4.1. Distortion of Drops With or Without Electric Field
 The measured axis ratios (b/a) for uncharged drops of different diameters in vertical electric fields of 0, 1, 3, and 5 kV cm−1 in this experiment are compared to the wind tunnel experiment data of Rasmussen et al.  in vertical electric fields of 0, 2, 4, and 5 kV cm−1 in Figure 3. Vertical electric fields of <5 kV cm−1 do not have any appreciable effect on b/a in case of drops of diameter <3.5 mm. The axis ratio b/a decreases with the increase in drop size but increases with the increase in vertical electric field. For example, a drop of 5-mm diameter falling in a vertical electric field of 5 kV cm−1 undergoes an increase in its axis ratio of about 10.5% as compared with that when the electric field is equal to zero. As the external electric field increases, the shape of a drop, as Rasmussen et al.  puts it, “is the result of a complicated, continuously changing interplay between aerodynamic, surface tension, hydrostatic and electric forces.” Experimental observations of Rasmussen et al.  and theoretical model results of Coquillat et al.  show that with further increase in electric field, the decreasing trend in b/a reverses and large drops become eventually spherical and then prolate. In still higher electric fields, larger water drops break up under the influence of the electric field. Rasmussen et al.  extrapolated their experimental results and found the critical electric fields for drop’s breakup to be equal to 10.38 and 9.23 kV cm−1 for two drops of 3.4- and 5.0-mm diameters, respectively. Also shown in Figure 3 are the axis ratios from the model results of Chuang and Beard  and Coquillat and Chauzy . Present results appear to be consistent with those of the theoretical models in the respect that the axis ratio decreases with the increasing drop diameter in all ambient electric field conditions. As compared with the theoretical model values, our results show slightly lower values of axis ratio in case of drops of diameter <4.5 mm and slightly higher values of axis ratio in case of drops of diameter >5.5 mm when these drops are subjected to vertical electric fields of up to 5 kV cm−1. Enhanced influence of electrical forces on an oscillating drop in changing its axis ratio is expected because of larger accumulation of charge resulting in larger electric force per unit area on drop’s deformed surface as compared to a drop which is prevented from oscillating and is forced to keep an equilibrium shape as in most of the theoretical treatments of the problem [Pruppacher and Klett, 1998]. The experimental data of Rasmussen et al.  show an opposite trend of the increasing axis ratios when water drops exceed a critical size in the range of 3.4–5.2 mm for the range of electric fields examined in their experiments. Our observations in vertical electric field do show some flattening of the axis ratio versus drop diameter curve in this drop size range but not the increase in axis ratio with diameter as observed by Rasmussen et al.  Values in the experiments of Rasmussen et al.  and ours, however, will fall within the error bars if it is assumed that our results are slightly biased upwards or Rasmussen et al.'s  results are slightly biased downward because of the difference in the airflow characteristics possibly resulting because of different experimental setups in their wind tunnels. There are no data available for comparison of our results for deformation of very large drops of diameter exceeding 6 mm.
 Figure 4 shows the change in axis ratio with drop diameter in absence as well as in presence of horizontal/vertical electric field. Vertical bars show standard errors along with the mean axis ratios. The numbers marked above the vertical bars show the number of images of each drop size used to calculate the average axis ratio of the drop. A comparison of the various curves in Figure 4 effectively demonstrates the stretching and elongation of the drop in the direction of electric field. Decrease in axis ratio with the increasing drop size is amply demonstrated for all values of electric field. However, as compared with the case when E = 0, vertical electric field decreases the oblateness and tends to make the drop more spherical. On the other hand, horizontal electric fields increase the oblateness of the drop as compared with the case when there is no electric field. Moreover, horizontal electric fields are more effective than the vertical in distorting the drop; the larger the drop, the larger is the difference between the axis ratios produced by the vertical and the horizontal field configurations. For example, an electric field of 3 kV cm−1 changes the axis ratio of a 4.05-mm drop by 6.3% if the electric field is horizontal, but only by 1.74% if the electric field is vertical. The observation well illustrates the fact that both aerodynamic and electrostatic distortions act together in a horizontal electric field but counteract in a vertical field. It is important to note, however, that there is sizable difference in the ratio b/a between the field and no-field configurations even in case of drops of diameter < 4 mm when the electric field is horizontal. For example, vertical electric field of 1 kV cm−1 or less has no or negligible influence in distorting the drops of diameter < 4 mm. On the other hand, horizontal electric field of the same magnitude changes the axis ratio of 2.6 mm diameter drops by ∼3% of the value when E = 0. Effect of electric field in changing axis ratio of the drops larger than 4 mm in diameter is much stronger if the field is horizontal rather than vertical.
Figure 4. Change in axis ratio (b/a) of the drop with drop diameter in absence and presence of horizontal/vertical electric field strength of 1, 3, and 5 kV cm−1. All values of the vertical and horizontal electric field, Ev and Eh, respectively, are in kV cm−1.
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 Behavior of the curves in Figure 4 again significantly changes for very large drops exceeding 6.5 mm in diameter. While the curves in case of vertical electric field become steeper for drops of diameter > 6.5 mm, the curve in case of horizontal electric field of 3 kV cm−1 for such large drops shows a tendency to flatten and level off when the value of axis ratio becomes ∼0.5. Moreover, value of axis ratio does not become lower than this value even when higher values of horizontal electric fields are applied. For example, the lowest value of axis ratio still remains at 0.5 even when horizontal electric field of 5 kV cm−1 is applied around such very large drops. It is likely that at this value of average axis ratio, distortion of the drop is sufficient to cause its breakup. In the absence of electric field, drops can attain this value as their size increases. For example, the wind-tunnel measurements of Pruppacher and Pitter  also show that the largest stable drop in quiet air is 9.0 mm in diameter whose axis ratio is 0.55. However, the electrostatic forces acting in presence of the horizontal electric field cause even smaller drops to attain these values: the higher the electric field, the smaller is the drop size which can attain this axis ratio. Observations of Kamra et al.  show that half-life of drops decreases with the increase in horizontal electric field and that a higher number of drops break up if the value of applied horizontal electric field is increased. For example, the number of 6.3-mm diameter drops that breaks up increases from 20% to 70% or 90% when the horizontal electric field is increased from 300 to 400 or 500 kV m−1, respectively.
 Coquillat et al.  have recently studied the distortion of uncharged drops falling at their terminal velocities in quiescent air in a horizontal electric field in a theoretical model. In Figure 5, we compare results of our experiment in horizontal electric field with the model results of Coquillat et al. . Somewhat lower values of axis ratio in our experimental results as compared to theoretical values in Figure 5 are most likely due to neglect of the oscillations of the drop in theoretical models. As explained in detail in section 4.1, enhanced influence of electrical forces on an oscillating drop in changing its axis ratio is not considered in theoretical models (see also Pruppacher and Klett  for details). The theoretical and experimental curves in Figure 5, however, show two similar features. First, both sets of curves show nonlinear increase in drop distortion with the increase in drop size and horizontal electric field. Second, although theoretical curves are limited to 5.0-mm drops only, both sets of curves indicate a tendency of leveling off when the axis ratio attains a value of about 0.5 under the combined effect of increasing either drop size or electric field.
4.2. Drop Oscillations in Electric Field
 The water drops freely suspended in an airstream are known to oscillate in the prolate-oblate mode. Magnitude of oscillations, however, differs from one oscillation to the other. Most of the experimental studies and all theoretical models compute the average axis ratios for distorted drops. The average axis ratio of an oscillating drop differs from its equilibrium value. Beard  has shown that prolate-oblate oscillations about an equilibrium raindrop shape produce a shift in the average axis ratio toward higher values. The shift would increase or decrease in the presence of electric field, depending on its direction, because the stresses acting on the drop change as the drop changes its shape. Moreover, it is important to know the extreme values of axis ratio which an oscillating drop undergoes. Knowledge of such maximum distortion is particularly important when the drop is oscillating in presence of an electric field, as such extreme values of drop’s distortion may initiate instability and cause corona discharge from water drops [Kamra et al., 1993].
 In this experiment, we study the frequency distribution of axis ratios which an oscillating drop attains in its deformed state in each oscillation under different electric fields. To compute the frequency of axis ratio of an oscillating drop in an electric field, the axis ratio of every individual drop image in electric field is subtracted from the average value of axis ratio in the no electric field case. This difference is plotted on the x axis in 0.05 interval. The number of times this difference attains a value is plotted on the y axis as percentage of the total number of drop images counted in a particular value of electric field. Figures 6a and 6b show these values for all drops oscillating in the vertical and horizontal electric field, respectively, of 0, 1, 3, and 5 kV cm−1.
Figure 6. (a) Histograms showing the variation of − Xi with N0.05/NT in vertical electric field of 0, 1, 3, and 5 kV cm−1. − Xi is the difference between the mean axis-ratio value in no electric field and the axis ratio of individual drop image in electric field. N0.05/NT is the ratio of number of drops in 0.05 interval (N0.05) and total number of drops (NT) of all sizes, in percentage. (b) As in Figure 6a but in horizontal electric field.
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 In Figure 6a, the center of gravity of histogram shifts toward negative side of the x axis as the electric field increases, indicating that the drop becomes less oblate more often during its oscillations in higher vertical electric field. On the other hand, in Figure 6b, the center of gravity of histogram shifts toward positive side of the x axis as the electric field increases, indicating that the drop becomes more oblate more often during its oscillations in higher horizontal electric field. Moreover, when the drop is subjected to the vertical or horizontal electric field, the maximum value of the oblateness of the drop increases although for a very small number of times, as compared with the case when electric field is absent. This is likely to happen because of the feedback action of distortion and the electric field enhancement at the drop’s surface as suggested by Kamra et al. . Although these extreme values of distortion may be attained very rarely, the drop’s shape in such oscillations may cause initiation of corona discharge at their surfaces which may eventually result in triggering a lightning discharge. Any effect of the cross-wire screen/electrode on drop’s oscillations can be ignored here in view of the fact that for taking drop’s photographs in both cases, with and without electric field, the screen and electrode were kept in the same positions.