Showing papers by "Ganesan Narsimhan published in 1985"

The Brownian coagulation of aerosols over the entire range of Knudsen numbers: Connection between the sticking probability and the interaction forces

Abstract: The existing models for Brownian coagulation of aerosols account for the effect of interparticle forces through a phenomenological sticking probability, i.e., the probability of coagulation upon collision. This probability is usually assumed to be equal to unity. A model for Brownian coagulation of equal-sized electrically neutral aerosol particles is proposed, which takes into account explicitly the van der Waals attraction and Born repulsion, instead of the phenomenological sticking probability. In this model, the relative motion between two particles in the vicinity of the sphere of influence is considered to be free molecular, the thickness of this region is taken to be equal to the average correlation length for the relative Brownian motion. The relative motion of the particles outside this region is described by the Fokker-Plank equation. The sticking probability predicted by the model, in terms of the interaction potential between two particles, becomes vanishingly small for very small particles. The collisions with the medium that a particle experiences during its escape from the potential well and the corresponding energy dissipation, neglected in this model, will increase the coagulation coefficient, in particular for the large particles because they stay longer in the region in which the interaction potential is acting. For this reason the model is likely to be valid for sufficiently small particles and to provide a lower bound for the coagulation coefficient of the larger particles. However, for large particles the interaction potential is deep and the decay length of the potential is small compared to the particle sizes. As a result, the region of the interaction potential can be replaced by a sink. This is equivalent to considering the sticking probability as equal to unity. In contrast to the earlier models, the expression derived for the coagulation coefficient in the latter case displays the proper continuum and free molecular limits and agrees well with the Fuchs empirical formula. It yields an upper bound for sufficiently small particles but can be exceeded for particles of intermediate sizes. Comparison with the experimental data seem to indicate the validity of this upper bound for particles as small as 0.01 μm.

Monte Carlo simulation of brownian coagulation over the entire range of particle sizes from near molecular to colloidal: Connection between collision efficiency and interparticle forces

Abstract: The effect of interparticle forces on Brownian coagulation of aerosols is usually accounted for through a phenomenological sticking probability, i.e., the probability of coagulation upon collision. This probability is customarily assumed to be equal to unity even though it is recognized that it is smaller than unity for very small particles. A Monte Carlo method for the simulation of Brownian coagulation of equal-sized electrically neutral spherical aerosol particles is presented, which takes into account the interparticle forces due to van der Waals attraction and Born repulsion instead of the phenomenological sticking probability. The particle motion is described by the generalized Brownian dynamics. The Brownian coagulation coefficient for particles of unit density, for a Hamaker constant of 10−12 erg, is calculated over the entire range of Knudsen numbers. For large particles, the results of the simulation agree very well with those provided by the model proposed previously by the authors (1) and also with the Fuchs interpolation formula. In this case the results indicate that the sticking probability is close to unity. For sufficiently small particles, the coagulation coefficient agrees with the lower bound provided by the model proposed by the authors (1). The extrapolation to sufficiently small particles of the model (1) proposed for large particles provides an upper bound with much larger values. For particles of intermediate sizes, the coagulation coefficient is found to be even higher than the values predicted by the model valid for large particles (1). The coagulation coefficients of the particles of intermediary size are greater than those corresponding to a sticking probability of unity whereas those of the sufficiently small particles are much smaller because of the following two opposite effects: (i) As the particle size decreases, the ratio of the decay length of the interaction potential (based on the shortest distance between the particles) and the particle size increases; this relative increase in the range of the van der Waals attraction increases the rate of collisions between particles. (ii) As the particle size decreases, the interaction potential becomes less deep and, as a result, the probability of escape of the particles from the potential well increases. In the intermediary size range, the former effect, which was not accounted for in the model for large particles (being negligible in that case), is more important, whereas for very small particle sizes, the latter effect predominates. The calculated values of the collision efficiency are small for sufficiently small particles, increase with particle size and eventually reach the value of unity for large particles. Extrapolating to particles of molecular dimensions, one can understand why in the cases in which only physical interactions are involved the collision efficiency is negligibly small.