Drop Size Distribution

In support of the NASA Tropical Rainfall Measuring Mission (TRMM) Ground Validation Program, a suite of surface instruments and vertical pointing Doppler radar profilers were deployed in central Florida to quantify the number and size of the rain drops reaching the surface. Analyzing 276 minutes of simultaneous observations from two surface disdrometers and one profiler revealed good agreement among the instruments for drop sizes > 1.5 mm diameter but poor agreement for smaller drop sizes. The magnitude of the difference in small drop estimation was proportional to the reflectivity (and rainrate). At reflectivities greater than 40 dBZ, the differences in the estimation of the number of small drops yielded differences in estimates of mass-weighted diameter of > 13% and of rainrate > 25%. The combined effect of these uncertainties impact the interpretation of the precipitation processes and the development and validation of space-based precipitation retrieval algorithms.

Ultrasound techniques for the characterization of liquid-liquid dispersions have previously shown their value and promise, but still require refinement and careful, preferably non-invasive, implementation. Their combination with drop size distribution measurement techniques is also an important area for further development. A new non-invasive implementation has been developed, studied and evaluated in detail, which leads to accurate hold-up fraction measurements (to within −0.0123 units), surpassing that of most previous techniques. The largest error incurred by the effect of the propagation through the vessel wall glass has been shown to be negligible, the same applying to the effect of the propagation across the agitator shaft. Actual experimental dispersed phase hold-up fractions of up to 40% were tested and successfully correlated, in addition to 100% organic phase.

Interfacial properties of polyoxyethylene(2) oleyl ether and drop size distributions of emulsions prepared with this surfactant are investigated experimentally in this work; 80, 88 and 94% (v) internal phase ratio W/O type emulsions were prepared, where the aqueous phase was 1% sorbitol solution and the oil phase, a 1:1 v/v mixture of surfactant and paraffin oil. Experimental evidence indicated an interaction between the hydrocarbon chains of surfactant molecules and the solvent paraffin oil through van der Waals forces and between the ethoxylate groups and sorbitol, a polyalcohol, in the aqueous phase through hydrogen bonds, notably below the transition temperature. Continuous phase liquid present in the plateau borders was found to act as a reservoir of surface active agents, minimizing the effect of stretching of the film under shear. In cases where the amount of liquid hold up in plateau borders is negligible, the drop size distributions were found to be very sensitive to shearing rate. Interplay between the interfacial shear viscosity and the interfacial tension was found to control the rate of coalescence of drops less than 0.48 mm only in the case of 94% emulsions, corresponding to maximum stretching of interfacial area. In other cases, interfacial film stability seems to control the rate of coalescence.

Dimensionless spray flux W a is a dimensionless group that characterises the three most important variables in liquid dispersion: flowrate, drop size and powder flux through the spray zone. In this paper, the Poisson distribution was used to generate analytical solutions for the proportion of nuclei formed from single drops ( f single ) and the fraction of the powder surface covered by drops ( f covered ) as a function of W a . Monte-Carlo simulations were performed to simulate the spray zone and investigate how W a , f single and f covered are related. The Monte-Carlo data was an excellent match with analytical solutions of f covered and f single as a function of W a . At low W a , the proportion of the surface covered by drops ( f covered ) was equal to W a . As W a increases, drop overlap becomes more dominant and the powder surface coverage levels off. The proportion of nuclei formed from single drops ( f single ) falls exponentially with increasing W a . In the ranges covered, these results were independent of drop size, number of drops, drop size distribution (mono-sized, bimodal and trimodal distributions), and the uniformity of the spray. Experimental data of nuclei size distributions as a function of spray flux were fitted to the analytical solution for f single by defining a cutsize for single drop nuclei. The fitted cutsizes followed the spray drop sizes suggesting that the method is robust and that the cutsize does indicate the transition size between single drop and agglomerate nuclei. This demonstrates that the nuclei distribution is determined by the dimensionless spray flux and the fraction of drop controlled nuclei can be calculated analytically in advance. D

In the study of soil erosion, specifically on detachment of soil particles by raindrop impact, kinetic energy is a commonly suggested indicator of the raindrop's ability to detach soil particles from the soil mass. Since direct measurement of kinetic energy requires sophisticated and costly instruments, the alternative approach is to estimate it from rainfall intensity. The present study aims at establishing a relationship between rainfall intensity and kinetic energy for rainfalls in Central Cebu, Philippines as a preface of a wider regional investigation.

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...

Venturi scrubbers are high e ciency gas cleaners in which suspended particles are removed from gas streams by drops formed by liquid atomisation, usually in the Venturi throat. The size of the drops formed are of fundamental importance to the performance of the equipment, both in terms of pressure drop and dust removal e ciency. In this study, drop sizes in a cylindrical laboratory-scale Venturi scrubber were measured using a laser di raction technique. Gas velocity and liquid to gas ratios varied from 50 to 90 m=s and 0.5 to 2:0 l=m 3 , respectively. Water was injected using two di erent arrangements: either as jets in the throat or as a im just upstream of the convergence. Drop size measurements were performed at three positions in the case of jet injection: two located along the throat, and the last one at the end of the di user. The present data shows that the Sauter mean diameter of the spray can be well correlated by the equation of Boll et al. (J. Air Pollut. Control Assoc. 24 (1974) 932). Drop size distributions are satisfactorily represented by a Rosin-Rammler function. This paper also provides a simple method for calculating the parameters of the Rosin-Rammler function. As a result of this work, drop sizes in Venturi scrubbers can be estimated with much higher accuracy. ?

The procedure proposed by Packer and Rees (J. Colloid Interface Sci. 40 (1972) 206) to interpret pulsed field gradient spin-echo (PGSE) experiments on emulsions is commonly used to resolve for the distribution of droplet sizes via nuclear magnetic resonance (NMR). Nevertheless, such procedure is based on several assumptions that may restrict its applicability in many practical cases. Among such constrains, (a) the amplitude of the spin-echo (signal) must be influenced solely by the drop phase, and not by the continuous phase; and (b) the shape of the drop size distribution must be assumed a priori. This article discusses new theory to interpret results from PGSE experiments and a novel procedure that couples diffusion measurements (PGSE) with transverse relaxation rate experiments (the so-called CPMG sequence) to overcome the above limitations. Results from experiments on emulsions of water dispersed in several crude oils are reported to demonstrate that the combined CPMG-PGSE method renders drop size distributions with arbitrary shape, the wateryoil ratio of the emulsion and the rate of decay of magnetization at the interfaces, i.e. the surface relaxivity. It is also shown that the procedure allows screening if the dispersion is oil-inwater (oyw) or water-in-oil (wyo) in a straightforward manner and that it is suitable to evaluate stability of emulsions. ᮊ

The quantitative description of particle size distribution development in suspension polymerization reactors is very complex. The exact mechanisms of breakage and coalescence/aggregation of the polymerizing drops are generally not very well understood, and are closely related and controlled by the spectrum of turbulent energy dissipation rate in the reactor. In the present investigation, a two-compartment population balance model was developed for taking into account the large spatial variations of the local turbulent kinetic energy, in order to predict the evolution of droplet sizes in a high holdup (i.e., 47}50 vol%) suspension polymerization system as a function of the most important process conditions, such as type of suspending agent, monomer/water-phase ratio, polymerization temperature, quality of agitation, and evolution of the dispersed-phase density, interfacial tension and viscoelasticity during the polymerization. Phenomenological expressions of the literature were modi"ed for drops in the viscous dissipation range and were applied for describing the breakage and coalescence rates of the polymerizing dispersed phase as a function of the basic hydrodynamics and evolving physical properties of the system. Computational #uid dynamics simulations were used for estimating the volume ratio of the impeller and circulation regions, the ratio of turbulent dissipation rates and the exchange #ow rate of the two compartments at di!erent agitation rates and continuous-phase viscosities. The theoretical model can predict reasonably well the experimentally observed inhomogeneities of the drop size distribution as well as the evolution of particle size distribution in VCM suspension polymerization, especially considering the various assumptions in formulating the drop breakage and coalescence rates and in the two-compartment approximation of the inhomogeneities of the turbulent #ow "eld in the suspension polymerization reactor.

Increasing our understanding of the small scale variability of drop size distributions (DSD), and therefore of several bulk characteristics of rainfall processes, has major implications for our interpretation of the remote sensing based estimates of precipitation and its uncertainty. During the spring and summer of 2002 the authors conducted the DEVEX experiment (disdrometer evaluation experiment) to compare measurements of natural

The aim of this work is to compare the oil-in-water emulsions produced by mechanical agitation (Ultra-Turrax, 10000rpm, P=170W) or power ultrasound (ultrasound horn, 20kHz, 130W) using the same model system : water/kerosene/polyethoxylated (20EO) sorbitan monostearate. The following parameters were varied : emulsification time, surfactant concentration, consumed power and volume fraction of oil. With ultrasound, the drop size (Sauter diameter, d32)

Polarimetric radar measurements are sensitive to the size, shape and orientation of raindrops and provide information about drop size distribution (DSD), canting angle distribution and rain rate. In this paper, we propose and demonstrate a method for retrieving DSD parameters for calculating rain rate and the characteristic particle size. The DSD is assumed to be a Gamma distribution and the governing parameters are retrieved from radar measurements: reflectivity ( ), differential reflectivity ( ), and a constrained relation between the shape ( ) and slope (3) parameters derived from video disdrometer observations. The estimated rain rate is compared with that obtained from more traditional methods and the calculated characteristic size is compared with the measured values. The calculated based on the retrieved Gamma DSD is also compared with measurements. The proposed method shows improvement over the existing models and techniques because it can retrieve all three parameters of the Gamma distribution. For maintaining the continuity of earlier published results, raindrop shape is assumed to be equilibrium. (NCAR), Boulder, CO.

New data are presented on drop size distribution at high dispersed phase fractions of organicin-water mixtures, obtained with a light back scattering technique (3 Dimensional Optical Reflectance Measurement technique, 3D ORM). The 3D ORM technique, which provides fast, in-situ and on-line drop distribution measurements even at high concentrations of the dispersed phase, is validated using an endoscope attached to a high-speed video recorder. The two techniques compared favourably when used in a dispersion of oil (density (ρ) = 828 kg m −3 , viscosity (µ) = 5.5 mPa s, interfacial tension (σ i ) = 44.7 mN m −1 ) in water for a range of 5-10% dispersed phase fractions. Data obtained with the ORM instrument for dispersed phase fractions up to 60% and impeller speeds 350-550 rpm showed a decrease in the maximum and the Sauter mean drop diameters with increasing impeller speed. Phase fractions did not seem to significantly affect drop size. Both techniques showed that drop size distributions could be fitted by the log-normal distribution.

This paper examines drop size distributions in a 0.063 m pipe for a two-phase mixture of kerosene and aqueous potassium carbonate solution. Measurements have been made for both vertical up¯ow and horizontal geometries, for mixture velocities ranging from 0.8 to 3.1 m/s. Two optical measurement techniques, a backscatter technique using a Par-Tec 300C and a diraction technique using a Malvern 2600, have been used to obtain the drop size distributions of the dispersions created. Both measurement techniques have been found to be limited to dierent concentration ranges. Strati®cation of drop size was observed for low mixture velocities in a horizontal geometry. This did not occur for the vertical geometry.

Using a matrix of drop size distributions (DSDs), measured by a microscale array of disdrometers, a method of spatial and temporal DSD interpolation is presented. The goal of this interpolation technique is to estimate the DSD above the disdrometer array as a function of three spatial coordinates, time and drop diameter. This interpolation algorithm assumes simpli ed drop dynamics, based on cloud advection and terminal velocity of raindrops. Once a 3D DSD has been calculated, useful quantities such as radar re ectivity Z and rainfall rate R can be computed and compared with corresponding rain gauge and weather radar data.

Gamma model is fitted using the second, fourth, and sixth moments to model the rain drop size distribution (DSD) of Singapore. As the Joss distrometer measures the number of rain drops between the drop diameters from 0.3 to 5 mm, the truncated moment fitting between these drop diameter ranges is also used for modeling the DSD. Gamma DSD requires three-parameter estimation: N 0 , the intercept parameter; μ, the shape parameter; and Λ, the slope parameter. The aim of this paper is to find a suitable fixed μ and derive an appropriate μ−Λ relation for the tropical region in order to form a two-parameter gamma model. To find an appropriate μ value, observed DSDs are fitted with different μ values to estimate the rain rates, which are assessed by rain rate observations of the distrometer. Shape-slope relationships are fitted for different categories according to the rain rate and the number of drops. The derived μ−Λ relationships for the Singapore region are compared to the published results from two other regions, and the analysis is presented. Two-parameter gamma models are compared by retrieving the rain rate using the polarimetric radar variables. The effect of truncation on rain rate retrieval is also studied, and the use of the μ−Λ relationship for rain retrieval is recommended for the tropical region. The μ−Λ relation using the truncated moment method for the rain category R ≥ 5 mm/hr and rain counts ≥ 1000 drops retrieves the rain rates well compared to other μ−Λ relations.

Control over drop size distributions, injection rates, and geometrical distribution of fuel and oxidizer sprays in bi-propellant rocket engines has the potential to produce more efficient, more stable, less polluting rocket engines. This control also offers the potential of an engine that can be throttled, working efficiently over a wide range of output thrusts. Inkjet printing technologies, MEMS fuel atomizers, and piezoelectric injectors similar in concept to those used in diesel engines are considered for their potential to yield a new, more active injection scheme for a rocket engine. Inkjets are found to be unable to pump at sufficient pressures, and have possibly dangerous failure modes. Active injection is found to be feasible if high pressure drop along the injector plate are used. A conceptual design is presented and its basic behavior assessed.

The information on the time variability of drop size distributions (DSDs) as seen by a disdrometer is used to illustrate the structure of uncertainty in radar estimates of precipitation. Based on this, a method to generate the space-time variability of the distributions of the size of raindrops is developed. The model generates one moment of DSDs that is conditioned on another moment of DSDs; in particular, radar reflectivity Z is used to obtain rainfall rate R. Based on the fact that two moments of the DSDs are sufficient to capture most of the DSD variability, the model can be used to calculate DSDs and other moments of interest of the DSD. A deterministic component of the precipitation field is obtained from a fixed R-Z relationship. Two different components of DSD variability are added to the deterministic precipitation field. The first represents the systematic departures from the fixed R-Z relationship that are expected from different regimes of precipitation. This is generated using a simple broken-line model. The second represents the fluctuations around the R-Z relationship for a particular regime and uses a space-time multiplicative cascade model. The temporal structure of the stochastic fluctuations is investigated using disdrometer data. Assuming Taylor hypothesis, the spatial structure of the fluctuations is obtained and a stochastic model of the spatial distribution of the DSD variability is constructed. The consistency of the model is validated using concurrent radar and disdrometer data.

T h e microscopic phenomena occurring in an agitated vessel are extremely complex. The exact mechanisms of coalescence and breakage in bubble and drop systems are generally not very well understood. Several attempts have been made in the literature to improve our understanding of these phenomena in multiparticle systems. In the present work, the most comprehensive models describing the coalescence and breakage processes in a styrene/water dispersion system are incorporated in a numerical algorithm to calculate the steady-state drop size distributions in a batch stirred vessel. A new breakage distribution function is introduced that considers droplet broken into two daughter and several satellite droplets. As a result, bimodal diameter density distributions are obtained. It is shown that the proposed model has the ability t o fit reasonably well a series of experimental data obtained for a low-coalescence system a t different impeller speeds, temperatures, and dispersed phase hold-up fractions.

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.

Die Gruppe drallfreier und verdrallter turbulenter Freistrahlen bildet eine Grundströmungsform, die bereits von zahlreichen Autoren analytisch behandelt und verstanden wurde. Diese Freistrahlen nehmen in zahlreichen verfahrenstechnischen Apparaten und Prozessen eine zentrale Rolle ein. Mit dem steten Ansteigen von Rechnerkapazität und dem damit verbundenen verstärkten Einsatz von CFD für komplexe verfahrenstechnische Anwendungen stellt sich hier immer öfter die Frage nach der Qualität, mit der gängige CFD-Codes in der Lage sind, diese Strömungsform zu beschreiben. Der kritische Faktor bei dieser Fragestellung ist die Turbulenzmodellierung. In der vorliegenden Arbeit soll diese Frage anhand zahlreicher Strömungssimulationen unter Verwendung aktueller Turbulenzmodelle sowie durch Vergleich mit experimentellen Daten beantwortet werden. Zuletzt sollen Empfehlungen abgegeben werden, welche Turbulenzmodelle die betrachteten Freistrahlen mit ausreichender Genauigkeit beschreiben, wobei stets die Anwendbarkeit in der Ingenieurs-Praxis im Auge behalten werden soll.

The extent to which dispersed-phase viscosity influences equilibrium mean drop size and drop size distribution at constant interfacial tension is determined for dilute suspensions by dispersing silicone oils of various viscosity grades in water. A mechanistic model for mean drop size is developed which predicts the moderate-viscosity data and whose parameters correlate the high-viscosity results. Trends in the mean size data coincide with those for the drop size distribution, which broadens considerably as viscosity increases and suggests a dependency on breakage mechanism.

The installation of a rainfall simulator inside the wind tunnel of I.C.E. International Center for . Eremology, Ghent, Belgium enables to study the combined effect of wind and rain on the erosion processes. Simulated rainfall characteristics assessed were: the spatial distribution of the intensity in the working area of wind tunnel and the drop size distribution under different operating pressures and wind speed. The rainfall intensities varied between 37.9 mm h y1 to 143.0 mm h y1 depending on the number of operating nozzles, the applied pressure and the wind speed. Areas for different rain intensities with a uniformity coefficient higher than 80% were determined in the working area of the wind tunnel. Under simulated rainfall the raindrop diameter varied between 0.2 and 3 mm and this was affected by the operating pressure and by the wind speed. A narrower Ž . raindrop distribution and a smaller sorting coefficient, D y D rD , was obtained under 75 25 50 Ž . Ž . wind-driven rain oblique rain compared to vertical rainfall without wind . q 1998 Elsevier Science B.V. All rights reserved.

Liquid-liquid mixing is a key process in industries that is commonly accomplished in mechanical agitation systems. Liquid-liquid mixing performance in a stirred tank can be evaluated by various parameters, namely minimum agitation speed, mixing time, circulation time, power consumption, drop size distribution, breakup and coalescence, interfacial area, and phase inversion. The importance of these liquid-liquid mixing parameters, the measurement method, and the results are discussed briefly. Input parameters such as impeller type, power number, flow pattern, number of impellers, and dispersed phase volume fraction, in addition to physical properties of phases such as viscosity and density, are reviewed. Scale-up aspects are also included. © 2013 Copyright Taylor and Francis Group, LLC.

http://www.tandfonline.com/doi/pdf/10.1080/00986445.2012.717313

Optical disdrometers have the potential to be low maintenance instruments that can measure drop-size distributions and drop-size distribution moments such as rainfall rate, radar reflectivity, optical extinction, and others. As with any other measurement device, their output is affected by different sources of uncertainty. To better understand these uncertainties, we compared rainfall accumulations that were measured by three dual tipping bucket stations, three Vaisala WXT510 compact weather stations, and four Thies optical disdrometers. We detected considerable bias between disdrometers and tipping buckets, as well as among disdrometers, that we attempted to minimize through calibrating diameter measurements. Although the calibration successfully decreased bias among disdrometers, it increased bias between disdrometer rainfall accumulations and tipping bucket accumulations, indicating that there are other relevant sources of error in the estimation of rainfall accumulation from disdrometer measurements. We developed a simulation capable of mimicking the disdrometer's operation during the calibration procedure and studied the effects of using three arbitrary laser beam patterns into the measurement of the spheres' diameters. The simulation successfully reproduced some of the behavior observed in calibration data, showing the dependence of the bias and the spread of sphere diameter measurements on the studied beam patterns. Furthermore, we designed a Monte-Carlo-based simulation to propagate the uncertainties of the measurement of spheres' diameters into the estimation of rainfall accumulations. We used the calculated uncertainties to correct rainfall accumulations which improved the agreement among disdrometers, although apparently overcorrected the accumulation for one of the instruments. Moreover we found the average correction to be related to both average and standard deviation of the diameter error and insensitive to the diameter error skewness. Overall we observed considerable bias between instruments with different principles of measurements, which could not be solely explained by uncertainty in the evaluation of the diameters, or by wind effects, indicating that difficulties in the determination of the optical disdrometer's sensing area could be the cause.► We detected bias between disdrometers and rain gauges, as well as among disdrometers. ► Detected bias could only be partially addressed by calibrating diameter measurements. ► We discarded wind effects as causes for the observed errors. ► The presented simulation framework allows the assessment of optical induced errors.

A combined polarimetric estimator for rainfall rate (R) retrievals from polarimetric radar measurements at X band is proposed. This estimator uses the horizontal polarization radar reflectivity Z e , differential reflectivity Z DR , and specific differential phase shift K DP , and it intrinsically accounts for changes in how drop oblateness increases with size. Because this estimator uses power measurements (i.e., Z e and Z DR ), a procedure for correcting these measurements for effects of partial attenuation and differential attenuation using the differential phase measurement is suggested. An altitude correction for estimates of rainfall rates is also suggested. The proposed combined polarimetric estimator that uses K DP , Z DR , and Z e , an estimator that uses K DP alone for equilibrium drop shapes, and different Z e -R relations were applied to the 15 rain events observed with the NOAA X-band transportable polarimetric radar during the eight-week field campaign at the NASA Wallops Island facility in Virginia. The observed rains ranged from very light stratiform events to very heavy convective ones with cells producing rainfall rates in excess of 100 mm h Ϫ1 . The three different ground validation sites were equipped with high-resolution (0.01 in.) tipping-bucket rain gauges. One of these sites also was equipped with disdrometers. In terms of the relative standard deviation, the combined polarimetric estimator provided the best overall agreement with gauge data (22%), closely followed by a case-tuned Z e -R relation (23%) that was determined for each observational case from drop size distributions (DSD) measured in situ by a disdrometer and was available only a posteriori. The use of the K DP -only estimator and a mean Z e -R relation resulted in 30% and 32% relative standard deviations, correspondingly. The combined polarimetric estimator, the K DP -only estimator, and the casetuned Z e -R relation estimator provided about a 6%-9% negative bias in comparison with the gauge data; the mean Z e -R relation estimator provided a larger negative bias (18%).

1] Multiple scattering returns from spherical water particles of uniform diameter are studied for pulsed radar operation. The Gaussian transverse beam-profile and the rectangular pulse-duration are taken into account. A second-order analytical solution is derived for a single layer structure, based on the time-dependent radiative transfer theory. The method itself can be extended to higher-order scatterings in a multiple layered structure with general drop size distributions. The calculation results show that the effect of second-order scattering becomes larger, as the footprint radius, range, and range resolution, which are normalized by the mean free path, increase.

Drop size distribution is a fundamental property of rainfall for two main reasons: the shape of the distribution reflects the physics of rain formation processes, and it is of basic importance in determining most parameters used in radar-meteorology. Therefore, several authors have proposed in the past different parameterizations for the drop size distribution (DSD). The present work focuses attention on the gamma DSD properties, assumed to be the most suitable for describing the observed DSD and its variability.

This study proposes a Bayesian approach to retrieve raindrop size distributions (DSDs) and to estimate rainfall rates from radar reflectivity in horizontal polarization Z H and differential reflectivity Z DR. With this approach, the authors apply a constrained-gamma model with an updated constraining relation to retrieve DSD parameters. Long-term DSD measurements made in central Oklahoma by the two-dimensional video disdrometer (2DVD) are first used to construct a prior probability density function (PDF) of DSD parameters, which are estimated using truncated gamma fits to the second, fourth, and sixth moments of the distributions. The forward models of Z H and Z DR are then developed based on a T-matrix calculation of raindrop backscattering amplitude with the assumption of drop shape. The conditional PDF of Z H and Z DR is assumed to be a bivariate normal function with appropriate standard deviations. The Bayesian algorithm has a good performance according to the evaluation with simulated Z H and Z DR. The algorithm is also tested on S-band radar data for a mesoscale convective system that passed over central Oklahoma on 13 May 2005. Retrievals of rainfall rates and 1-h rain accumulations are compared with in situ measurements from one 2DVD and six Oklahoma Mesonet rain gauges, located at distances of 28-54 km from Norman, Oklahoma. Results show that the rain estimates from the retrieval agree well with the in situ measurements, demonstrating the validity of the Bayesian retrieval algorithm.

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.

Knowledge of drop size distributions is important for deriving various rain erosivity parameters. This study investigates the potential of an optical spectro pluviometer (OSP) to measure drop size distributions. Particular attention is paid to the impact of drop sample size and derived erosivity parameters. An experimental set-up using a rainfall simulator and an OSP is described. The OSP allows a continuous real-time sampling of the drops. Results on drop size distributions and sampling effects are discussed. A simulation aimed at reproducing the sampling made with the widely used flour-pellet or filter-paper method is described. From this simulation, recommendations on the sample size of the collected drops needed for an accurate determination of median drop size and kinetic energy are given. Past studies reporting drop size characteristics have often used too small a sample for an adequate description of rain erosivity.

In the separation process using emulsion liquid membranes, the polydispersity affects mass transport of metal ions from the external phase because under steady operating conditions, drop size and size distribution are proportional to the interfacial area. The present study aims to assess the importance of polydisperse character of the emulsion globules. An advancing reaction front model considering emulsion globules of various sizes with same sauter mean diameter has been proposed for this purpose. In this paper, the important variables affecting sauter mean diameter of the emulsion drops, including injection method of emulsion, stirring speed, oil phase viscosity, composition of inner water phase and solute permeation rate are also systematically investigated. #

Simultaneous observations by the lower fuselage (LF) radar, the tail (TA) radar, and the Stepped Frequency Microwave Radiometer (SFMR) on board the NOAA WP-3D aircraft are used to validate the rainfall rate estimates from microwave emission measurements of SFMR in tropical cyclones. Data collected in Hurricane Bonnie (1998) and Hurricane Humberto (2001) with a total of 820 paired samples are used in the comparisons. The SFMR 10-s path-integrated rain rates are found to have an overestimate in light rain and an underestimate in heavy rain relative to radar rainfall estimates. Examination of the existing SFMR algorithm shows that the coefficient should be changed in the attenuation-rain-rate relationship used in the inversion algorithm. After this correction, a linear regression result with a correlation coefficient of 0.8 and a slope close to 1 is obtained. But an overall high bias of 5 mm h Ϫ1 of the SFMR rainfall estimate relative to radar is also found. The error analysis shows that the bias is nearly independent of rain type, a result confirming Jorgensen and Willis's conclusion that the drop size distributions between convective and stratiform rain in hurricanes are similar. It is also shown that the bias is a weak function of wind speed, as well as a weak inverse function of radial distance to the hurricane center. Temperature dependence has been ruled out as the main explanation. After doing sensitivity tests, the authors conclude that the bias results from a combination of two factors: an underestimate of the freezing-level height, and a downward increase of radar reflectivity in the high wind regions. If the true downward increase is 1-2 dBZ km Ϫ1 , a 0.5-km underestimate of the freezing-level height could account for up to a 3-5 mm h Ϫ1 bias.

Disdrometer data measured during the passage of tropical continental squall lines in Darwin, Australia, are analyzed to study characteristics of raindrop size distribution (DSD). Fifteen continental squall lines were selected for the DSD analysis. An observed squall line was partitioned into three regions based on radar reflectivity pattern, namely, convective line, stratiform, and reflectivity trough. A convective line was further

The drop size distributions and the drop velocity function that characterize simulated rainfall at three intensities are modelled in terms of expressions developed for natural rainfall. As a result, the continuous relationship between kinetic energy per unit of mass (or time) and intensity is defined for the simulated case, and is compared with that for natural rainfall at similar intensities. The similarity characterizing drop size distributions of natural rainfall is found also in simulated rainfall. However, the drop fragmentation process in the simulator differs from the process that occurs in natural rainfall, and the dimensionless expression of the resulting drop size distributions differs from the theoretical function proposed by Assouline and Mualem (1989, Trans. ASAE, 32(4): 1216-1222). For a falling distance of 5.5 m, the velocity at the soil surface of the simulated drops is similar to the terminal velocity of natural raindrops of equivalent diameters. The simulated rainfall kinetic energy per unit of mass is close to the natural rainfall value at similar intensity, and the maximal difference is about 10%. However, the differences in the respective drop size distributions induce different trends in the kinetic energy-intensity relationship. The simulated rainfall kinetic energy per unit of time is not a linear function of the intensity. Therefore, cumulative rainfall is not equivalent to cumulative kinetic energy, and cannot be used as the independent variable in models dealing with processes affected by the rainfall energy without error. ᭧ 1997 Elsevier Science B.V.

Recent studies using vertically pointing S-band profiling radars showed that coastal winter storms in California and Oregon frequently do not display a melting-layer radar bright band and inferred that these nonbrightband (NBB) periods are characterized by raindrop size spectra that differ markedly from those of brightband (BB) periods. Two coastal sites in northern California were revisited in the winter of 2003/04 in this study, which extends the earlier work by augmenting the profiling radar observations with collocated raindrop disdrometers to measure drop size distributions (DSD) at the surface. The disdrometer observations are analyzed for more than 320 h of nonconvective rainfall. The new measurements confirm the earlier inferences that NBB rainfall periods are characterized by greater concentrations of small drops and smaller concentrations of large drops than BB periods. Compared with their BB counterparts, NBB periods had mean values that were 40% smaller for mean-volume diameter, 32% smaller for rain intensity, 87% larger for total drop concentration, and 81% larger (steeper) for slope of the exponential DSDs. The differences are statistically significant. Liquid water contents differ very little, however, for the two rain types. Disdrometer-based relations between radar reflectivity (Z ) and rainfall intensity (R) at the site in the Coast Range Mountains were Z ϭ 168R 1.58 for BB periods and Z ϭ 44R 1.91 for NBB. The much lower coefficient, which is characteristic of NBB rainfall, is poorly represented by the Z-R equations most commonly applied to data from the operational network of Weather Surveillance Radar-1988 Doppler (WSR-88D) units, which underestimate rain accumulations by a factor of 2 or more when applied to nonconvective NBB situations. Based on the observed DSDs, it is also concluded that polarimetric scanning radars may have some limited ability to distinguish between regions of BB and NBB rainfall using differential reflectivity. However, differential-phase estimations of rain intensity are not useful for NBB rain, because the drops are too small and nearly spherical. On average, the profiler-measured echo tops were 3.2 km lower in NBB periods than during BB periods, and they extended only about 1 km above the 0°C altitude. The findings are consistent with the concept that precipitation processes during BB periods are dominated by ice processes in deep cloud layers associated with synoptic-scale forcing, whereas the more restrained growth of hydrometeors in NBB periods is primarily the result of orographically forced condensation and coalescence processes in much shallower clouds. FIG. 1. Map of the Sonoma County area of northern California showing the primary observing sites for this study. Cazadero (CZD) as at 475 m MSL in the Coast Range Mountains; Bodega Bay (BBY) and Fort Ross (FRS) are near sea level on the coastline. The city of San Francisco is approximately 75 km southeast of CZD.

The present paper reports an experimental investigation on atomizing liquid flows produced by simplified cavity nozzles. The Weber number being kept low, the sprays produced by these injectors depend on the liquid flow characteristics only, and more precisely, on the non-axial kinetic energy and of the turbulent kinetic energy at the nozzle exit. The investigation reported here concentrates on the characterization of liquid flows during atomization by measuring the spatial variation of the local interface length and of the local interface fractal dimension. Both parameters were found representative of the physics of atomization process: they depend on the characteristics of the flow issuing from the nozzle and they are related to the subsequent drop size distribution. The local interface length is representative of the amount of liquid-gas interface surface area, and is a function of both the non-axial and the turbulent kinetic energies at the nozzle exit. The fractal dimension is representative of the tortuosity of the liquid-gas interface and, as expected, is mainly related to the turbulent kinetic energy at the nozzle exit. As far as the drop size distribution is concerned, it is found that the local interface length at the instant of break-up determines a representative drop diameter of some kind, whereas the fractal dimension at the same instant controls the dispersion of the distribution.

The depolarization of a satellite signal due to scattering by rain drops has been studied at a tropical location.
The depolarization phenomenon is observed in terms of an enhancement of cross-polar component of a horizontally
polarized Ku-band signal. The differential phase shifts, dominantly responsible for causing depolarization at Kuband
due to scattering by spheroidal raindrops, are computed by employing the point matching technique and using
experimentally obtained rain drop size distribution (DSD) data. The differential phase shift is significant for large
drops (> 3mm). Consequently, DSD plays an important role in determining the depolarization of the satellite signal.

The raindrop size distributions had been measured at three locations in Nigeria -Calabar, Ile-lfe and Zaria. The data collected over a period of three years have been utilized to obtain models of drop size distributions for drizzle, shower, widespread and thunderstorm rain. The lognormal distribution provides a good fit for all the rain types at these tropical locations except drizzle, where the exponential model is adequate. The implications of the models for specific attenuation calculations for tropical rain are discussed.

A propagation correction algorithm utilizing the differential propagation phase ( dp ) was developed and tested on C-band polarimetric radar observations of tropical convection obtained during the Maritime Continent Thunderstorm Experiment. An empirical procedure was refined to estimate the mean coefficient of proportionality a (b) in the linear relationship between dp and the horizontal (differential) attenuation throughout each radar volume. The empirical estimates of these coefficients were a factor of 1.5-2 times larger than predicted by prior scattering simulations. This discrepancy was attributed to the routine presence of large drops [e.g., differential reflectivity Z dr Ն 3 dB] within the tropical convection that were not included in prior theoretical studies.

A trajectory ensemble model (TEM) is used to investigate aqueous processing of gases and cloud condensation nuclei (CCN) in the boundary layer. The coupled aqueous chemistry/cloud microphysics model driven by a set of boundary layer parcel trajectories derived from a large eddy simulation is used to study the effects of variations in the initial chemical fields and initial aerosol number concentration on chemical heterogeneity, and the broadening of CCN and drop spectra. The differences in the overall fractional conversion between the TEM and a single parcel experiencing mean conditions in a stratocumulus-capped marine boundary layer are also investigated. Results show that the 03 oxidation rate is larger than the H202 oxidation rate in the base case, whereas the volume-mean pH might suggest that H202 oxidation dominates.

The fragmentation of a laminar undulating liquid sheet flowing in quiescent air is investigated. Combining various observations and measurements we propose a sequential atomization scenario describing the overall sheet-drop transition in this configuration. The undulation results from a controlled primary Kelvin-Helmholtz instability. As the liquid travels through the undulating pattern, it experiences transient accelerations perpendicular to the sheet. These accelerations trigger a secondary instability responsible for the amplification of spanwise thickness modulations of the sheet. This mechanism, called the 'wavy corridor', is responsible for the sheet free edge indentations from which liquid ligaments emerge and break, forming drops. The final drop size distribution is of a Gamma type characterized by a unique parameter independent of the operating conditions once drop sizes are normalized by their mean.

The influence of the nature of the oil phase on the zeta potential and the time course evolution of mean droplet-size of emulsions stabilized with mesquite gum have been investigated. Mesquite gum-stabilized emulsions of D-limonene, n-decane, n-dodecane, n-tetradecane n-hexadecane, and orange oil were prepared in the range of 9-22% w/w mesquite gum concentrations to investigate the emulsion stability by analyzing creaming, zeta potential, and drop size distribution. An electrosteric mechanism of stabilization is proposed to explain the long term stability observed for orange oil-water emulsions in the range of 9-22% w/w mesquite gum concentrations, similar to the one suggested to operate for gum arabic interfaces. Experiments of creaming for the different emulsions, showed that orange oilwater emulsions observed strong stability in time. By contrast, mesquite gum-stabilized emulsions of D-limonene, n-decane, n-dodecane, n-tetradecane, and n-hexadecane produced less stable emulsions. Light scattering measurements were performed to analyse the Ostwald ripening phenomenon on diluted oil in water emulsions stabilized with mesquite gum of n-hexadecane, D-limonene, and orange oil. The averaged hydrodynamic radius showed a linear-like behavior with time except for orange oil drops which kept their size almost constant for more than hundred hours.

Vertically pointing Micro Rain Radars (MRRs) provide profiles of drop size distributions (DSDs) from the measured Doppler reflectivity spectra. However, in the presence of strong vertical winds, the measured spectra can suffer from aliasing errors. These errors can considerably affect the derived DSD, and hence, the retrieved rain parameters. In this work, we show that such aliasing can be automatically detected and that this detection can be used at our benefit to identify strong vertical winds and eliminate incorrect retrievals. Likewise, we show that when this aliasing is adequately corrected, the retrieved DSD is then fit for further parameter retrievals.

1] To move toward spaceborne weather radars that can be deployed routinely as part of an instrument set consisting of passive and active sensors requires the development of smaller, lighter-weight radars. At the same time, the addition of a second frequency and an upgrade to Doppler capability are essential to retrieve information on the drop size distribution (DSD), vertical air motion, and storm dynamics. One approach to the problem is to use a single broadband transmitter-receiver and antenna where two narrowband frequencies are spaced apart by 7-10%. Use of Ka-band frequencies (26.5-40 GHz) provides adequate spatial resolution with a relatively small antenna. Moreover, the differential reflectivity and mean Doppler signals in this band are directly related to the median mass diameter of the snow and raindrop size distributions. We present in the paper theoretical calculations of the differential reflectivity and Doppler for several frequency pairs including those proposed for the Global Precipitation Mission (GPM) at 13.6 and 35 GHz. Measurements from a zenith-directed radar operated at 9.1 and 10 GHz are used to investigate the qualitative characteristics of the differential signals. Disdrometer data taken at the surface, just below the radar, show that the differential signals are related to characteristics of the raindrop size distribution. The stability of the DSD estimation procedure is tested using a simulation. The results indicate that reasonably stable estimates of the particle size distribution are feasible with a [31.5 GHz, 35 GHz] combination as long as a large number of independent samples are obtained.