The internal circulation and the shape of water drops falling at terminal velocity in air of 20°C at sea level pressure, and nearly water saturated, were studied by means of a wind tunnel. Drops with an equivalent radius a0 smaller than 140 um had within the experimental error no detectable deformation from spherical shape. Drops of sizes 140 μm ≤ a0 ≤ 500 μm were slightly deformed into an oblate spheroid. The deviation of these drops from spherical shape was found to be in fair agreement with that theoretically predicted by Imai (1950) and others. The deformation of drops of sizes 0.5 mm < a0 < 4.5 mm was found to be linearly related to the drop size. Such a linear relationship is predicted by the semi-empirical calculations of Savic (1953).



By means of a tracer technique it was established that water drops falling at terminal velocity in air have a well developed internal circulation. The flow pattern inside a drop was found to be consistent with the flow pattern of the air around the drop and that predicted theoretically by Hadamard (1911) and by Hamielec and Johnson (1962). The surface velocity at the equator of a drop was found to be about 1/100 of the drop's terminal velocity. The experimentally determined internal velocities were compared with those predicted theoretically by McDonald (1954) from boundary layer theory and by Hadamard (1911) based on Stokes flow.

A wind tunnel investigation of the internal circulation and shape of water drops falling at terminal velocity in air

http://directory.umm.ac.id/Data%20Elmu/jurnal/A/Atmospheric%20Research/Vol55.Issue3-4.2000/889.pdf

Notes on the state-of-the-art numerical modeling of cloud microphysics

Particle–bubble collision models — a review

Empirical correlations for the prediction of mass transfer coefficients for single drops are presented. Published experimental results for both circulating and oscillating drops are considered. Correlation for the individual continuous-phase mass transfer coefficient, which is based on data from 596 measurements taken from 10 different groups of investigators, reproduces the data with an average absolute error of 14.1%. This is then used to determine a correlating equation for the individual dispersed-phase mass transfer coefficient on the basis of data for overall dispersed-phase mass transfer coefficient taken from 21 sources. The average absolute value of the relative error in the predicted values of overall dispersed-phase mass transfer coefficient from the experimental points by using the correlations for individual mass transfer coefficients is 24.5%. It is further shown that by allowing for the effects of power input per unit mass and dispersed-phase hold-up, the correlations for single drops can be extended to extraction columns. The correction factors required for this purpose have been obtained by using simulated values of overall mass transfer coefficients for pulsed perforated-plate, Karr reciprocating-plate, Kuhni, and rotating disc columns.

Correlations for Prediction of Mass Transfer Coefficients in Single Drop Systems and Liquid–Liquid Extraction Columns

An approach is developed enabling one to calculate the collision efficiency and the collision kernel within a wide range of the Reynolds numbers (from 0 to 100) corresponding to drops up to 300-mm radii. The flow velocity field induced by falling drops is obtained by interpolation of two analytical solutions: the Stokes solution suitable for description of cloud droplets with radii below 30 mm (Re , 0.4) and the solution given by Hamielec and Johnson suitable for drops with radii ranging from 40 to 300 mm. The collision efficiency and the collision kernel are calculated at different heights of 1000, 750, and 500 mb. It is shown that both the collision efficiencies and the collision kernel significantly increase with height. This increase of the collision kernel is by 90% caused by the increase in the collision efficiency, and only by 10% is related to the increase of the swept volume. This is because of the high sensitivity of the collision efficiency to the relative drop‐drop velocity. The increase of the collision kernel with height is different for different drop pairs. It is maximal for droplets of 5‐10 mm colliding with comparably small drop collectors of 15‐25-mm radii. For these drop pairs the collision kernel at the 500-mb level is twice as large as (and even more than) that at the 1000-mb level. The collision efficiencies are calculated and presented in tables, with the high resolution required to describe sharp gradients for small droplets. The drop spectrum broadening and the rate of precipitation formation are found to be sensitive with respect to the variations of the collision rate with height. This is illustrated by solving the stochastic equation of collisions. The increase of the drop‐drop collision rate with height turned out to be significant and thus should be incorporated in numerical cloud models. The increase of the collision kernels with height for certain drop sizes can be of much importance in the context of the problem of the effect of ‘‘coalescence nuclei’’ arising on ultragiant cloud condensation nuclei, on the rain formation. This effect can also be important in rain enhancement by means of hygroscopic seeding. Possible effects of the density of colliding particles and the air density on the rate of riming are discussed.

Collision Efficiency of Drops in a Wide Range of Reynolds Numbers: Effects of Pressure on Spectrum Evolution

Approximate velocity profiles and terminal velocities have been predicted for fluid spheres moving in viscous media under the influence of gravity. The equations of motion were satisfied approximately using a numerical method after Kawaguti(1).



Predicted terminal velocities are compared with literature data and with data measured by one of the authors(2). The agreement is reasonable for Reynolds numbers up to about 80.



The effect of the asymmetry of the exterior flow upon the symmetry of the interior flow is discussed.



Les auteurs predisent les profils de vitesse approximatifs et les vitesses terminales pour des spheres fluides qui se deplacent dans un milieu visqueux, sous l'influence de la gravite. On satisfait de facon approximative aux equations du mouvement en utilisant une methode numerique proposee par Kawaguti.1



On compare les vitesses terminales predites avec les donnees de la litterature et avec les valeurs mesurees par un des auteurs.2 L'accord est satisfaisant pour des nombres de Reynold allant jusqu'a 80.



On discute l'effet de l'asymetrie de l'ecoulement exterieur sur la symetrie de l'ecoulement interieur.

J. M. Whitehead

Papers

Viscous flow around fluid spheres at intermediate reynolds numbers (II)