The self-preserving particle size distribution for coagulation by Brownian motion—III. Smoluchowski coagulation and simultaneous Maxwellian condensation

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Abstract

A theoretical study has been made of the dynamics of coagulation with simultaneous condensation and of the behavior of the particle size distribution function. For coagulation and condensation in the continuum region the existence of self-preserving spectra—as defined in previous papers in this series—depends on a nondimensional parameter C = (3μ/4kT)[2B(S − 1)/φ23 N13] where μ and T are the viscosity and temperature of the medium, k Boltzmann's constant, φ the total volume concentration, N the total number concentration of particles, B the proportionality coefficient in the equation for the condensation rate and S the supersaturation. For C = 0 phase equilibrium exists while for C > 0 simultaneous condensation and coagulation occur. For C = 1·09 the total surface concentration (surface area of particles per unit volume of gas) is invariant with respect to time. For other values of C the supersaturation must vary with time in a particular way in order for the system to be self-preserving. The shapes of the self-preserving spectra are strongly dependent on C. Analytical solutions of the transformed kinetic equation have been found for the lower and upper ends of the spectrum and numerical solutions for the entire spectrum have been calculated for four values of C. The theory is limited to values of C smaller than of order unity.

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For presentation at “Un colloque international sur les atmospheres polluees”, Paris 27–28 November 1969.

Permanent address: Institute of Physical Chemistry, Czechoslovak Academy of Sciences, Prague 2, Machova 7, Czechoslovakia.

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