M.A. Rodríguez Braña

Parametric study of selective removal of atmospheric aerosol by below-cloud scavenging

Abstract This work studies the scavenging efficiencies of aerosol particles after a given rain regime as a function of time by below-cloud scavenging. We also analyse the health impact of aerosol before and after rain by comparing the respirable dust fractions. The well-known equations of below-cloud scavenging are applied to three atmospheric conditions (clear, hazy and urban) in two precipitation regimes (drizzle and heavy rain) with four different drop size distributions (DSDs) in each case. From this study it is inferred that respirable dust is hardly scavenged by rain, and DSDs have minor importance in each rain regime in the results. As compared with the volume of respirable aerosol before rain, it remains roughly 60% after 12 h of drizzle and after 1 h of heavy rain.

A modified semi-implicit method to obtain the evolution of an aerosol by coagulation

Abstract In the present work we improve the semi-implicit method previously developed by Jacobson et al. (1994. Atmospheric Environment 28, 1327–1338). In this the particle size distribution has to be discretized in several volume bins, and we must use partition coefficients that relate the particle formed in thecollision to the bin discretization. The original method has the problem of some numerical diffusion and we present two different methods for calculating the coefficients that provide better results. We compare the original and our methods with several analytical solutions for concrete cases of coagulation kernels. Finally, we apply our methods to a typical urban mono-component aerosol and to a multi-component case. More work has to be developed in the comparison of our methods with the original one when growth is present, because this phenomenon swamps out coagulation at large sizes.

A flux-based characteristics method to solve particle condensational growth

We develop a new numerical method to predict the evolution of the particle size distribution of an aerosol by heterogeneous nucleation. We begin with a flux-based modified characteristics method. It is conservative and, therefore, maintains constant the total number of aerosol particles and the amount of the total vapor mass and initial particle mass, as is theoretically required. The advantages of the proposed method are: it is fast and with few complex calculations, although its use sometimes demands more computer memory than other methods. The proposed method is compared with exact cases and with the results of other authors for the cases with only numerical solution.

Difficulties inherent to the use of analytic solution of the condensation-evaporation equation for multicomponent aerosols

Abstract We present the analytic solution to the problem of multicomponent aerosol evolution due to condensation and/or evaporation of its components. We pose the general equation that governs the evolution of the particle size distributions of each species, and then solve it through the method of characteristic curves. The obtained solution is of interest because it permits an approximate analysis of cases of practical importance without numerical methods. Furthermore, the analytic solutions can be used to validate the numerical methods which, up to now, are only compared with mono-component cases. When all components condense, the obtained solution is valid for all time values. When some of the components evaporate the problem is more complex, due to the fact that no component exists in a negative amount. This suggests the formation of shock waves (high peaks in particle size distribution) and rare-faction waves, which are difficult to handle. Finally, we apply the method to several interesting cases.

Analytic Solution of the Aerosol Rigorous General Dynamic Equation Without Coagulation in Multidimension

ABSTRACT We present the analytic solution to the problem of multicomponent aerosol evolution due to condensation and/or evaporation of its components, sources, and deposition mechanisms. We use the rigorous formulation, which utilizes a particle number distribution depending on time and on the amount of each component, being that the particle size is a derived variable. This allows us to analyze the aerosol without the usual assumption of internal mixing. We solve the hyperbolic equation obtained through the method of characteristic curves. When all components condense, the obtained solution is always valid. When some of the components evaporate, the problem is more complex and its solution (which is not provided here) has to incorporate nonlinear phenomena such as shock and rarefaction waves, which are difficult to handle. The analytic solutions can be used to validate the numerical methods that could be developed in the future for more complex cases. We have analyzed a bicomponent case, and we have show...

The Goodness of the Internally Mixed Aerosol Assumption Under Condensation-Evaporation

The hypothesis of internally mixed aerosol is broadly used to analyze the evolution of the atmospheric aerosols. This seems to be physically plausible, and furthermore it is the only possible characterization of the aerosols until more advanced instruments for measuring the aerosol composition have been developed. Expanding upon a previous article, in which the evolution of a generally mixed aerosol is obtained under condensation-evaporation, we are able to analyze the goodness of the internally mixed aerosol assumption with regard to this phenomenon. We have obtained the result that this is a valid assumption.

Integrators of several orders in time to study the evolution of an aerosol by coagulation

We have obtained some numerical methods to integrate the coagulation equation for an aerosol. They are semi-implicit and stable regarding the time integration step, which can be freely chosen (a very important matter in numerical solution of differential equations). The methods are of two types: extrapolative (based on a previously known first-order semi-implicit formula) and purely semi-implicit, both mass-conservative. The same methodology used here to develop these new methods can be applied to improve the well-known sectional ones. The extrapolative and the semi-implicit methods are really of the order we had deduced from their analysis. However, as the order of the method increases, for small time steps, the roundoff causes the error no longer to behave as expected. The extrapolative methods are self-starting but the semi-implicit ones are not, so we need the first ones to start the others. If we take into account both the error and the CPU time, the second-order methods are comparable, but the third-order semi-implicit one is better than the extrapolative one. The comparison of higher order methods is disturbed by the roundoff error. Both methods can be used with fixed and moving bins with respect to the discretization of the size in the particle size distribution. These methods are valid to complement the specific ones developed to solve the growth and other phenomena in the time-splitting method which is used to analyse the evolution of an aerosol in the general case.