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CHARGING MECHANISMS IN CLOUDS AND THUNDERSTORMS 121 particles the relaxation time is too long to permit charging to the maximum value given by Eq. (9.8). As stated above, the charge attained by an ice pellet is less than one hundredth that of drizzle in a comparable time. In addition, the average contact angle of 45Â° yields only a factor-of-2 increase over the 70Â° angle assumed for drizzle. Thus, induction charging between dry hail and ice particles is severely limited by the long relaxation time for ice. In collisions between wet hail and cloud drops or ice crystals, charge relaxation should be controlled by liquid water and the charging rate comparable to induction in the rain stage. The maximum charge attained would be governed by the average contact angle in Eq. (9.8) of over 85Â° for wet hail and cloud droplets (or small drizzle drops) and 45Â° for wet hail and rebounding ice crystals. Thus, the most powerful interaction for induction charging in the hail stage would appear to be collisions between wet hail and ice crystals. Thermoelectric Charging Up to this point, we have discussed mechanisms that depend on the ambient electric field. We now turn to charge transfer between cloud and precipitation particles where an external field is unnecessary. This class of microscale separation mechanism originates from intrinsic charge carriers and their relationship to bulk properties. Thermoelectric charging is the result of a thermally induced gradient in the concentration of carriers that transport positive and negative charges. For a linear gradient in temperature, the steady-state balance between carrier diffusion and drift produces a field of E = kdT/dx with an empirically determined coefficient of k = 2 mV/Â°C (Latham and Mason, 1961). The corresponding surface charge density from Gauss's law is about (10â15 C/cm Â°C) dT/dx (where the gradient is in degrees per centimeter). We can estimate the steadystate charge (in coulombs) for a short ice cylinder of radius r by for a temperature difference âT (Â°C) across a length of Ïr (cm) and a surface charge on an area of Ïr2. In the hail stage a temperature gradient would occur during the contact between a precipitation particle, warmed by the freezing of rime (e.g., soft hail) and a smaller particle. A negative charge would be transferred to the precipitation particle with Q = 10â16 C for a small particle using r = 100 Âµm and with a rather large temperature difference of âT = 10Â°C. Thus, the charging in a single collision is rather insubstantial when compared with values of greater than 1 pC measured for soft hail in thunderstorms. These estimates of thermoelectric charging are further reduced when we account for the limitation imposed by transient contact. Both theory and experiment show that about 10 msec are required to reach a maximum charge comparable to Eq. (9.9) (Latham and Stow, 1967). Since the contact time between precipitation and cloud particles is many orders of magnitude smaller we can reasonably expect that our estimate of 10â16C for a single collision would be reduced to well below 10â18 C. Even under the most favorable conditions (i.e., 104 collisions within 20 minutes for high ice crystal concentrations at 100 per liter), the accumulated charge would be less than 10â14 C. In contrast to the estimate of considerably less than 10â18 C per event for thermoelectric charging, recent laboratory studies have yielded up to 0.3 pC per collision between a small ice particle and a simulated hailstone (Gaskell and Illingworth, 1980). Thus, there is evidence to demonstrate that mechanisms far more powerful than thermoelectric charging are at work in the hail stage. Interface Charging Two types of interface charging will be discussed: freezing potentials involving impurities and contact potentials. Charge can be transferred across a freezing interface by selective incorporation of ions, originating from dissolved salts and gases, into the advancing ice. In the steady state, a balance is reached between the selection process and the relaxation of charge in the ice. A transient in potential is observed when a plane interface advances past an electric probe. Early workers measured large potentials in the freezing of aqueous solutions containing naturally occurring salts over the range of concentrations found in precipitation (Workman and Reynolds, 1948). Subsequent researchers have made more refined measurements and developed a theoretical description of freezing potentials (e.g., see Caranti and Illingworth, 1983a). Others have investigated charge transfer between solution drops and simulated hailstones (e.g., Latham and Warwicker, 1980). As a result of these later studies and related ones (Gaskell and Illingworth, 1980; Jayaratne et al., 1983; Caranti and Illingworth, 1983b), the role of interface charging in hailstage electrification is being clarified. As indicated above, two methods are used to study interface charging: (1) potentials are measured as a function of solute impurities and supercooling, with differing growth rates and interface areas; and (2) transfer
CHARGING MECHANISMS IN CLOUDS AND THUNDERSTORMS 122 of charge is measured for collisions between particles and a much larger ''target" electrode coated with ice as a function of solute impurity, supercooling, and speed of impacting drops. Other conditions have also been varied, such as the target temperature and the riming rate of the target for a mixture of supercooled drops and ice crystals. Investigation of these various parameters covers many of the conditions found in the hail stage and helps to sort out contributions of freezing potentials from contact potentials and the thermoelectric effect. Recent studies have shown that interface potentials for bulk solutions near 0Â° C are substantially reduced by supercooling, apparently from the effects of the dendritic interface (Caranti and Illingworth, 1983a). Potentials could not be measured for 100-Âµm-diameter droplets, in the range â 1 to â 20Â°C, impacting on an ice substrate because the potential was either too small (less than 100 mV) or it decayed too rapidly (in less than 5 msec). A reduction in charge transfer was also found by Latham and Warwicker (1980) for millimeter-size drops splashing from ice targets in comparison with earlier findings for drops not completely cooled by the air (Workman, 1969). In fact, the charging was of the wrong sign for the freezing of sodium chloride solutions and independent of concentration, indicating that the freezing potential was not the dominating mechanism. A more likely cause was a common form of interface charging associated with the disruption of an air-water interface (i.e., spray electrification). The charges on the air- water interface are readily overwhelmed by polarization charges. For example, Latham and Warwicker (1980) found that charge transfer was substantially increased by applying a field of only 100 V/m. As the above comparisons demonstrate, the relative importance of charge transfer during the freezing of aqueous solutions is greatly diminished by supercooling. The effect of dissolved ions on charging seems to be negligible in the splashing of supercooled solution drops from ice targets. However, the above considerations do not rule out the freezing potential as a factor in the transfer of charge for a target collecting solution drops and also colliding with ice crystals. Before examining collisions involving ice crystals during rime formation, we will consider the transfer of charge between an ice-coated target and rebounding ice particles in the absence of droplets. Experiments have shown that a target of ice accumulates either negative or positive charge in collision with ice particles depending on whether the target surface has undergone sublimation or deposition (Buser and Aufdermaur, 1977). It was concluded from an additional experiment that the condition of the surface was controlling the charge transfer rather than a thermal gradient as would have been expected for the thermoelectric effect. Buser and Aufdermaur (1977) also found that the transfer of charge between ice particles and targets of various metals was proportional to the contact potential. Thus variations in the surface state and, in particular, the free energy of the charge carriers is a major factor in this type of charge separation. The differing signs in the ice-target experiments can be attributed to differing surface characteristics of the target. The surface exposed during sublimation was composed of ice originally formed near 0Â°C, whereas a frosted surface was produced by deposition at the experimental condition of â 45Â°C. More recently Gaskell and Illingworth (1980) studied interface charging in the temperature range from â 5 to â 25Â°C. They also found negative charging for a subliming target and positive charging during deposition without any direct evidence of the thermoelectric effect. Frozen droplets of 100-Âµm diameter transferred charges of about â 0.015 pC for sublimation and + 0.10 pC for deposition. Little variation in charging was found over the temperature range or when the ice target contained ion impurities. These results are consistent with interface charging by a contact potential mechanism whereby the surface states of the charge carriers differ between the smooth surface formed near 0Â°C, exposed during sublimation, and the frosted surface formed by deposition. Additional support for the contact potential hypothesis comes from measurements of the effects of impact velocity and droplet size on charging, since the transfer of charge was found to increase with both of these parameters in a manner consistent with an increase in contact area (Gaskell and Illingworth, 1980). Charging was also examined by Gaskell and Illingworth (1980) for a target undergoing simultaneous collisions with ice particles of 100 Âµm diameter and supercooled droplets at low to moderate liquid water contents (0.05 to 0.85 g/ m3). The charge transferred to the target was positive at â 5Â°C and negative at â 15Â°C with the transition near â 10Â°C. The sign reversal was possibly caused by changes in the contact potential with rime structure at different temperatures (Caranti and Illingworth, 1980). An estimate of interface charging in collisions between various sizes of cloud and precipitation particles can be obtained from the work of Gaskell and Illingworth (1980) in which the charge was found to be related to the contact area through the impact speed and ice particle size. In the following formula, we have combined their relation for impact velocity (Q Âµ U 1.6) with an expression for the velocity of hail (U Âµ R 0.8, e.g., see Pruppacher and Klett, 1978) and have included their scaling for ice particle size (Q Âµ r 1.7):
CHARGING MECHANISMS IN CLOUDS AND THUNDERSTORMS 123 The factor F is a function of the interface potential, depends on the nature of the contact surfaces, and may be evaluated from laboratory data. For example, in the riming experiment of Gaskell and Illingworth (1980) the collisional charge was Q â 0.04 pC in the range â 15 to â 20Â°C for r = 50 Âµm and R = 0.43 cm (a size with a terminal velocity at the laboratory impact speed, 8 m/sec). Thus, for the interface conditions corresponding to these experiments the factor for the interface potential is F = â 970 (with Q in picocoulombs and the radii in centimeters). The latest investigation of ice crystals rebounding from riming targets provides additional evidence for interface charging (Jayaratne et al., 1983). In this study the target electrode was moved through a cloud of supercooled droplets that was seeded to produce ice crystals. Charging of the target began shortly after seeding and ended after about 4 minutes when the ice crystals settled out of the cloud. At low liquid-water contents the maximum current was positive at a temperature below about â 10Â°C and negative at temperatures above, indicating a reversal in sign of the charge in a manner similar to that of Gaskell and Illingworth (1980). The results of Jayaratne et al. are difficult to interpret in terms of charge transfer because of transients in the ice crystal size, the liquid-water content, and the current measured at the target. However, the charge was estimated for single events by the investigators from the target current and ice crystal concentration. In one case they estimated Q 0.01 pC for an ice crystal size of 125 Âµm diameter, where the target speed was 2.9 m/sec, the temperature â 6Â°C, and the liquid-water content 2 g/m3. The factor for the interface potential that corresponds to these experimental conditions is F = 870 (with Q in picocoulombs and the radii in centimeters). The variation in the sign-reversal temperature with liquid-water content was attributed to changes in the freezing process or to variations in the structure and density of the rime. This view is consistent with interface charging by the contact potential mechanism. However, sufficient data are unavailable to express the factor for the interface potential as a function of the riming rate or fundamental parameters such as temperature and liquid-water content. Another aspect investigated by Jayaratne et al. (1983) was the variation in charging with solute impurities in the cloud droplets. For cloud water containing natural amounts of sodium chloride they determined that about â 0.003 pC was transferred by ice crystals of 50-Âµm diameter at â 10Â°C and 1 g/m3. A charge of the same magnitude but of the reverse sign was found for ammonium sulfate under the same conditions. At â 20Â°C the charge was â 0.08 pC for sodium chloride and +0.08 pC for ammonium sulfate. It should be noted that with these impurities there was no sign reversal in charging over the temperature range investigated (â 4 to â 20Â°C). The factor for the interface potential based on the sodium chloride measurements is F â 1100 for â 10Â°C and F â 3100 at â 20Â°C. The corresponding factors for the ammonium sulfate measurements are the same but have a positive value. In contrast to the above study, Caranti and Illingworth (1983b) found that solute impurities at natural concentrations did not have a measurable effect on the contact potential of a riming substrate. Thus there seems to be contradictory evidence on the role of solutes in contact charging. A direct comparison between these two studies may be inappropriate because the rime structure and the resultant factor for the interface potential may have been affected by differing experimental conditions. If the solute influenced the rime structure in the experiments of Jayaratne et al. (1983) either directly during the freezing or indirectly by alternating the cloud properties, then their results would have been affected by the contact potential mechanism. In summary, interface charging occurs between riming precipitation particles and ice crystals with a negative charge acquired by the precipitation for temperatures below about â 15Â°C or â 20Â°C depending on the liquid-water content. The separation of charge appears to result from an interface potential with an amount given by Eq. (9.10) that incorporates the variation in contact area through the ice crystal size and hail size (i.e., impact speed). The interface potential enters Eq. (9.10) through an empirical factor, F. Natural amounts of solute also affect the magnitude and sign of charging. However, it is unclear whether the resultant change in interface potential occurs as a freezing potential or indirectly as a contact potential through an altered rime structure. Before applying the results of these laboratory findings to the hail stage we first consider the appropriate value of the factor for the interface potential. In the evaluations presented here F was found to be in the range â 3100 to + 3100. Thus the charge obtained by a precipitation particle of R = 1 mm in a collision with an ice particle of r = 50 Âµm has a range, according to Eq. (9.10), of â 0.02 to + 0.02 pC. This range is increased to + 0.15 pC for R = 2 mm and r = 100 Âµm. These calculated values also correspond to the measured range presented in this section because the particle sizes correspond approximately to the experimental sizes (r) and impact speeds. For a particular application to the hail stage we consider a situation similar to the experiment of Gaskell and Illingworth (1980) at low to moderate liquid-water contents and in the temperature range â 15 to â 20Â°C. For this set of conditions the type of rime is appropriate for soft hail. The estimated charge transfer