribution. After establishing an analytical expression to estimate the Sauter Mean Diameter, a qualitative validation of the model was performed by comparing predictions with experimental measurements of the dropsize distribution. The dynamic model is shown to be sensitive to operating conditions and physical properties of the fluid. The prediction capabilities of the model were found to be adequate, paving the way for optimization of the atomizer. The evolution of the drop-size distribution, under the coalescence effect, was also assessed using a convergent Monte Carlo method to solve the distribution equation. This was formulated in a mass flow algorithm, leading to a more physically relevant distribution.

Results of the first measurements of differential reflectivity (ZDR) in rain are reported. ZDR = 10 log (ZH/ZV) dB involves copolar measurements of ZH and Zv, the radar reflectivity factors at horizontal and vertical polarizations, respectively. The data were obtained with the University of Chicago-Illinois State Water Survey (CHILL) radar facility in Oklahoma during Spring 1977 and confirmed theoretical expectations that ZDR should be positive, ranging between around 0-4 dB. By combining ZDR measurements with ZH, it is shown how estimates of No and Do, the parameters of an exponential raindrop size distribution, can be obtained. These estimates were subsequently used to compute rainfall rates as a function of range along a radar ray. These results illustrate that ZDR can have important applications in the quantitative, remote measurement of drop-size distributions and rainfall.

A method is proposed to obtain by theoretical considerations the size distribution of sprays for a thick layer in the presence of gaseous flow. First, a maximum disturbance wave length is deduced from linear theory. This wave length is injected into a Stuart vortex in which the deformation of an initially planar liquid surface leads to the formation of a ligament. Droplets are formed by breakup of this transversal detached -or longitudinal attached -ligament and a theoretical mean diameter can be determined. Maximum entropy principles are then applied to deduce the size distribution.

C-FOG is a comprehensive bi-national project dealing with the formation, persistence, and dissipation (life cycle) of fog in coastal areas (coastal fog) controlled by land, marine, and atmospheric processes. Given its inherent complexity, coastal-fog literature has mainly focused on case studies, and there is a continuing need for research that integrates across processes (e.g., air–sea–land interactions, environmental flow, aerosol transport, and chemistry), dynamics (two-phase flow and turbulence), microphysics (nucleation, droplet characterization), and thermodynamics (heat transfer and phase changes) through field observations and modeling. Central to C-FOG was a field campaign in eastern Canada from 1 September to 8 October 2018, covering four land sites in Newfoundland and Nova Scotia and an adjacent coastal strip transected by the Research Vessel Hugh R. Sharp. An array of in situ, path-integrating, and remote sensing instruments gathered data across a swath of space–time sca...

Modern optical diagnostics for quantitative characterization of polydisperse sprays and other aerosols which contain a wide range of droplet size encounter difficulties in the dense regions due to the multiple scattering of laser radiation with the surrounding droplets. The accuracy and efficiency of optical measurements can only be improved if the radiative transfer within such polydisperse turbid media is understood. A novel Monte Carlo code has been developed for modeling of optical radiation propagation in inhomogeneous polydisperse scattering media with typical drop size ranging from 2 µm to 200 µm in diameter. We show how strong variations of both particle size distribution and particle concentration within a 3D scattering medium can be taken into account via the Monte Carlo approach. A new approximation which reduces ~20 times the computational memory space required to determine the phase function is described. The approximation is verified by considering four log-normal drop size distributions. It is found valid for particle sizes in the range of 10-200 µm with increasing errors, due to additional photons scattered at large angles, as the number of particles below than 10 µm increases. The technique is applied to the simulation of typical planar Mie imaging of a hollow cone spray. Simulated and experimental images are compared and shown to agree well. The code has application in developing and testing new optical diagnostics for complex scattering media such as dense sprays.

The focus of this paper is on the numerical solution of the stochastic collection equation–stochastic breakup equation (SCE–SBE) describing the evolution of raindrop spectra in warm rain. The drop size distribution (DSD) is discretized using the fixed-pivot scheme proposed by Kumar and Ramkrishna, and new discrete equations for solving collision breakup are presented. The model is evaluated using established coalescence and breakup parameterizations (kernels) available in the literature, and in that regard this paper provides a substantial review of the relevant science. The challenges posed by the need to achieve stable and accurate numerical solutions of the SCE–SBE are examined in detail. In particular, this paper focuses on the impact of varying the shape of the initial DSD on the equilibrium solution of the SCE–SBE for a wide range of rain rates and breakup kernels. The results show that, although there is no dependence of the equilibrium DSD on initial conditions for the same ...

Agitating two immiscible liquids or a solid-liquid suspension is an operation frequently performed in the chemical and metallurgical industries, for example, in suspension/emulsion polymerization, heterogeneous/phasetransfer catalytic chemical reactions, and hydrometallurgical solvent extraction. For emulsification, suspension polymerization, solid particle dispersion, and crystallization, it is essential to be able to predict the mean drop/particle size and the drop/particle size distribution. A simple model was proposed for predicting the time evolution of drop size distribution during drop breaking, and was successfully tested on data published by Ruiz and

In this paper, we study the primary atomization characteristics of liquid jet injected into a gaseous crossow through direct numerical simulations (DNS) and large eddy simulations (LES). The DNS use a coupled level set volume of uid (CLSVOF) sharp interface capturing method resolving all relevant scales to predict the drop size distribution (DSD) for drops larger than the grid spacing. The LES use a volume of uid (VOF) diused interface method modelling the sub grid droplets. The purpose of this paper is to provide a comparison of the results of drop data between DNS and LES. The simulations are performed for a liquid jet injection with liquid-gas momentum ux ratio of 6.6, liquid jet Reynolds number of 14,000

Ahstrac-A population balance model has been developed accounting for coalescence and redispersion of drops in an agitated liquid-liquid dispersion. It is assumed that drop coalescence is followed by immediate redispersion into two drops whose sizes are distributed according to a uniform distribution in the ratio of the daughter drop-volume to the parent drop-volume. If it is assumed that the coalescence frequency is independent of drop-size, the resulting non-linear integral equation admits an exponential solution for the equilibrium dropvolume distribution in a batch vessel. On comparing experimental data obtained from several sources with the prediction of this model, it is found that for M-blade turbine agitated systems, the agreement is very good; in fact, the sign test ranks the model as better fitting than empirical expressions for dropsixes proposed by other workers. For circulation stirring systems, e.g. those having Waldhof agitator, the model predictions are substantially improved by assuming that the coalescence frequency is proportional to the diameters of the interacting drops.

In recent studies it is shown that in variable rain the spatial distribution of drops is not Poissonian. However, these past studies were limited to 1-min drop counts, which likely correspond to spatial scales of a few hundred to several hundreds of meters. In this work results based on 1-s drop counts using a video disdrometer are reported. It is shown that the clustering of raindrops previously found during intervals of 1 min also occurs during 1 s as well in convective rain. These latter temporal scales likely correspond to spatial features having dimensions from only a few to tens of meters. Combined with the authors' earlier results, these findings suggest that clustering of raindrops and meteorological variability span the range of scales from at least as small as a few meters to several hundreds of meters in convective precipitating systems. Consequently, non-Poissonian clustering reported in previous work (analyzing data accumulated over hours using 1-min drop counts) cannot be dismissed as artifacts in the data or errors in the processing. These studies appear to reflect accurately the true probabilistic character of rainfall. Moreover, it is shown that the clustering is more prevalent and occurs over longer coherence times for larger than for smaller drops. An argument is given suggesting that the clustering of larger drops is likely associated with the larger scales of convection, whereas the clustering of smaller drops is likely more strongly influenced by smaller-scale turbulence. Furthermore, in convective rain it appears that the coherence times of drop size distributions will often be governed by the smaller drops. Using current technology, this will make it very difficult, at times, to adequately sample the larger drops in variable rain without mixing observations from more than one drop size distribution at the smaller sizes. Nevertheless, care must be taken since oversampling destroys information just as effectively as undersampling misses it.

It was recently demonstrated that, infiltration into mountain-tilled soils with highly stable microaggregates, increases with increasing slope gradient. In this work we investigate the processes that underpin this phenomenon by means of field experiments and modelling. The study area is located in northern Laos. Rainfall simulations were conducted in two 1-m 2 plots using a portable field simulator. The drop size distribution and kinetic energy were similar to that occurring on the occasion of tropical downpours. Soils exhibited a clay loam texture and very similar organic matter contents across experimental plots, but differed greatly in slope gradient (30% and 75%). Runoff water samples were collected at intervals ranging from 1 to 3 min, depending on the runoff intensity. Plots microtopography was measured before and after rainfall simulations using an automatic surface roughness meter on a 1-cm grid. High-resolution bulk density images were obtained from soil slices using a standard X-ray generator. Final infiltration rates of 6 and 21 mm h -1 ; soil detachment of 667 and 310 g m -2 ; surface lowering due to soil loss of 0.82 and 0.38 mm; surface lowering due to compaction of 1.21 and 0.90 mm; percentage area with sieving crust of 36% and 90%; percentage area with erosion crust of 63% and 0%; were obtained for the 30% and 75% slopes, respectively. Three main conclusions can be drawn from this work: (1) high intensity rainfall can rapidly transform soil surface features of steep bare soil; (2) on steeper slopes, the micro-relief tends to form micro-terraces much more pervious and less erodible than the ripple-like roughness that formed on gentler slopes; and (3) there was a more pronounced lowering of the soil surface due to compaction and denser microlayers on gentler slopes. The latter conclusion confirms the hypothesis that higher effective rainfall intensity is responsible for the formation of less permeable erosion crusts under 30% slope gradients while more permeable structural crusts develop under 75% slope gradients. The runoff results were modelled with the Green and Ampt model which accounts for time evolution of soil hydraulic conductivity. This modelling shows that soil is undoubtedly non homogeneous, evolves with time and that infiltration kinetics is slower and soil permeability greater for the 75% slope.

The drop size distribution of sprinkler spray is of practical importance for two reasons. The first one is because the small droplets are subject to wind drift, distorting the application pattern. Second, large droplets possess greater kinetic energy which is transferred to the soil surface causing particle dislodgment and pudding that may result in surface crusting and runoff. We present in this paper a technique based on image processing for measure drop size distribution from agricultural sprinklers in automatic mode. This technique has the advantage of being a direct measurement method that allows to know the characteristics of agricultural sprinklers, which allows to study the effects of pressure and nozzle size on the distributions. The method was obtained using properties of the Fourier for correlation analysis in frequency domain. Results allow both farmers to change on existing irrigation systems to cope with field problems caused by low intake rates and runoff and development work to improve the uniformity of distribution of sprays from agricultural sprinklers.

The use of polarization diversity to measure properties of hydrometeors is not new and was first mentioned by Seliga and Bringi from an engineering perspective in 1976 and by Hendry et al (again in 1976) from a measurement perspective shortly thereafter. In the forty years that have passed since these accomplishments there have been several key data-sets that have guided the development of retrieval science and the use of polarimetry in understanding the nature of precipitation. One such data set has been collected using the CBand POLarimetric radar (Keenan et al, 1998), which collected 15 years of observations of break/buildup and monsoon season phenomena when it was sited 23km from Darwin, Australia. This presentation will report on the progress of a collaboration aimed at producing a quality controlled set of polarimetric measurements and microphysical retrievals for this 15-year data set. Techniques such as calibration offset, specific differential phase and attenuation retrieva...

Spray systems contain a large amount of small droplets, which are responsible for multiple light scattering phenomena. When detected, photons that have been scattered multiple times blur the shape of liquid bodies present in the spray as well as the overall spray structure. This blurring causes issues with spray visualization and furthermore; multiple light scattering introduces large errors in quantitative measurements from image ratio techniques (e.g. LIF/Mie droplet sizing, two-color LIF thermometry, etc). The simulation of light propagation and scattering through spray systems is then necessary to understand the effects introduced by multiple scattering and to efficiently tackle the aforementioned issues. A reliable and predictive simulation tool allows for: * Predicting the amount of multiple light scattering. * Estimating the errors introduced by multiple scattering in quantitative spray measurements. * Testing strategies for suppressing the intensity contribution from multiple scattering. * Optimizing and assisting the development of different spray imaging techniques. In this article we present an open-access software called "Multi-Scattering". It is a versatile online Monte Carlo simulation tool where photons are tracked through a cloud of spherical droplets. During the simulations process, each scattering event is described by the Lorenz-Mie theory. The numerical simulation is accelerated with the use of the parallel processing capabilities of modern computer graphics cards, known as general-purpose computing on graphics processing units, making those Monte Carlo simulations potentially in less than a minute. The simulations exemplified here demonstrate the use of Multi-Scattering for spray imaging application. This open access software is freely accessible to any researcher who would like to use it for their own spray application.

Mass transfer analysis of the extraction of Nickel(II) by emulsion liquid membrane Mousumi Chakraborty*", Chiranj ib Bhattac haryah & Siddhartha Dattab " De partme nt of C he mi cal Eng ineerin g, S V Reg io nal Co llege of Eng in ee ri ng &Tec hn o logy, Sura t 395 007 . Ind ia hDe partm e nt o f C he mica l Eng in ee ring, Jada vpu r Uni ve rsity. Ko lk a ta 700 032 , India

The Ethiopian Highlands are subjected to important land degradation. Though spatial variability of rain depth is important, even at the catchment scale, this variability has never been studied. In addition, little is known on rain erosivity for this part of the world. The objectives of this study are (a) to assess the spatial variation of rain in a 80 km 2 mountain area (2100-2800 m a.s.l.) in the Northern Tigray region, and how this variation is influenced by topography, geographical position and lithology, (b) to analyse the temporal variations and (c) to quantify rain erosivity and the different factors determining it, such as rain intensity, drop size and kinetic energy. Spatial variation of rain was measured over a 6-y period by installing 16 rain gauges in the study area. Topographical factors, especially general orientation of the valley and slope gradient over longer distances, determine the spatial distribution of annual rain, which is in the order of 700 mm y K1. Precipitation is highest nearby cliffs and other eminent slopes, perpendicular to the main valleys which are preferred flow paths for the air masses. Rain intensity is smaller than expected: 88% falls with an intensity !30 mm h K1. High intensities have a short duration; maximum recorded rain depth over 1 h (32 mm) is only 2 mm less than that over 24 h. Using the blotting paper method 65,100 rain drops were sampled. For all observed rain intensities, the median volume drop diameters (D 50) are significantly larger than those reported for other regions of the world. A relation between rain intensity (I) and volume specific kinetic energy (Ek vol) was developed for the Ethiopian Highlands: Ek vol Z 36:65ð1 K ð0:6=IÞÞ ðR 2 Z 0:99; n Z 18Þ; ðEk vol in J m K2 mm K1 ; I in mm h K1 Þ: Due to the occurrence of large drop sizes, probably linked to the prevailing semi-arid to subhumid mountain climate, this relation yields, within the intensity range [0.6-84 mm h K1 ], larger values for Ek vol than elsewhere in the world.

In this work we use values of effective radius of cloud drop size distribution and modal radius of liquid water content generated with a parcel model with detailed treatment of liquid phase microphysical process to evaluate the warm rain formation suppression over the Amazon due to the presence of aerosols generated by forest burning. Four cases based on observations are simulated: a clean marine environment as the one observed close to Fortaleza; a clean environment as the ones observed over the apparently unpolluted Amazon forest; a environment observed during the intense burning season in the polluted part of the Amazon; and the same polluted environment observed during the transition season from dry to wet. It is shown that the model reproduces quantitatively some of the observed features of clouds in different environments. The model indicated that in very polluted environment the warm rain formation process can be completely suppressed. Nevertheless, in certain situations the ...

The quality of the propellant injection process in a rocket engine is key to the performance and life-span
of a rocket engine.
The present work focuses on the development of an ethanol-liquid oxygen injector from its conceptual
design to its cold-flow testing.
After introducing the principles at the foundation of injection systems for rocket engines and discussing
the most common families of injection systems, this work aims to explain the design choices made for
the selected type of injector. The thesis will then present experimental data gathered by cold-flow testing
of said injector and suggest possible improvements for future developments. The development of this
injection system was performed in the context of the Nixus Project of the Rocketry team at the Scientific
Workgroup for Rocketry and Spaceflight (Wissenschaftliche Arbeitsgemeinschaft für Raketentechnik
und Raumfahrt, WARR), a student research group at the Technical University of Munich.

The phase inversion that undergoes an emulsion while being sheared is a sudden phenomenon that is still puzzling. In this Letter, we report an experimental investigation on propagative coalescence by using a microfluidic device where a calibrated two-dimensional emulsion is created and destabilized. The velocity of propagation and the probability of the coalescence are reported as a function of the size and the spatial distribution of the drops, respectively. We then discuss the efficiency of this novel scenario of phase inversion and suggest that inversion can be favored by the existence of a drop size distribution.

This paper describes the Tropical Rainfall Measuring Mission (TRMM) standard algorithm that estimates the vertical profiles of attenuation-corrected radar reflectivity factor and rainfall rate. In particular, this paper focuses on the critical steps in the algorithm. These steps are attenuation correction, selection of the default drop size distribution model including vertical variations, and correction for the nonuniform beam-filling effect. The attenuation correction is based on a hybrid of the Hitschfeld-Bordan method and a surface reference method. A new algorithm to obtain an optimum weighting function is described. The nonuniform beam-filling problem is analyzed as a two-dimensional problem. The default drop size distribution model is selected according to the criterion that the attenuation estimates derived from the model and the independent estimates from the surface reference with the nonuniform beam-filling correction are consistent for rain over ocean. It is found that the drop size distribution models that are consistent for convective rain over ocean are not consistent over land, indicating a change in the size distributions associated with convective rain over land and ocean, respectively.

In this paper, precipitation rate retrieval algorithms for the Global Precipitation Measurement mission's Dualfrequency Precipitation Radar (DPR) are developed. The DPR consists of a Ku-band radar (KuPR; 13.6 GHz) and a Ka-band radar (KaPR; 35.5 GHz). For the KuPR, an algorithm similar to the Tropical Rainfall Measuring Mission's Precipitation Radar algorithm is developed, with the relation between precipitation rate R and massweighted mean diameter D m (R−D m relation) replacing the relation between the specific attenuation k and effective radar reflectivity factor Z e. The R−D m relation can also be applied to the KaPR and dual-frequency algorithms. In both the single-frequency and dual-frequency algorithms, the forward retrieval method is applied with an as

In this paper, precipitation rate retrieval algorithms for the Global Precipitation Measurement mission's Dualfrequency Precipitation Radar (DPR) are developed. The DPR consists of a Ku-band radar (KuPR; 13.6 GHz) and a Ka-band radar (KaPR; 35.5 GHz). For the KuPR, an algorithm similar to the Tropical Rainfall Measuring Mission's Precipitation Radar algorithm is developed, with the relation between precipitation rate R and massweighted mean diameter D m (R−D m relation) replacing the relation between the specific attenuation k and effective radar reflectivity factor Z e. The R−D m relation can also be applied to the KaPR and dual-frequency algorithms. In both the single-frequency and dual-frequency algorithms, the forward retrieval method is applied with an as

This paper describes the basic structure and flow of the rain profiling algorithm for the TRMM Precipitation Radar, and discusses the major assumptions and sources of error in the algorithm. In particular, it describes how the uncertainties in individual parameters affect the attenuation correction and rain estimates. Major parameters involved are the drop size distribution, the phase state of precipitating particles, their density and shape, inhomogeneity of precipitation distribution within the footprint, attenuation due to cloud liquid water and water vapor, freezing height, uncertainty of the surface scattering cross section, and fluctuation of the radar echo signal. Among these parameters that affect the rain estimates, the effect of inhomogeneity of rain distribution is summarized in detail. The paper also describes how these parameters are taken into account in different versions of the standard algorithm 2A25.

In developing the upcoming Global Precipitation Measurement (GPM) mission, a dual-frequency Ku-Ka-band radar system will be used to measure rainfall in such a fashion that the reflectivity ratio intrinsic to the measurement will be sensitive to underlying variations in the drop size distribution (DSD) of rain. This will enable improved techniques for retrieving rain rates, which are dependent upon several key properties of the DSD. This study examines this problem by considering a three-parameter set defined by liquid water content (W), DSD effective radius (r e), and DSD effective variance (e). Using radiative transfer simulations, this parameter set is shown to be related to a radar reflectivity factor and specific attenuation in such a fashion that details of the DSDs are immaterial under constant W, and thus effectively represent important variations in DSD that affect rain rate but with a minimal number of parameters. The analysis also examines the effectiveness of including some measure of mean Doppler fall velocity of raindrops (), given that the fundamental properties of a given precipitation situation are uniquely defined by a combination of a drop mass spectrum and drop vertical velocity spectrum. The results of this study have bearing on how future dual-frequency precipitation retrieval algorithms could be formulated to optimize the sensitivity to underlying DSD variability, a problem that has greatly upheld past progress in radar rain retrieval.

The Tropical Rainfall Measuring Mission (TRMM) version‐6 rainfall products show the reduced bias between Precipitation Radar (PR) and TRMM Microwave Imager (TMI) rainfall estimates during the 1997/1998 El Niño event noted in version 5, but need to be verified. We investigate consistency between TMI‐observed brightness temperatures (TBs) at 10 and 19 GHz channels and those simulated from the PR and TMI rainfall estimates using a radiative transfer model. Simulated TBs from PR V6 exhibits better agreement with observed ones than those from PR V5, implying the algorithm improvements. However, discrepancies at 19 GHz suggest that uncertainty in the assumed drop size distribution still remains in PR V6. Simulated TBs from TMI V6 also exhibits better agreement with observed ones than those from TMI V5. However, the simulated 10‐GHz TBs from TMI V6 exhibits more scatter against TMI‐observed ones than those from PR V6 do.

Here, we investigate experimentally and theoretically the factors that determine the size of the emulsion droplets produced by membrane emulsification in "batch regime" (without applied crossflow). Hydrophilic glass membranes of pore diameters between 1 and 10 µm have been used to obtain oil-in-water emulsions. The working surfactant concentrations are high enough to prevent drop coalescence. Under such conditions, the size of the formed drops does not depend on the surfactant type and concentration, on the interfacial tension, or on the increase of viscosity of the inner (oil) phase. The drops are monodisperse when the working transmembrane pressure is slightly above the critical pressure for drop breakup. At higher pressures, the size distribution becomes bimodal: a superposition of a "normal" peak of monodisperse drops and an "anomalous" peak of polydisperse drops is observed. The theoretical model assumes that, at the moment of breakup, the hydrodynamic ejection force acting on the drop is equal to the critical capillary force that corresponds to the stability-instability transition in the drop shape. The derived equations are applied to predict the mean size of the obtained drops in regimes of constant flow rate and constant transmembrane pressure. Agreement between theory and experiment is established for the latter regime, which corresponds to our experimental conditions. The transition from unimodal to bimodal drop size distribution upon increase of the transmembrane pressure can be interpreted in terms of the transition from "dripping" to "jetting" mechanisms of drop detachment.

We investigate the process of membrane emulsification in the presence of the nonionic surfactant Tween 20, and the milk proteins Na-caseinate and beta-lactoglobulin (BLG). Our goal is to examine the factors which control the drop-size distribution in the formed emulsions. The drops are produced at the outer surface of a cylindrical microporous glass membrane, so that the process of their formation and detachment can be directly observed by an optical microscope. In the case of 2 wt.% aqueous solution of Tween 20 we obtain a relatively fine and monodisperse oil-in-water emulsion with a mean drop diameter about three times that of the pore. The microscopic observations show that in this case the oil drops intensively pop out of separate pores. In contrast, for the lower concentrations of Tween 20, as well as for the investigated solutions of Na-caseinate and BLG, we observe that the membrane is covered by a layer of growing attached emulsion drops, which are polydisperse, with a relatively large mean drop size. This fact can be explained with a greater dynamic contact angle solid-water-oil. In such a case, after a drop protrudes from an opening, it does not immediately detach, but instead, the contact area drop/membrane expands over several pore openings. The smaller drop size in the emulsions stabilized by BLG, in comparison with those stabilized by Na-caseinate, is related to the circumstance that BLG adsorbs faster at the oil-water interface than Na-caseinate. In the investigated emulsions we did not observe any pronounced coalescence of oil drops. Hence, the generation of larger and polydisperse oil drops in some of the studied solutions is attributed mostly to the effect of expansion of the drop contact line and formation of hydrophobized domains on the membrane surface. Therefore, any factor, which leads to decrease of the dynamic three-phase contact angle, and thus prevents the contact-line expansion, facilitates the production of fine and monodisperse emulsions.

The Tropical Rainfall Measuring Mission TRMM satellite which carries the world rst spaceborne pre cipitation radar has been collecting precipitation data awlessly for more than ve years Simultaneous meas urements of rain with the Precipitation Radar PR the TRMM Microwave Imager TMI and the Visible and Infrared Scanner VIRS onboard the satellite enable us to intercompare the data and products from three di er ent kinds of sensors and to reveal problems associated with the rain retrieval algorithms for these sensors The data brought by TRMM and comparisons among them have deepened our knowledge of global rain distribution and characteristics Based on the success of the TRMM mission a new satellite mission called the Global Precipitation Measurement mission GPM was proposed Its ma jor objective is to measure precipitation globally and frequently so that the data can be used not only for scienti c research but also for operational applications such as weather forecasts and water resourc...

This paper concerns precipitation retrieval algo rithms for a spaceborne or airborne dual frequency radar in particular for the Dual frequency Precipitation Radar DPR onboard the Global Precipitation Meas urement GPM core satellite From the dual frequency radar data we can in principle estimate two parameters of the drop size distribution DSD at each range bin In practice however estimates from such algorithms are not reliable in many cases unless we are given other information such as the attenuation to the rst gate or to the farthest range gate that mitigates the e ect of uncertainties in radar calibration and attenuation due to unobservable gases and particles i e water vapor and cloud water This paper rst reviews the general principles of dual frequency algorithm and then examines some pos sible alternative algorithms that do not require addi tional information but can estimate reliable rain pa rameters by abandoning the possibility of estimating two independent DSD parameters a...

Tech. Reg. (2) UNCLASSIFIED CONTENTS. Introduction. List of' Svmbols. Section I. The inf'luence of droplet size on combustion. Section II. The atomigation off liquids; a review. Secton II. The weasurei.ient of' spray dro-olet size; a revicw. Summary Bibliography Appendix A. The Use of' the Rosin Rammler distribution law in the representation of' propellant sprays. Appendix B. Calculation of' the rate of' combustion of' monopropEllant droplets.,

Polarimetric radar is now widely recognised as a tool for measuring the variability in rainfall drop-size distribution and improving estimates of the resultant rain rate (e.g. Ryzhkov et al., 2005; Bringi & Chandrasekar, 2001). However, the accuracy varies as a function of rain rate, with some polarimetric estimates exhibiting high error at low rainrates. Consequently, various methods have been developed to optimise such estimates, typically using decisiontree logic to determine which algorithm to use in specific conditions (e.g. Ryzhkov et al., 2005) or highly complex algorithms based on dropsize distribution characteristics (e.g. Bringi et al., 2004; Brandes et al., 2004).

The effect of ship motion on shipborne polarimetric radar measurements is considered at C band. Calculations are carried out by (i) varying the “effective” mean canting angle and (ii) separately examining the elevation dependence. Scattering from a single oblate hydrometeor is considered at first. Equations are derived (i) to convert the measured differential reflectivity for nonzero mean canting angles to those for zero mean canting angle and (ii) to do the corresponding corrections for nonzero elevation angles. Scattering calculations are also performed using the T-matrix method with measured drop size distributions as input. Dependence on mean volume diameter is examined as well as variations of the four main polarimetric parameters. The results show that as long as the ship movement is limited to a roll of less than about 10°–15°, the effects are tolerable. Furthermore, the results from the scattering simulations have been used to provide equations for correction factors that ca...

Raindrop images obtained on research flights of the NCAR Electra aircraft in the Tropical Oceans Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA COARE) are analyzed. The drop size distributions, based on the images obtained in 6-s samples (about 750 m of flight track), are used to calculate both radar reflectivity Z and rain rate R. Airborne radar data from the NOAA P-3 aircraft flying in coordination with the Electra are used to categorize the particle-image data according to whether the drop images were obtained in regions of convective or stratiform precipitation. Within stratiform precipitation, the same rain rate could be produced by a drop spectrum dominated by numerous small drops (lower reflectivity) or by a few large drops (higher reflectivity). The reflectivity values varied by as much as 9 dB for a given rain rate. Reflectivity data from the airborne radar and flight-level data reveal that the stratiform regions often contain fallstreaks of about 0.1-2 km in horizontal dimension. The fallstreaks are associated with large-drop spectra and local maxima in reflectivity up to approximately 40 dBZ and in rain rates up to 25 mm h Ϫ1. The fallstreaks extend downward from the melting band and bend with the low-level wind shear, but do not usually reach the surface. Thus, although relatively more uniform than convective regions, stratiform regions can be variable in reflectivity and rain rate at fine spatial scales in both the horizontal and vertical directions. Stratiform regions are therefore best characterized by their ensemble properties rather than the values of individual high-resolution measurements. The variability of stratiform drop size spectra arises primarily from the occurrence of fallstreaks and the discontinuous nature of regions favoring aggregation of snow crystals, and it implies that Z-R distributions associated with convective and stratiform precipitation are not statistically distinct. Thus, separate Z-R relations for convective and stratiform precipitation are not justified, and techniques to distinguish between convective and stratiform precipitation based solely on the characteristics of drop size distributions are not likely to be accurate. The variability of the drop size spectra in tropical precipitation makes an exponential fit to the Z-R relation sensitive to the spatial scale over which Z and R are determined. This sensitivity can be avoided by using a probability-matched Z-R relation. The probability-matched Z-R relation for all the raindrop image data from the Electra collected between altitudes of 2.7 and 3.3 km in TOGA COARE is similar to the Z-R relation obtained at the sea surface in the Global Atmospheric Research Program Atlantic Tropical Experiment.

Raindrop images obtained on research flights of the NCAR Electra aircraft in the Tropical Oceans Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA COARE) are analyzed. The drop size distributions, based on the images obtained in 6-s samples (about 750 m of flight track), are used to calculate both radar reflectivity Z and rain rate R. Airborne radar data from the NOAA P-3 aircraft flying in coordination with the Electra are used to categorize the particle-image data according to whether the drop images were obtained in regions of convective or stratiform precipitation. Within stratiform precipitation, the same rain rate could be produced by a drop spectrum dominated by numerous small drops (lower reflectivity) or by a few large drops (higher reflectivity). The reflectivity values varied by as much as 9 dB for a given rain rate. Reflectivity data from the airborne radar and flight-level data reveal that the stratiform regions often contain fallstreaks of about 0.1-2 km in horizontal dimension. The fallstreaks are associated with large-drop spectra and local maxima in reflectivity up to approximately 40 dBZ and in rain rates up to 25 mm h Ϫ1. The fallstreaks extend downward from the melting band and bend with the low-level wind shear, but do not usually reach the surface. Thus, although relatively more uniform than convective regions, stratiform regions can be variable in reflectivity and rain rate at fine spatial scales in both the horizontal and vertical directions. Stratiform regions are therefore best characterized by their ensemble properties rather than the values of individual high-resolution measurements. The variability of stratiform drop size spectra arises primarily from the occurrence of fallstreaks and the discontinuous nature of regions favoring aggregation of snow crystals, and it implies that Z-R distributions associated with convective and stratiform precipitation are not statistically distinct. Thus, separate Z-R relations for convective and stratiform precipitation are not justified, and techniques to distinguish between convective and stratiform precipitation based solely on the characteristics of drop size distributions are not likely to be accurate. The variability of the drop size spectra in tropical precipitation makes an exponential fit to the Z-R relation sensitive to the spatial scale over which Z and R are determined. This sensitivity can be avoided by using a probability-matched Z-R relation. The probability-matched Z-R relation for all the raindrop image data from the Electra collected between altitudes of 2.7 and 3.3 km in TOGA COARE is similar to the Z-R relation obtained at the sea surface in the Global Atmospheric Research Program Atlantic Tropical Experiment.

Self-propelled jumping drops are continuously removed from a condensing superhydrophobic surface to enable a micrometric steady-state drop size. Here, we report that subcooled condensate on a chilled superhydrophobic surface are able to repeatedly jump off the surface before heterogeneous ice nucleation occurs. Frost still forms on the superhydrophobic surface due to ice nucleation at neighboring edge defects, which eventually spreads over the entire surface via an interdrop frost wave. The growth of this interdrop frost front is shown to be up to 3 times slower on the

C-FOG is a comprehensive bi-national project dealing with the formation, persistence, and dissipation (life cycle) of fog in coastal areas (coastal fog) controlled by land, marine, and atmospheric processes. Given its inherent complexity, coastal-fog literature has mainly focused on case studies, and there is a continuing need for research that integrates across processes (e.g., air–sea–land interactions, environmental flow, aerosol transport, and chemistry), dynamics (two-phase flow and turbulence), microphysics (nucleation, droplet characterization), and thermodynamics (heat transfer and phase changes) through field observations and modeling. Central to C-FOG was a field campaign in eastern Canada from 1 September to 8 October 2018, covering four land sites in Newfoundland and Nova Scotia and an adjacent coastal strip transected by the Research Vessel Hugh R. Sharp. An array of in situ, path-integrating, and remote sensing instruments gathered data across a swath of space–time sca...

In this paper we propose the method of transition from the complex full polarimetric radar signals to univariate uniformly distributed marginals that can be used for more precise copula analysis of statistical dependence between the complex samples of signals received at orthogonally polarized sounding waveforms. The method is applied to meteorological radar signal processing.

The paper summarizes state of art in the description of the droplet breakup, coalescence, and competition between them in flowing immiscible polymer blends. It has been shown that, in contrast to the conditions for the start of droplet breakup, knowledge of the dependence of the droplet breakup frequency on system parameters is quite limited. It has been demonstrated that the switch between expressions for the matrix drainage between spherical and highly deformed droplets leads to a reasonable description of the flow induced coalescence. This method makes it possible to include the effect of the matrix elasticity into the calculation of the probability of coalescence. The analysis of the competition between the droplet breakup and coalescence leads to the conclusion that knowledge of the mechanism and frequency of the droplet breakup is essential for at least qualitative prediction of the droplet size dependence on system parameters. The article addresses main features of flowing polymer blends, not adequately reflected in available theories.

The research presents the inter-comparison of atmospheric variables measured by 9 automatic weather stations. This set of data was compared with the measurements of other weather stations in order to standardize the values that must be adjusted when taken to different areas. The data of a set of a total of 9 GMX500, which measures conventional meteorological variables, and 10 WS100 sensors, which measures precipitation parameters. The automatic stations were set up at the Huancayo Observatory (Geophysical Institute of Peru) for a period of 5 months. The data set of GMX500 were evaluated comparing with the average of the 9 sensors and the WS100 was compared with an optical disdrometer Parsivel2. The temperature, pressure, relative humidity, wind speed, rainfall rate, and drop size distribution were evaluated. A pair of GMX500 sensors presented high data dispersion; it was found found that the errors came from a bad configuration; once this problem was solved, good agreement was archi...

Rainfall prediction is crucial for various aspects of human life, environmental sustainability, and agriculture. Understanding rainfall intensity and its dependence on factors such as drop size distribution (DSD) is essential. This study investigates the relationship between drop size distribution and rainfall rate at Shillong station, Meghalaya, India, utilizing RD-80 disdrometer data for the year 2005. DSD plays a pivotal role in quantitative precipitation estimation, impacting rainfall properties like water content, intensity, and kinetic energy. Moreover, it is integral to satellite communication, aiding in the prediction of wave attenuation. We analyze the data to ascertain the correlation between rainfall rate and DSD, with an assumption of an exponential form for DSD. The analysis categorizes the daytime into four segments: Morning (6:00 AM-12:00 PM), Afternoon (12:00 PM-6:00 PM), Evening (6:00 PM-12:00 AM), and Night (12:00 AM-6:00 AM) to observe rain's diurnal variations. Notably, variations in correlation coefficients suggest differing rainfall patterns and intensity levels throughout the day and across months. These insights contribute to a deeper understanding of rainfall dynamics in the region, which is critical for effective water resource management and disaster preparedness.

Cold model studies have been carried out to characterize the drop-size distribution in liquid-liquid emulsions formed by bottom gas injection. The emulsion was formed by injecting compressed air through the bottom of a tank containing water and kerosene. A polycondensation technique was used to take samples of the dispersed water drops inside the plume, using a specially designed pneumatic trap. Thedrop samples were photographed and size analysis was done using an image analysis software. The drop-size distribution closely obeyed the Gaudin-Schuhmann equation. Correlations have been developed between the drop size distribution characteristics (the Sauter diameter and standard deviation) and appropriate dimensionless numberscharacterizing the operating conditions. Theexperimental conditions covered the industrial range of these dimensionless numbers. Typical drop diameters were in the range of 0.5 to 8mm.The values of the Sauter diameter were between 4 and 6mm and those for the standard deviation were between 0.8 and I .6 mm.

The maximum entropy principle (MEP), which has been popular in the modeling of droplet size and velocity distribution in sprays, is, strictly speaking, only applicable for isolated systems in thermodynamic equilibrium; whereas the spray formation processes are irreversible and non-isolated with interaction between the atomizing liquid and its surrounding gas medium. In this study, a new model for the droplet size distribution has been developed based on the thermodynamically consistent concept – the maximization of entropy generation during the liquid atomization process. The model prediction compares favorably with the experimentally measured size distribution for droplets, near the liquid bulk breakup region, produced by an air-blast annular nozzle, a planar nozzle and a practical gas turbine nozzle. Therefore, the present model can be used to predict the initial droplet size distribution in sprays. Corresponding author Introduction Since the later 1980s, Maximum Entropy Principle...

The flow of oil-in-water emulsions through quartz micro-capillary tubes was analyzed experimentally. The capillaries were used as models of connecting pore-throats between adjacent pore body pairs in high-permeability media. Pressure drop between the inlet and outlet ends of the capillary was recorded as a function of time, for several values of the volumetric flow rate. Several distinct emulsions were prepared using synthetic oils in deionized water, stabilized by a surfactant (Triton X-100). Two oils of different viscosity values were used to prepare the emulsions, while two distinct drop size distributions were obtained by varying the mixing procedure. The average oil drop size varied from smaller to larger than the neck radius. The results are presented in terms of the extra-pressure drop due to the presence of the dispersed phase, i.e. the difference between the measured pressure drop and the one necessary to drive the continuous phase alone at the same flow rate. For emulsions with drops smaller than the capillary throat diameter, the extra-pressure drop does not vary with capillary number and it is a function of the viscosity ratio, dispersed phase concentration and drop size distribution. For emulsions with drops larger than the constriction, the large oil drops may partially block the capillary, leading to a high extra pressure difference at low capillary numbers. Changes in the local fluid mobility by means of pore-throat blockage may help to explain the additional oil recovery observed in laboratory experiments and the sparse data on field trials.

Rainfall simulators have often been used to mimic natural rainfall for studies of various land-surface and water interaction processes. The characteristics of the simulated rainfall are the main indicators used to judge the performance of the rainfall simulators. The aim of this study is to investigate the potential of piezoelectric transducers for measuring and evaluating a dripper-type simulated rainfall drop-size distribution (DSD) and kinetic energy (KE). The directly measured KE was significantly correlated with the estimated KE using the drop-size distribution and empirical rain drop fall velocity relationships. This result emphasizes the potential use of the piezoelectric sensor to directly measure and evaluate rainfall kinetic energy. Also, the relationship between rainfall intensity and KE showed good patterns of agreement between simulated rainfall and natural rainfall.

Multiyear measurements from a Joss–Waldvogel disdrometer (5 years) and X-band dual-polarization radar (2 years) made at Gadanki (13.5◦ N, 79.18◦ E), a low-latitude station, are used to (i) retrieve appropriate raindrop size distribution (DSD) relations for monsoonal rain, (ii) understand their dependency on temperature, the raindrop size shape model and season and (iii) assess polarimetric radar DSD retrievals by various popular techniques (the exponential (Exp), constrained Gamma (CG), normalized Gamma (N-Gamma) and β methods). The coefficients obtained for different DSD relations for monsoonal rain are found to be different from those of existing relations elsewhere. The seasonal variation in DSD is quite large and significant, and as a result, the coefficients also vary considerably between the seasons. The slope of the drop size–shape relation, assumed to be constant in several studies, varies considerably between the seasons, with warmer seasons showing a smaller slope value than the cold season. It is found that the constant (0.062) used in linear drop shape models is valid only for the cold season. The derived coefficients for the CG method for different seasons coupled with those available in the literature reveal that the warm seasons/regions typically have larger curvature and slope values than in the cold seasons/regions. The coefficients of the mass-weighted mean diameter (Dm) and differential reflectivity (ZDR) exhibit a strong dependency on the drop shape model, while those for the derivation intercept parameter exhibit a strong seasonal dependency. Using the retrieved relations and X-band polarimetric radar at Gadanki, four popular DSD methods are evaluated against disdrometer measurements collected over 12 events. All the methods estimated Dm reasonably well with the small root mean square error but failed to estimate the intercept parameter accurately. Only the N-gamma method estimated the normalized intercept parameter reasonably. Problems associated with specific differential-phase (KDP)-based estimates close to the radar location, particularly during overhead convection, are also discussed.

Polarimetric radar measurements are used to retrieve drop size distributions (DSD) in subtropical thunderstorms. Retrievals are made with the single-moment exponential drop size model of Marshall and Palmer driven by radar reflectivity measurements and with a two-parameter constrained-gamma drop size model that utilizes reflectivity and differential reflectivity. Results are compared with disdrometer observations. Retrievals with the constrained-gamma DSD model gave better representation of total drop concentration, liquid water content, and drop median volume diameter and better described their natural variability. The Marshall-Palmer DSD model, with a fixed intercept parameter, tended to underestimate the total drop concentration in storm cores and to overestimate significantly the concentration in stratiform regions. Rainwater contents in strong convection were underestimated by a factor of 2-3, and drop median volume diameters in stratiform rain were underestimated by 0.5 mm. To determine possible DSD model impacts on numerical forecasts, evaporation and accretion rates were computed using Kessler-type parameterizations. Rates based on the Marshall-Palmer DSD model were lower by a factor of 2-3 in strong convection and were higher by about a factor of 2 in stratiform rain than those based on the constrainedgamma model. The study demonstrates the potential of polarimetric radar measurements for improving the understanding of precipitation processes and microphysics parameterization in numerical forecast models.