Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
CHARGING MECHANISMS IN CLOUDS AND THUNDERSTORMS 119 Induction Charging In addition to coalescence and breakup, the collision between drops can result in interactions where the two drops bounce apart. The amount of charge transferred between drops that are polarized depends on the contact angle relative to the field, the contact time, the charge relaxation time, and the net charge on the drops as well as the magnitude of the polarization. Induction charging was first considered by Elster and Geitel (see Chalmers, 1967) for contact between a large and small sphere along a line parallel to the field. Later studies included the effects of image charges, contact angle, and net charge with extensions of theory to ice particles. In the rain stage we will consider only induction charging for drops while reserving the ice aspects of this mechanism for the hail stage. The importance of contact angle is immediately obvious from the induced surface charge on a conducting sphere in a uniform electric field given by 3ÏÎµ0 E cos Î¸ and shown schematically on Figure 9.5a. However, the contact angle is a hydrodynamic problem of two deformable bodies in a gaseous medium with its own set of governing parameters. Even in the absence of electric effects, such interactions are understood only in terms of broad categories in a manner similar to the breakup phenomena. For example, contact angles of 50-90Â° are associated with bouncing drops, and angles of 60-80Â° with partial coalescence. These phenomena occur over sizes intermediate to the ranges for coalescence and breakup. Laboratory experiments indicate bouncing between large and small drizzle drops and partial coalescence between drizzle and large cloud drops. We will emphasize the charge transfer between dissimilar sizes, as the above ranges suggest. Interactions between similar size drops are relatively unimportant because their similar fall speeds lead to infrequent collisions. Figure 9.5 Charge transfer by the induction mechanism for colliding drops in a downward-directed field: a, charge distribution on a polarized drop; b, contact at moderate angle; c, charge generation after separation. The maximum charge on a large drop (R) acquired by collision with a small drop (r) for dissimilar sizes is given approximately by If we assign an average contact angle of 70 (whereby 12 cos Î¸ = 4), the result is similar to Eqs. (9.6) and (9.7) except for the scaling by r 2 instead of R 2 . It should be obvious from the r 2 dependency that the induction mechanism is not a powerful means of direct charge separation. However, as Figure 9.5 demonstrates, the microscale charge separation followed by differential sedimentation reinforces the existing field. Therefore the induction mechanism may be capable of significant charge separation on the cloud scale through positive feedback to Eq. (9.8). There are several possible limitations on induction charging between drops. First, charge transfer must occur on a time scale compatible with contact. When we consider the interaction between drizzle drops and large cloud droplets, appropriate for partial coalescence or bouncing, the contact time ranges from 1 to 50 Âµsec. This is several orders of magnitude longer than the charge-relaxation time for cloud and rain water. Therefore the contact time is not a limitation for charge transfer between drops. A second possible limitation occurs because an electric field can transform partial coalescence (or bounce) into complete coalescence. This effect has not been studied in detail; however, laboratory simulations of induction charging (Jennings, 1975) showed that the separation probability is reduced by an order of magnitude when the field is increased from 10 kV/m to 30 kV/m. Other studies with charged drops of similar sizes show suppression of bounce at charges comparable with those induced by the above fields. Hence, there is evidence suggesting a limit on induction charging but at fields well above those found in the rain stage (typically less than 1 kV/m). A third possible limitation, one that applies to bouncing drops but not to partial coalescence, is that charge transfer must occur across an air gap. Transfer mechanisms such as field emission or corona, in a small air gap, usually require very high fields (greater than 107 V/m). Since the field between drizzle drops is enhanced by induced charges by a factor of only about 50 to 500, thunderstorm fields appear to be required for charge transfer across the air gap between bouncing drops. However, neither charge transfer between bouncing drops nor the limitation of field-induced coalescence have been adequately investigated.