Drop Diameter

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Jaber Safdari - One of the best experts on this subject based on the ideXlab platform.

  • prediction of the mean Drop Diameter dispersed phase hold up and slip velocity in a horizontal pulsed sieve plate column for uranium stripping from loaded alamine 336 by ammonium carbonate
    Progress in Nuclear Energy, 2019
    Co-Authors: Seyedeh Leila Mirmohammadi, Rezvan Torkaman, Mohammad Hassan Mallah, Jaber Safdari
    Abstract:

    Abstract This study has investigated the effects of operational parameters on the mean Drop Diameter (d 32 ), the dispersed phase holdup (φ) and the slip velocity (V s ) in uranium (VI) stripping of the loaded Alamine 336 using ammonium carbonate (0.64 M) by a horizontal pulsed sieve plate column. The main operational and physical parameters are the continuous and the dispersed phase flow rates, the pulsation intensity, the density, the continuous and the dispersed phase viscosities and the interfacial tension. Experimental results showed that an increase in the pulsation intensity led to a decrease in φ and d 32 , and an increase in the phase flow rates cause an increase in both φ and d 32 , although the impact of the flow rates on the d 32 was much milder than the pulsation intensity. Also, it was observed that the V s increase by increasing the pulsation intensity and the phase flow rates. Based on the experimental results and dimensional analysis, three experimental-theoretical correlations for predicting d 32 , φ, and V s are proposed. The Average Absolute Relative Errors (AARE) of these parameters were 9.90%, 14.45%, and 8.58%, respectively, signifying their accuracy and usefulness for horizontal pulsed sieve plate column scaling up.

  • using maximum entropy gamma inverse gaussian and weibull approach for prediction of Drop size distribution in a liquid liquid extraction column
    Chemical Engineering Research & Design, 2017
    Co-Authors: Mehdi Asadollahzadeh, Jaber Safdari, Meisam Torabmostaedi, Rezvan Torkaman, Rezvan Torkaman, Jaber Safdari
    Abstract:

    Abstract In this study, Drop size distribution and Sauter mean Drop Diameters were measured and correlated under operating variables and physical properties of the systems using a 113 mm Diameter Kuhni column. Three systems including toluene-water, n -butyl acetate-water and n -butanol-water were experimented in this column. The countercurrent flow pattern of the liquid phases was characterized regarding the Sauter mean Drop Diameter and Drop size distribution; a photographic method was used to assess Drop sizes. The following operating variables were studied: rotor speed, flow rate of both liquid phases and interfacial tension. The Drop size distribution and Sauter mean Drop Diameter were found to depend largely on the rotor speed and interfacial tension, albeit, only partially dependent on the phase velocities. The maximum entropy principle and the conventional probability distribution functions (Gamma, Inverse Gaussian, Weibull) have already been applied to estimate the Drop size distribution. Experimental results show that the maximum entropy function describes the Drop size distribution better than the conventional probability distribution functions for three systems in a Kuhni column extractor. An empirical correlation is proposed for the estimation of the Sauter mean Drop Diameter. The acquired information would be useful in design of liquid–liquid extraction columns.

  • a comparison between Drop size distributions derived from the probability distribution functions and maximum entropy principle case study pilot plant scheibel extraction column
    Chemical Engineering Research & Design, 2017
    Co-Authors: Mehdi Asadollahzadeh, Meisam Torabmostaedi, Rezvan Torkaman, Jaber Safdari
    Abstract:

    Abstract A new model for prediction of Drop size distribution is proposed in an eleven stage Scheibel extraction column by the maximum entropy density approximation technique. In addition, the conventional probability distribution functions (Gamma, Inverse Gaussian, Weibull) have already been applied to estimate the Drop size distribution. The experimental procedures were carried out by three different systems such as toluene–water, n -butyl acetate–water and n -butanol–water. The Drop size distribution was measured with an image analysis technique as a function of the operating conditions and physical properties of the liquid–liquid systems. The results show that the agitation speed has the main effect on the Drop size distribution in the column. However, the effects of phase flow rates are not significant. An empirical correlation is proposed for estimation of the Sauter mean Drop Diameter in terms of operating variables, column geometry and physical properties. The results show that the maximum entropy function describes the Drop size distribution better than the conventional probability distribution functions. The Shannon maximum entropy method provided a novel prediction method for the Drop size distributions in the liquid–liquid extraction columns. The latter that could be used for modeling approaches.

  • a new model for prediction of Drop size distribution in a liquid liquid extraction column
    RSC Advances, 2016
    Co-Authors: Mehdi Asadollahzadeh, Jaber Safdari, Meisam Torabmostaedi, Rezvan Torkaman, Rezvan Torkaman, Jaber Safdari
    Abstract:

    In this study, a new model for prediction of Drop size distribution is proposed in the asymmetric rotating disc pilot plant column (ARDC) by the maximum entropy density approximation technique. The liquid extraction systems including toluene–water, n-butyl acetate–water and n-butanol–water were used with this column. An image analysis technique was applied to determine the Drop size distribution as a function of operating parameters and physical properties. By applying abrupt changes of the operating parameters, the Drop behaviors in the column were investigated. The results show that the agitation speed has a main effect on the Drop size distribution in the column. However, the effects of phase flow rates are not significant. The empirical correlations are proposed to describe Lagrange multipliers in the maximum entropy function in terms of operating variables and physical properties of the systems. Except for these findings, an empirical correlation is proposed for estimation of the Sauter mean Drop Diameter in terms of operating variables, column geometry and physical properties. The proposed correlations are evaluated based on the goodness of fit statistics, namely, χ2, R2 and RMSE. The fitting results by the maximum entropy principle method seem to be fairly accurate and reasonable on the basis of the experimental data. These completed sets of data could be used for modeling approaches in the liquid–liquid extraction columns.

Mehdi Asadollahzadeh - One of the best experts on this subject based on the ideXlab platform.

  • using maximum entropy gamma inverse gaussian and weibull approach for prediction of Drop size distribution in a liquid liquid extraction column
    Chemical Engineering Research & Design, 2017
    Co-Authors: Mehdi Asadollahzadeh, Jaber Safdari, Meisam Torabmostaedi, Rezvan Torkaman, Rezvan Torkaman, Jaber Safdari
    Abstract:

    Abstract In this study, Drop size distribution and Sauter mean Drop Diameters were measured and correlated under operating variables and physical properties of the systems using a 113 mm Diameter Kuhni column. Three systems including toluene-water, n -butyl acetate-water and n -butanol-water were experimented in this column. The countercurrent flow pattern of the liquid phases was characterized regarding the Sauter mean Drop Diameter and Drop size distribution; a photographic method was used to assess Drop sizes. The following operating variables were studied: rotor speed, flow rate of both liquid phases and interfacial tension. The Drop size distribution and Sauter mean Drop Diameter were found to depend largely on the rotor speed and interfacial tension, albeit, only partially dependent on the phase velocities. The maximum entropy principle and the conventional probability distribution functions (Gamma, Inverse Gaussian, Weibull) have already been applied to estimate the Drop size distribution. Experimental results show that the maximum entropy function describes the Drop size distribution better than the conventional probability distribution functions for three systems in a Kuhni column extractor. An empirical correlation is proposed for the estimation of the Sauter mean Drop Diameter. The acquired information would be useful in design of liquid–liquid extraction columns.

  • a comparison between Drop size distributions derived from the probability distribution functions and maximum entropy principle case study pilot plant scheibel extraction column
    Chemical Engineering Research & Design, 2017
    Co-Authors: Mehdi Asadollahzadeh, Meisam Torabmostaedi, Rezvan Torkaman, Jaber Safdari
    Abstract:

    Abstract A new model for prediction of Drop size distribution is proposed in an eleven stage Scheibel extraction column by the maximum entropy density approximation technique. In addition, the conventional probability distribution functions (Gamma, Inverse Gaussian, Weibull) have already been applied to estimate the Drop size distribution. The experimental procedures were carried out by three different systems such as toluene–water, n -butyl acetate–water and n -butanol–water. The Drop size distribution was measured with an image analysis technique as a function of the operating conditions and physical properties of the liquid–liquid systems. The results show that the agitation speed has the main effect on the Drop size distribution in the column. However, the effects of phase flow rates are not significant. An empirical correlation is proposed for estimation of the Sauter mean Drop Diameter in terms of operating variables, column geometry and physical properties. The results show that the maximum entropy function describes the Drop size distribution better than the conventional probability distribution functions. The Shannon maximum entropy method provided a novel prediction method for the Drop size distributions in the liquid–liquid extraction columns. The latter that could be used for modeling approaches.

  • a new model for prediction of Drop size distribution in a liquid liquid extraction column
    RSC Advances, 2016
    Co-Authors: Mehdi Asadollahzadeh, Jaber Safdari, Meisam Torabmostaedi, Rezvan Torkaman, Rezvan Torkaman, Jaber Safdari
    Abstract:

    In this study, a new model for prediction of Drop size distribution is proposed in the asymmetric rotating disc pilot plant column (ARDC) by the maximum entropy density approximation technique. The liquid extraction systems including toluene–water, n-butyl acetate–water and n-butanol–water were used with this column. An image analysis technique was applied to determine the Drop size distribution as a function of operating parameters and physical properties. By applying abrupt changes of the operating parameters, the Drop behaviors in the column were investigated. The results show that the agitation speed has a main effect on the Drop size distribution in the column. However, the effects of phase flow rates are not significant. The empirical correlations are proposed to describe Lagrange multipliers in the maximum entropy function in terms of operating variables and physical properties of the systems. Except for these findings, an empirical correlation is proposed for estimation of the Sauter mean Drop Diameter in terms of operating variables, column geometry and physical properties. The proposed correlations are evaluated based on the goodness of fit statistics, namely, χ2, R2 and RMSE. The fitting results by the maximum entropy principle method seem to be fairly accurate and reasonable on the basis of the experimental data. These completed sets of data could be used for modeling approaches in the liquid–liquid extraction columns.

  • studies of Drop behavior and prediction of sauter mean Drop Diameter in various rotary agitated extraction columns
    International Journal of Engineering Transactions B: Applications, 2016
    Co-Authors: Mehdi Asadollahzadeh, Meisam Torabmostaedi, Rezvan Torkaman
    Abstract:

    Knowledge of Droplet behavior is one of the most important criteria for determination of mass transfer kinetics for choosing the type of liquid-liquid extraction columns. Mean Drop size data of dispersed phase Droplets in continuous phase have been obtained for Various Rotary Agitated Liquid-Liquid Extraction Columns . The effects of operational variables such as mass transfer directions with acetone transfer, rotor speed and dispersed and continuous phase velocities have been investigated. The Satuer mean Drop Diameter was influenced mainly by mass transfer direction and agitation speed. In this research work, previous experimental works in agitated extraction columns (RDC, ARDC, PRDC, Scheibel, Oldshue-Rushton and Kuhni columns) are reviewed. Calculations with the literature correlations cannot predict experimental data, thus unified correlations considering the physical properties, operating conditions and geometric parameters were provided to predict the mean Drop size (d32). The results of the proposed correlation were compared with the experimental data obtained from the literature and the present investigation. This correlation covers several physical systems for various rotary agitated extractors. Findings of this study demonstrated that the proposed correlation leads to an accurate prediction for the Satuer mean Drop Diameter in rotary extraction columns.

  • using maximum entropy approach for prediction of Drop size distribution in a pilot plant multi impeller extraction contactor
    RSC Advances, 2015
    Co-Authors: Mehdi Asadollahzadeh, Meisam Torabmostaedi, Shahrokh Shahhosseini, Ahad Ghaemi
    Abstract:

    In this study, the maximum entropy principle is used to predict the Drop size distributions in a multi-impeller column extractor. Three systems, including toluene–water, n-butyl acetate–water and n-butanol–water, were tested in this column. An experimental study of mass transfer conditions was performed in which acetone was transferred between the organic and aqueous phases. The Drop size distribution and Sauter mean Drop Diameter were found to depend largely on the rotor speed and interfacial tension, but were only partially dependent on the phase velocities. Empirical correlations are proposed to describe Lagrange multipliers in the maximum entropy function in terms of the operating variables and physical properties of the systems. In addition, an empirical correlation is proposed for estimation of the Sauter mean Drop Diameter. Also, the combination of computational fluid dynamics (CFD) and Droplet population balance modeling (PBM) has been carried out to predict the Drop size distributions. Comparison shows good agreement between the present models and the experimental data. Experimental results show that the maximum entropy function satisfies the Droplet size distributions for three systems in a multi-impeller column extractor. The acquired information would be useful in the design of liquid–liquid extraction columns.

Meisam Torabmostaedi - One of the best experts on this subject based on the ideXlab platform.

  • using maximum entropy gamma inverse gaussian and weibull approach for prediction of Drop size distribution in a liquid liquid extraction column
    Chemical Engineering Research & Design, 2017
    Co-Authors: Mehdi Asadollahzadeh, Jaber Safdari, Meisam Torabmostaedi, Rezvan Torkaman, Rezvan Torkaman, Jaber Safdari
    Abstract:

    Abstract In this study, Drop size distribution and Sauter mean Drop Diameters were measured and correlated under operating variables and physical properties of the systems using a 113 mm Diameter Kuhni column. Three systems including toluene-water, n -butyl acetate-water and n -butanol-water were experimented in this column. The countercurrent flow pattern of the liquid phases was characterized regarding the Sauter mean Drop Diameter and Drop size distribution; a photographic method was used to assess Drop sizes. The following operating variables were studied: rotor speed, flow rate of both liquid phases and interfacial tension. The Drop size distribution and Sauter mean Drop Diameter were found to depend largely on the rotor speed and interfacial tension, albeit, only partially dependent on the phase velocities. The maximum entropy principle and the conventional probability distribution functions (Gamma, Inverse Gaussian, Weibull) have already been applied to estimate the Drop size distribution. Experimental results show that the maximum entropy function describes the Drop size distribution better than the conventional probability distribution functions for three systems in a Kuhni column extractor. An empirical correlation is proposed for the estimation of the Sauter mean Drop Diameter. The acquired information would be useful in design of liquid–liquid extraction columns.

  • a comparison between Drop size distributions derived from the probability distribution functions and maximum entropy principle case study pilot plant scheibel extraction column
    Chemical Engineering Research & Design, 2017
    Co-Authors: Mehdi Asadollahzadeh, Meisam Torabmostaedi, Rezvan Torkaman, Jaber Safdari
    Abstract:

    Abstract A new model for prediction of Drop size distribution is proposed in an eleven stage Scheibel extraction column by the maximum entropy density approximation technique. In addition, the conventional probability distribution functions (Gamma, Inverse Gaussian, Weibull) have already been applied to estimate the Drop size distribution. The experimental procedures were carried out by three different systems such as toluene–water, n -butyl acetate–water and n -butanol–water. The Drop size distribution was measured with an image analysis technique as a function of the operating conditions and physical properties of the liquid–liquid systems. The results show that the agitation speed has the main effect on the Drop size distribution in the column. However, the effects of phase flow rates are not significant. An empirical correlation is proposed for estimation of the Sauter mean Drop Diameter in terms of operating variables, column geometry and physical properties. The results show that the maximum entropy function describes the Drop size distribution better than the conventional probability distribution functions. The Shannon maximum entropy method provided a novel prediction method for the Drop size distributions in the liquid–liquid extraction columns. The latter that could be used for modeling approaches.

  • a new model for prediction of Drop size distribution in a liquid liquid extraction column
    RSC Advances, 2016
    Co-Authors: Mehdi Asadollahzadeh, Jaber Safdari, Meisam Torabmostaedi, Rezvan Torkaman, Rezvan Torkaman, Jaber Safdari
    Abstract:

    In this study, a new model for prediction of Drop size distribution is proposed in the asymmetric rotating disc pilot plant column (ARDC) by the maximum entropy density approximation technique. The liquid extraction systems including toluene–water, n-butyl acetate–water and n-butanol–water were used with this column. An image analysis technique was applied to determine the Drop size distribution as a function of operating parameters and physical properties. By applying abrupt changes of the operating parameters, the Drop behaviors in the column were investigated. The results show that the agitation speed has a main effect on the Drop size distribution in the column. However, the effects of phase flow rates are not significant. The empirical correlations are proposed to describe Lagrange multipliers in the maximum entropy function in terms of operating variables and physical properties of the systems. Except for these findings, an empirical correlation is proposed for estimation of the Sauter mean Drop Diameter in terms of operating variables, column geometry and physical properties. The proposed correlations are evaluated based on the goodness of fit statistics, namely, χ2, R2 and RMSE. The fitting results by the maximum entropy principle method seem to be fairly accurate and reasonable on the basis of the experimental data. These completed sets of data could be used for modeling approaches in the liquid–liquid extraction columns.

  • studies of Drop behavior and prediction of sauter mean Drop Diameter in various rotary agitated extraction columns
    International Journal of Engineering Transactions B: Applications, 2016
    Co-Authors: Mehdi Asadollahzadeh, Meisam Torabmostaedi, Rezvan Torkaman
    Abstract:

    Knowledge of Droplet behavior is one of the most important criteria for determination of mass transfer kinetics for choosing the type of liquid-liquid extraction columns. Mean Drop size data of dispersed phase Droplets in continuous phase have been obtained for Various Rotary Agitated Liquid-Liquid Extraction Columns . The effects of operational variables such as mass transfer directions with acetone transfer, rotor speed and dispersed and continuous phase velocities have been investigated. The Satuer mean Drop Diameter was influenced mainly by mass transfer direction and agitation speed. In this research work, previous experimental works in agitated extraction columns (RDC, ARDC, PRDC, Scheibel, Oldshue-Rushton and Kuhni columns) are reviewed. Calculations with the literature correlations cannot predict experimental data, thus unified correlations considering the physical properties, operating conditions and geometric parameters were provided to predict the mean Drop size (d32). The results of the proposed correlation were compared with the experimental data obtained from the literature and the present investigation. This correlation covers several physical systems for various rotary agitated extractors. Findings of this study demonstrated that the proposed correlation leads to an accurate prediction for the Satuer mean Drop Diameter in rotary extraction columns.

  • using maximum entropy approach for prediction of Drop size distribution in a pilot plant multi impeller extraction contactor
    RSC Advances, 2015
    Co-Authors: Mehdi Asadollahzadeh, Meisam Torabmostaedi, Shahrokh Shahhosseini, Ahad Ghaemi
    Abstract:

    In this study, the maximum entropy principle is used to predict the Drop size distributions in a multi-impeller column extractor. Three systems, including toluene–water, n-butyl acetate–water and n-butanol–water, were tested in this column. An experimental study of mass transfer conditions was performed in which acetone was transferred between the organic and aqueous phases. The Drop size distribution and Sauter mean Drop Diameter were found to depend largely on the rotor speed and interfacial tension, but were only partially dependent on the phase velocities. Empirical correlations are proposed to describe Lagrange multipliers in the maximum entropy function in terms of the operating variables and physical properties of the systems. In addition, an empirical correlation is proposed for estimation of the Sauter mean Drop Diameter. Also, the combination of computational fluid dynamics (CFD) and Droplet population balance modeling (PBM) has been carried out to predict the Drop size distributions. Comparison shows good agreement between the present models and the experimental data. Experimental results show that the maximum entropy function satisfies the Droplet size distributions for three systems in a multi-impeller column extractor. The acquired information would be useful in the design of liquid–liquid extraction columns.

Jochen Buchs - One of the best experts on this subject based on the ideXlab platform.

  • hydromechanical stress in shake flasks correlation for the maximum local energy dissipation rate
    Biotechnology and Bioengineering, 2006
    Co-Authors: Cyril P Peter, Yusuke Suzuki, Jochen Buchs
    Abstract:

    Shake flasks are widely used in biotechnological process research. Bioprocesses for which hydromechanical stress may become the rate controlling parameter include those where oils are applied as carbon sources, biotransformation of compounds with low solubility in the aqueous phase, or processes employing animal, plant, or filamentous microorganisms. In this study, the maximum local energy dissipation rate as the measure for hydromechanical stress is characterized in shake flasks by measuring the maximum stable Drop size. The theoretical basis for the method is that the maximum stable Drop Diameter in a coalescence inhibited liquid/liquid dispersion is only a function of the maximum local energy dissipation rate and not of the dispersing apparatus. The maximum local energy dissipation rate is obtained by comparing the Drop Diameters in shake flasks to those in a stirred tank reactor. At the same volumetric power consumption, the maximum energy dissipation rate in shake flasks is about 10 times lower than in stirred tank reactors explaining the common observation of considerable differences in the morphology of hydromechanically sensitive cells between these two reactor types. At the same volumetric power consumption, the maximum local energy dissipation rate in baffled and in unbaffled shake flasks is very similar. A correlation is presented to quantify the maximum local energy dissipation rate in shake flasks as a function of the operating conditions. Non-negligible Drop viscosity may be considered by known literature correlations. Further, from dispersion experiments a critical Reynolds number of about 60,000 is proposed for turbulent flow in unbaffled shake flasks. © 2006 Wiley Periodicals, Inc.

  • hydromechanical stress in shake flasks correlation for the maximum local energy dissipation rate
    Biotechnology and Bioengineering, 2006
    Co-Authors: Cyril P Peter, Yusuke Suzuki, Jochen Buchs
    Abstract:

    Shake flasks are widely used in biotechnological process research. Bioprocesses for which hydromechanical stress may become the rate controlling parameter include those where oils are applied as carbon sources, biotransformation of compounds with low solubility in the aqueous phase, or processes employing animal, plant, or filamentous microorganisms. In this study, the maximum local energy dissipation rate as the measure for hydromechanical stress is characterized in shake flasks by measuring the maximum stable Drop size. The theoretical basis for the method is that the maximum stable Drop Diameter in a coalescence inhibited liquid/liquid dispersion is only a function of the maximum local energy dissipation rate and not of the dispersing apparatus. The maximum local energy dissipation rate is obtained by comparing the Drop Diameters in shake flasks to those in a stirred tank reactor. At the same volumetric power consumption, the maximum energy dissipation rate in shake flasks is about 10 times lower than in stirred tank reactors explaining the common observation of considerable differences in the morphology of hydromechanically sensitive cells between these two reactor types. At the same volumetric power consumption, the maximum local energy dissipation rate in baffled and in unbaffled shake flasks is very similar. A correlation is presented to quantify the maximum local energy dissipation rate in shake flasks as a function of the operating conditions. Non-negligible Drop viscosity may be considered by known literature correlations. Further, from dispersion experiments a critical Reynolds number of about 60,000 is proposed for turbulent flow in unbaffled shake flasks.

C De Michele - One of the best experts on this subject based on the ideXlab platform.

  • skewness as measure of the invariance of instantaneous renormalized Drop Diameter distributions part 1 convective vs stratiform precipitation
    Hydrology and Earth System Sciences, 2012
    Co-Authors: M Ignaccolo, C De Michele
    Abstract:

    We investigate the variability of the shape of the renormalized Drop Diameter instantaneous distribution using of the third order central moment: the skewness . Disdrometer data, collected at Darwin Australia, are considered either as whole or as divided in convective and stratiform precipitation intervals. We show that in all cases the distribution of the skewness is strongly peaked around 0.64. This allows to identify a most common distribution of renormalized Drop Diameters and two main variations, one with larger and one with smaller skewness. The distributions shapes are independent from the stratiform vs. convective classification.

  • skewness as measure of the invariance of instantaneous renormalized Drop Diameter distributions part 2 orographic precipitation
    Hydrology and Earth System Sciences, 2012
    Co-Authors: M Ignaccolo, C De Michele
    Abstract:

    Here we use the skewness parameter, and the procedure developed in the companion paper (Ignaccolo and De Michele, 2012), to investigate the variability of instantaneous renormalized spectra of rain Drop Diameter in presence of orographic precipitation. Disdrometer data, available at Bodega Bay and Cazadero, California, are analyzed either as a whole, or as divided (using the bright band echo) in precipitation intervals weakly and strongly influenced by orography, and compared to results obtained at Darwin, Australia. We find that also at Bodega Bay and Cazadero exists a most common distribution of the skewness values of instantaneous spectra of Drop Diameter, but peaked at values greater than 0.64, found at Darwin. No appreciable differences are found in the skewness distributions of precipitation weakly and strongly influenced by orography. However the renormalized Drop Diameter spectra of precipitation with strong orographic component have fatter right tail than precipitation with a weaker orographic component. The differences between orographic and non-orographic precipitation are investigated within the parametric space represented by number of Drops, mean value and standard deviation of Drop Diameter. A filter is developed which is able to identify 1 min time intervals during which precipitation is mostly of orographic origin.

  • statistical collapse of stratiform and convective Drop Diameter distributions at the ground
    Geophysical Research Letters, 2010
    Co-Authors: Massimiliano Ignaccolo, C De Michele
    Abstract:

    [1] The probability density function of the Drop Diameter at the ground is investigated during stratiform and convective precipitation intervals at Darwin, Australia. We show how, after a renormalization procedure of the Drop Diameter, the empirical probability density functions of both types of precipitation collapse in a single curve, indicating the possible existence of an invariant distribution of the Drop Diameter at the ground.