| Numerical computations have been carried out to determine the efficiency with which electrically charged cloud droplets, of radii 10mum, 7mum, and 5mum, collide with electrically charged particles of radii ranging from 1.0mum to 10mum, at 100% relative humidity, temperature of -17°C, and pressure of 540mb, under the influence of gravity and inertia. Charges on the cloud droplet are 10e, 100e and 1000e and charges on the particle are 10e, 20e, 50e, and 100e. The density of the cloud droplet is that of water, 1000 kg/m3 and the densities on the particle are 500 kg/m 3, 1000 kg/m3, and 2000 kg/m3. The work involved in programming the Chebychev polynomials of the electrostatic boundary value problem solved by Davis (1964), to determine an accurate value for the electrical force; verification that the program runs accurately; and a comparison between the results computed and those from the image charge theory presented by Tinsley et al. (2000, 2001), are covered. The use of the Davis expression is called the conducting spheres method. This method is then incorporated into the program used by Tinsley et al. (2000, 2001) as an alternative to the approximation to the force, called the image charge method that is utilized in that program. Comparisons are presented for the trajectory calculations between the two electrostatic methods for two different flow regimes. The two flow regimes are successive improvements over the previously used Stokes flow, the first being the asymmetric Proundman-Pearson-Oseen flow and the second an even more accurate treatment for larger particles that uses the superposition method. Collision efficiency calculations are also presented for the present conducting spheres model, and comparisons are made with collision efficiencies for the image charge model. |
