Boris Krasovitov

Evaporation and Condensation of Large Droplets in the Presence of Inert Admixtures Containing Soluble Gas

In this study the mutual influence of heat and mass transfer during gas absorption and evaporation or condensation on the surface of a stagnant droplet in the presence of inert admixtures containing noncondensable soluble gas is investigated numerically. The performed analysis is pertinent to slow droplet evaporation or condensation. The system of transient conjugate nonlinear energy and mass conservation equations was solved using anelastic approximation. Using the material balance at the droplet surface the authors obtained equations for Stefan velocity and the rate of change of the droplet radius taking into account the effect of soluble gas absorption at the gas–liquid interface. The authors also derived boundary conditions at gas–liquid interface taking into account the effect of nonisothermal gas absorption. It is demonstrated that the average concentration of the dissolved species in a droplet strongly depends on the relative humidity (RH) for highly soluble and for slightly soluble gaseous atmospheric pollutants. Therewith the difference between the average concentration of the dissolved species in water droplets attains tens of percent for different values of RH.

Effect of Altitude Concentration Gradient of Soluble Gaseous Pollutants on Their Scavenging by Falling Rain Droplets

Abstract This paper analyzes absorption of soluble atmospheric trace gases by falling rain droplets with internal circulation, which is caused by interfacial shear stresses. It is assumed that the concentration of soluble trace gases in the atmosphere varies in a vertical direction. In the analysis the accumulation of the absorbate in the bulk of the falling rain droplet was accounted for. The problem is solved in the approximation of a thin concentration boundary layer in the droplet and in the surrounding air. It was assumed that the bulk of a droplet, beyond the diffusion boundary layer, is completely mixed and that concentration of the absorbate is homogeneous and time dependent in the bulk. By combining the generalized similarity transformation method with Duhamel’s theorem, the system of transient conjugate equations of convective diffusion for absorbate transport in liquid and gaseous phases with time-dependent boundary conditions is reduced to a linear-convolution Volterra integral equation of the...

Isothermal absorption of soluble gases by atmospheric nanoaerosols.

We investigate mass transfer during the isothermal absorption of atmospheric trace soluble gases by a single droplet whose size is comparable to the molecular mean free path in air at normal conditions. It is assumed that the trace reactant diffuses to the droplet surface and then reacts with the substances inside the droplet according to the first-order rate law. Our analysis applies a flux-matching theory of transport processes in gases and assumes constant thermophysical properties of the gases and liquids. We derive an integral equation of Volterra type for the transient molecular flux density to a liquid droplet and solve it numerically. Numerical calculations are performed for absorption of sulfur dioxide (SO(2)), dinitrogen trioxide (N(2)O(3)), and chlorine (Cl(2)) by liquid nanoaerosols accompanied by chemical dissociation reaction. It is shown that during gas absorption by nanoaerosols, the kinetic effects play a significant role, and neglecting kinetic effects leads to a significant overestimation of the soluble gas flux into a droplet during the entire period of gas absorption.

Cell model of in-cloud scavenging of highly soluble gases

We investigate mass transfer during absorption of highly soluble gases such as HNO3 ,H 2O2 by stagnant cloud droplets in the presence of inert admixtures. Thermophysical properties of the gases and liquids are assumed to be constant. Diffusion interactions between droplets, caused by the overlap of depleted of soluble gas regions around the neighboring droplets, are taken into account in the approximation of a cellular model of a gas–droplet suspension whereby a suspension is viewed as a periodic structure consisting of the identical spherical cells with periodic boundary conditions at the cell boundary. Using this model we determined temporal and spatial dependencies of the concentration of the soluble trace gas in a gaseous phase and in a droplet and calculated the dependence of the scavenging coefficient on time. We found that scavenging coefficient for gas absorption by cloud droplets remains constant and sharply decreases only at the final stage of absorption. In the calculations we employed a Monte Carlo method and assumed gamma size distribution of cloud droplets. It is shown that despite of the comparable values of Henry’s law constants for the hydrogen peroxide (H 2 O2) and the nitric acid (HNO3), the nitric acid is scavenged more effectively by cloud droplets than the hydrogen peroxide due to a major affect of the dissociation reaction on HNO3 scavenging. It is demonstrated that scavenging of highly soluble gases by cloud droplets leads to strong decrease of soluble trace gas concentration in the interstitial air. We obtained also analytical expressions for the ‘‘equilibrium values’’ of concentration of the soluble trace gas in a gaseous phase and for concentration of the dissolved gas in a liquid phase for the case of hydrogen peroxide and nitric acid absorption by cloud droplets.

Evaporation and Growth of Multicomponent Droplets in Random Dense Clusters

Interaction between evaporating (growing) droplets in binary arrays and large random clusters of droplets of different sizes is analyzed in a quasi-steady approximation using the modified method of expansion into irreducible multipoles. Evaporation and condensation of binary arrays and clusters of droplets (i) composed of volatile components and ( ii ) composed of a volatile and a nonvolatile component was studied. The analytical and numerical results of the investigation are presented in terms of heat and mass correction factors. Solution of the transient problem is obtained, and the evaporation rate is determined. It is shown that for droplets of ideal solution with different compositions, Nusselt and Sherwood numbers depend on the concentration of components inside each droplet. When dense cloud contains both pure droplets and droplets containing soluble nuclei, interactions between temperature and concentration fields causes growth of some droplets in a cluster and evaporation of the other droplets. It is shown that inside an evaporating large cluster of multicomponent droplets composed of volatile components, recondensation occurs whereby evaporating droplets act as mass sources and heat sinks and growing droplets act as mass sink and heat sources. The results of this study are of relevance in the analysis of dynamics of droplet size distribution in clouds, artificial modification of clouds and precipitation, in-cloud pollutants scavenging, and in the analysis of evaporation and combustion of multicomponent (blended) liquid fuels.

Non-isothermal scavenging of highly soluble gaseous pollutants by rain in the atmosphere with non-uniform vertical concentration and temperature distributions

We suggest a non-isothermal one-dimensional model of precipitation scavenging of highly soluble gaseous pollutants in inhomogeneous atmosphere. When gradients of soluble trace gases’ concentrations and temperature in the atmosphere are small, scavenging of gaseous pollutants is governed by two linear wave equations that describe propagation of a scavenging and temperature waves in one direction. If wash-down front velocity is much larger than the velocity of the temperature front, scavenging is determined by propagating scavenging front in the atmosphere with inhomogeneous temperature distribution. We solved the derived equation by the method of characteristics and determined scavenging coefficient and the rates of precipitation scavenging for wet removal of sulfur dioxide using measured initial distributions of trace gases and temperature in the atmosphere. It is shown that in the case of exponential initial distribution of soluble trace gases and linear temperature distribution in the atmosphere, scavenging coefficient in the region between the ground and the position of a scavenging front is proportional to rainfall rate, solubility parameter in the under-cloud region, adjacent to a bottom of a cloud and to the growth constant in the formula for the initial profile of a soluble trace gas in the atmosphere. The derived formula yields the same value of scavenging coefficient for sulfur dioxide scavenging by rain as field estimates presented by McMahon and Denison (Atmos Environ 13:571–585, 1979). It is demonstrated that in the case when the altitude variation of temperature in the atmosphere is determined by the environmental lapse rate, scavenging coefficient increases with height in the region between the scavenging front and the ground. In the case when altitude temperature variation in the atmosphere is determined by temperature inversion, scavenging coefficient decreases with height in a region between the scavenging front and the ground. Theoretical predictions of the value of the scavenging coefficient for sulfur dioxide washout by rain and of the dependence of the magnitude of the scavenging coefficient on rain intensity are in good agreements with the atmospheric measurements of Martin (Atmos Environ 18:1955–1961, 1984).

Scavenging of radioactive soluble gases from inhomogeneous atmosphere by evaporating rain droplets

We analyze effects of inhomogeneous concentration and temperature distributions in the atmosphere, rain droplet evaporation and radioactive decay of soluble gases on the rate of trace gas scavenging by rain. We employ a one-dimensional model of precipitation scavenging of radioactive soluble gaseous pollutants that is valid for small gradients and non-uniform initial altitudinal distributions of temperature and concentration in the atmosphere. We assume that conditions of equilibrium evaporation of rain droplets are fulfilled. It is demonstrated that transient altitudinal distribution of concentration under the influence of rain is determined by the linear wave equation that describes propagation of a scavenging wave front. The obtained equation is solved by the method of characteristics. Scavenging coefficients are calculated for wet removal of gaseous iodine-131 and tritiated water vapor (HTO) for the exponential initial distribution of trace gases concentration in the atmosphere and linear temperature distribution. Theoretical predictions of the dependence of the magnitude of the scavenging coefficient on rain intensity for tritiated water vapor are in good agreement with the available atmospheric measurements.

Rain scavenging of soluble gases by non-evaporating and evaporating droplets from inhomogeneous atmosphere

We suggest a one-dimensional model of precipitation scavenging of soluble gaseous pollutants by non-evaporating and evaporating droplets that is valid for arbitrary initial vertical distribution of soluble trace gases in the atmosphere. It is shown that for low gradients of soluble trace gases in the atmosphere, scavenging of gaseous pollutants is governed by a linear wave equation that describes propagation of a wave in one direction. The derived equation is solved by the method of characteristics. Scavenging coefficient and the rates of precipitation scavenging are calculated for wet removal of sulfur dioxide (SO2) and ammonia (NH3) using measured initial distributions of trace gases. It is shown that scavenging coefficient for arbitrary initial vertical distribution of soluble trace gases in the atmosphere is non-stationary and height-dependent. In case of exponential initial distribution of soluble trace gases in the atmosphere, scavenging coefficient for non-evaporating droplets in the region between the ground and the position of a scavenging front is a product of rainfall rate, solubility parameter, and the growth constant in the formula for the initial profile of a soluble trace gas in the atmosphere. This expression yields the same estimate of scavenging coefficient for sulfur dioxide scavenging by rain as field estimates presented in McMahon and Denison (1979). It is demonstrated that the smaller the slope of the concentration profile the higher the value of a scavenging coefficient.

Wet precipitation scavenging of soluble atmospheric trace gases due to chemical absorption in inhomogeneous atmosphere

We analyze the effects of irreversible chemical reactions of the first and higher orders and aqueous-phase dissociation reactions on the rate of trace gas scavenging by rain in the atmosphere with non-uniform concentration and temperature. We employ an one-dimensional model of precipitation scavenging of chemically active soluble gaseous pollutants that is valid for small gradients of temperature and concentration in the atmosphere. It is demonstrated that transient altitudinal distribution of concentration under the influence of rain is determined by the partial hyperbolic differential equation of the first order. Scavenging coefficients are calculated for wet removal of chlorine, nitrogen dioxide and sulfur dioxide for the exponential and linear initial altitudinal distributions of trace gases concentration in the atmosphere and linear and uniform altitudinal temperature distributions. Theoretical predictions of the dependence of the magnitude of the scavenging coefficient on rain intensity for sulfur dioxide are in a good agreement with the available atmospheric measurements.

Precipitation scavenging of gaseous pollutants having arbitrary solubility in inhomogeneous atmosphere

We investigate scavenging of gaseous pollutants in the atmosphere under the combined influence of rain and varying temperature distribution that affects the rate of soluble gas scavenging. We employ a one-dimensional model of precipitation scavenging of gaseous pollutants having arbitrary solubility that is valid for small gradients and for non-uniform initial vertical distributions of temperature and soluble trace gases concentration in the atmosphere. It is showed that transient altitudinal distributions of temperature and concentration under the influence of rain are determined by linear wave equations that describe propagation of temperature and scavenging wave fronts. Scavenging coefficient and the rates of precipitation scavenging are calculated for wet removal of methanol (