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.
MODELS OF THE DEVELOPMENT OF THE ELECTRICAL STRUCTURE OF CLOUDS 134 may also be separated at Î¸ â¤ 90Â°, leading to their discharge (Al-Saed and Saunders, 1976). On the other hand, nonspherical solid or liquid particles can separate larger charges by the inductive process as a result of the much enhanced electric fields near them (Censor and Levin, 1974). The second and third terms on the right side of Eq. (10.1) represent the limitation of charge transfer due to the initial charge on the large (Q) and small (q) particles, respectively. The constant Ï then is a geometrical factor that represents the effect of the capacitance of the two on the charge transfer. The last term on the right represents the limitation to charge transfer due to the electrical conductivity of the materials that compose the particles (Sartor, 1970; Caranti and Illingworth, 1983; Illingworth and Caranti 1984). Ice particles at low temperatures, for example, have low bulk and surface electrical conductivities that lead to longer relaxation times Ï. This means that in any given collision there is the possibility that not all the available charge will be transferred, since the contact time t c might be shorter than Ï. Indeed a recent laboratory study by Illingworth and Caranti (1984) on the dependence of charge transfer during ice-ice collisions on the surface conductivity of ice, suggests that for ice-ice interactions the inductive mechanism is not efficient. Interactions of two particles can result in either collection or rebound. To describe the probability of these two end results a collision efficiency, E1 , and a coalescence efficiency, E 2 , are defined. E1 represents the probability of two cloud particles to interact, and E2 represents the probability of the interacting particles to coalesce. Therefore, the collection probability is E 1 Â· E 2 , and the rebound probability is (1 â E2 ) E1. To separate charge an electrical contact among rebounding particles must be achieved. Only a fraction, E 3, of the particles that collide and rebound make such electrical contact. We will refer to E3 as the electrical contact probability. Therefore, the probability for separating charge between two cloud particles is P = E1 (1 â E 2 ) E 3. The rate of charge buildup on the large particles per unit volume as a result of collisions of particles can be expressed as where R and r are the radii of the large and small particles, respectively, V and Ï are their fall speeds, and N and n are their concentrations. The term PâQ represents the charge separated per interaction, while E1 E2 q accounts for the discharge of the large particles resulting from collection of oppositely charged particles (Scott and Levin, 1975). Non-inductive Process Many noninductive mechanisms have been proposed to explain the formation of electricity in thunderstorms. Among the most powerful are the thermoelectric effect (Reynolds et al., 1957; Latham and Mason, 1961), freezing potentials (Workman and Reynolds, 1948), and contact potentials (Buser and Aufdermaur, 1977; Caranti and Illingworth, 1980). All of these rely on the electrochemical nature of water or ice for charge separation. Thermoelectric Effect Charge separation results from interactions of ice particles of different surface temperatures. On contact the temperature gradient across the surface causes the H+ ions to migrate from the warmer particle to the cold one, leaving OHâ ions on the warmer ice particle. Subsequent rebound of these particles will result in charge separation. The amount of charge separated in this process depends on the temperature and the temperature gradient. In most models, the value of the charge separation per interaction is taken as a constant, regardless of the temperature or temperature gradient. Freezing Potentials Workman and Reynolds (1948) and Pruppacher et al. (1968) observed that high electrical potentials develop across an ice-water interface when the water contains small amounts of impurities (~ 10â5 molar). These potentials develop as a result of preferential incorporation of certain ions from the solution into the ice lattice, leaving the ice and the liquid solution oppositely charged. In clouds, if such a situation occurs, fragments of the solution can be thrown off as a result of the impact of other particles. These fragments carry away charge of one sign, leaving the ice particle with the opposite charge. Gravitational settling can then separate the two charges in space. These early works suggested that the magnitude and sign of the separated charge depend critically on the amount and type of impurity used. Various laboratory experiments conducted to simulate this charging mechanism have resulted in a surprisingly wide range of charge transfer. Most investigators (e.g., Weickmann and Aufm Kampe, 1950; Latham and Mason, 1961) measured charging rates that correspond to roughly 3 Ã 10â16 to 3 Ã 10â15 C per collision. Schewchuk and Iribarne (1971) observed about 10â11 C per collision for very large water drops ( R = 2.9 mm), a value that decreased as the drop size and impact velocity decreased. On the other hand, they observed very little dependence on impurities but much stronger dependence on temperature. In most of these experiments the rebounding