Aerosol concentration distribution equation

The activity size distributions were determined from the calculated penetration values in the diffusion batteries using the method outlined for aerosol size measurement (equation (6) for RnWL and equations (8) and (9) for 222Pb concentration). 

Equation (12.135) suggests that the equilibration timescale will increase for larger aerosol particles and cleaner atmospheric conditions (lower mp). The timescale does not depend on the thermodynamic properties of A, as it is connected solely to the gas-phase diffusion of A molecules to a particle. The timescale in (12.135) varies from seconds to several hours as the particle radius increases from a few nanometers to several micrometers. We can extend the analysis from a monodisperse aerosol population to a population with a size distribution n(Rp). The rate of change for the bulk gas-phase concentration of A in that case is... 

An aerosol distribution can be described by the number concentrations of particles of various sizes as a function of time. Let us define Nk(t) as the number concentration (cm-3) of particles containing k monomers, where a monomer can be considered as a single molecule of the species representing the particle. Physically, the discrete distribution is appealing since it is based on the fundamental nature of the particles. However, a particle of size 1 pm contains on the order of 1010 monomers, and description of the submicrometer aerosol distribution requires a vector (N2, N-j,..., N10io) containing 1010 numbers. This makes the use of the discrete distribution impractical for most atmospheric aerosol applications. We will use it in the subsequent sections for instructional purposes and as an intermediate step toward development of the continuous general dynamic equation. 

In order to solve (13.72) we also need to know N(t). We have seen that the total number concentration N(t) for any aerosol distribution assuming constant coagulation coefficient is given by (13.66). Substituting this expression for N(t) into (13.72), we find that the continuous coagulation equation becomes... 

The first challenge concerns the involvement of multiple phases in wet deposition. Not only does one deal with the three usual phases (gas, aerosol, and aqueous), but the aqueous phase can be present in several forms (cloudwater, rain, snow, ice crystals, sleet, hail, etc.), all of which have a size resolution. To complicate matters even further, different processes operate inside a cloud, and others below it. Our goal will initially be to create a mathematical framework for this rather complicated picture. To simplify things as much as possible we consider a warm raining cloud without the complications of ice and snow. There are four media or phases present, namely, air, cloud droplets, aerosol particles, and rain droplets. A given species may exist in each of these phases for example, nitrate may exist in air as nitric acid vapor, dissolved in rain and cloud droplets as nitrate, and in various salts in the aerosol phase. Nonvolatile species like metals exist only in droplets and aerosols, while gases like HCHO exist only in the gas phase and the droplets. The size distribution of cloud droplets, rain droplets, and aerosols provides an additional complication. Let us initially neglect this feature. For a species i, one needs to describe mathematically its concentration in air C(,air, cloudwater C,[C 0ud, rainwater C .rain, and the aerosol phase Qpan- We assume that all concentrations are expressed as moles of i per volume of air (e.g., mol m 3 of air). These concentrations will be a function of the location (x,y,z) and time and can be described by the atmospheric diffusion equation... 

Very early on, Aitken (1923) showed that most particles in the atmosphere are smaller than 0.1 pm diameter and that their concentrations vary from some hundreds per cm over the ocean to millions per cm in urban areas. Junge (1955,1963,1972) measured the atmospheric aerosol number size distribution and concentration in urban and non-urban areas as functions of altitude and site. He established the standard form for plotting size distribution data log of AN/ADp versus logD, where N = number and Dp = particle diameter. He observed that this plot was a straight line that could be described by the equation AN/ADp = AD, where A and k were constants. He also noted that in the range from 0.1 to 10.0 pm particle diameter, k was approximately equal to 4.0. This distribution mode was widely known as the Junge distribution or the power law distribution. 

Table VIII summarizes the physical processes that affect the evolution of aerosol in a unit volxame of atmosphere. To develop the general dynamic.equation governing aerosol behavior let us assxime that the aerosol is composed of liquid droplets of M chemical species. We let c denote the concentration of species i in a droplet, i = 1,2,..., M, and Dp denote the diameter of the particle. We then define n(Dp, c, ..., cjyj,r,t) as the size-composition distribution function, such that n dDp dc. .. dcj is the n umber of particles per unit vol ume of atmosphere at location r at time t of diameter Dp to Dp + dDp and of composition c to spegies ...

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