The Log-Normal Size Distribution Theory for Brownian Coagulation in the Low Knudsen Number Regime
✍ Scribed by K.W. Lee; Y.J. Lee; D.S. Han
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 175 KB
- Volume
- 188
- Category
- Article
- ISSN
- 0021-9797
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✦ Synopsis
calculating the discretized size distribution of the particles An analytical solution to the Brownian coagulation of aerosol of an aerosol which undergoes coagulation. He also found particles in the low Knudsen number regime is presented which an analytical expression for an early coagulation stage of an provides time evolution of the particle size distribution. The theoaerosol consisting of particles of one size. The Smoluchowretical analysis used is based on representation of the size distribuski solution is often termed as the monodisperse aerosol tion of a coagulating aerosol with a time-dependent log-normal model and written as size distribution function and employs the method of moments together with suitable simplifications. The results are found in the form that extends the continuum coagulation solution that was
previously obtained by Lee (J. Colloid Interface Sci. 92, 315 (1983)). The results show that the Knudsen number has a significant effect on the size distribution evolution during coagulation. where N is the total number concentration, N 0 is the initial In addition, it was confirmed that a self-preserving size distribution value for N, t is the coagulation time, K is the collision does not exist in the low Knudsen number regime. The obtained coefficient (Å2kT/3m), k is the Boltzmann constant, T is the solution was compared with numerical results and good agreement absolute temperature, and m is the gas viscosity. was obtained. The present work represents the first analytic solu-It is believed that Mu ¨ller (2) first developed the following tion to the low Knudsen number regime Brownian coagulation integro-differential equation that governs the continuous size problem. ᭧ 1997 Academic Press distribution of a coagulating aerosol. The Mu ¨ller equation