Particle concentration, coagulation rate

A dynamic ordinary differential equation was written for the number concentration of particles in the reactor. In the development of EPM, we have assumed that the size dependence of the coagulation rate coefficients can be ignored above a certain maximum size, which should be chosen sufficiently large so as not to affect the final result. If the particle size distribution is desired, the particle number balance would have to be a partial differential equation in volume and time as shown by other investigators ( ). 

The rooms without aerosol sources and low ventilation rate (v<0.3 hf1 ) had low aerosol concentrations (2 103 - 104 cm-3) due to the small influence of the higher aerosol concentrations outdoors (aerosols by traffic and combustions) (Table la). In this case the aerosol in the room air was aged by coagulation and plateout and had less condensation nuclei of smaller sizes (d<100 nm). Rooms with a moderate ventilation show higher particle concentrations ((1-5) 10 cm 3) (Table Ila). With aerosol sources in a room (Table III) the aerosol concentrations can increase to 5 105 particles/cm3. The relative error of the measured particle concentration is in the order of 15% primary determined by the uncertainties of the absolute calibrations of the condensation nuclei counter. 

So-called self-coagulation, where the particles are approximately the same size, can, however, lead to changes in the size distribution of the aerosol particles. As one might expect, the rate of this process is a strong function of the particle concentration as well as the particle size. 

Perikinetic Coagulation. If colloidal particles are of such dimensions that they are subject to thermal motion, the transport of these particles is accomplished by this Brownian motion. Collisions occur when one particle enters the sphere of influence of another particle. The coagulation rate measuring the decrease in the concentration of particles with time, N (in numbers/ml.), of a nearly monodisperse suspension corresponds under these conditions to the rate law for a second order reaction (15) ... 

N0V0 = Total concentration of particles suspended volume of particles suspended at time t = 0 dN/dt = Coagulation rate [sec. 1 cm.3]... 

Aggregation of Particles. Sinclair 91) discusses the coagulation in a homogeneous aerosol. For ordinary concentrations of aerosols the coagulation rate is low. Stirred settling of the aerosol produces faster rates. Equations applicable to these processes are given. 

Therefore, the doublets of sufficiently small particles are continually formed (due to coagulation) and destroyed (because of their dissociation). If the rate of formation of a doublet (i.e., the rate of coagulation per particle) is greater than its rate of dissociation (i.e., the rate of dissociation per doublet), the doublet is stable. As a result, the concentration of doublets increases continuously with time. As will be shown later, the time scale of evolution of these stable doublets is of the order of the time scale of coagulation. Of course, these stable doublets interact with the particles to form triplets which, in turn, form quadruplets, etc., resulting in the growth of the particle size. 

Since the doublets are continually being formed by coagulation, their rate of formation depends on the rate of coagulation. The rate of formation of a doublet rf (or, equivalently, the rate of coagulation per particle) can be expressed in terms of the coagulation coefficient /3 and the particle number concentration n as... 

The turbulent coagulation rate is again proportional to the square of the particle concentration (Eq. 3.14),... 

Assuming additivity of tlie rates of coagulation by shesu and Brownian motion, the rate of change of the total particle concentration is... 

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