Andrew Fominykh

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...

Combined mass and heat transfer during nonisothermal absorption in gas-liquid slug flow with small bubbles in liquid plugs

Abstract A model for combined mass and heat transfer during nonisothermal absorption of a one component gas in a vertical gas–liquid slug flow with liquid plugs containing small bubbles is suggested. Under the assumptions of a perfect mixing of the dissolved gas in liquid plugs and uniform temperature distribution in liquid plugs, recurrent relations for the dissolved gas concentration and temperature in the n th liquid plug and mass and heat fluxes from the n th unit cell of a gas–liquid slug flow are derived. The total mass and heat fluxes in a gas–liquid slug flow are determined. Theoretical results are compared with the available experimental data.

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 nonisothermal gas absorption in gas-liquid bubbly media

A model for combined mass and heat transfer during nonisothermal gas absorption in a two-phase gasliquid bubbly medium with a high gas content and/or large times of gas-liquid contact is suggested. Diffusion and thermal interactions between bubbles is taken into account in the approximation of a cellular model of a bubbly medium whereby a bubbly medium is viewed as a periodic structure consisting of identical spherical cells with periodic boundary conditions at a cell boundary. Distribution of concentration of dissolved gas, temperature distribution in liquid and coefficients of mass and heat transfer during nonisothermal absorption of a soluble pure gas from a bubble by liquid are determined. In the limiting case of absorption without heat release the derived formulas recover the expressions for isothermal absorption.ZusammenfassungEs wird ein Modell vorgestellt, das den kombinierten Wärme- und Stoffaustausch während der nichtisothermen Gasabsorption in einem, von Blasen durchrührten Zweiphasen- Gas/Flüssigkeitsmedium mit hohem Gasgehalt und/oder langzeitigem Gas/Flüssigkeitskontakt zu ermitteln gestattet. Diffusion und thermischer Ausgleich zwischen den Blasen werden bei der Approximation des durchgasten Mediums durch ein Zellenmodell berücksichtigt, wobei das Medium als periodische Struktur, bestehend aus identischen Kugelzellen mit periodischen Randbedingungen zn den Zellgrenzen betrachtet wird. Die Verteilung der Konzentration gelösten Gases, die Temperaturverteilung in der Flüssigkeit und die Koeffizienten für Wärme- und Stoffaustausch während der nichtisothermen Absorption eines löslichen, reinen Gases aus einer Blase durch die Flüssigkeit werden ermittelt. lm Grenzfall der Absorption ohne Wärmefreisetzung liefern die abgeleiteten Formeln die für isotherme Absorption bekannten Beziehungen.

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.

Effect of an absorbate concentration level on the coupled mass and heat transfer during short gas plugs dissolution

Abstract We studied gas absorption from a rising gas plug when the concentration level of the absorbate in the absorbent is finite (finite dilution of absorbate approximation). It is shown that in the case of the finite dilution the lateral convective term in the equation of convective mass transfer in the absorbate must be taken into account. It is found that the mass transfer rate increases with the increase of the absorbate concentration level. Isothermal and nonisothermal absorptions are considered whereby the latter is described by the coupled equations of mass and heat transfer. It is found that the mass transfer rate decreases when the dimensionless heat of absorption increases.

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).

Mass transfer between a two-dimensional wall jet with a heterogeneous chemical reaction of the first order and a wall: analytical solution

Abstract The work studies mass transfer in a two-dimensional submerged wall jet flow with a chemical reaction of the first order at the surface. The approach suggested previously by Apelblat [1] for the analysis of a mass transfer with a first-order chemical reaction at the interface in a boundary layer flow is generalized for the case of a submerged two-dimensional wall jet flow. The solution of the problem is obtained in a closed analytical form.

Heat transfer during gas hydrate formation in gas-liquid slug flow

A model of heat transfer during gas hydrate formation at a gas-liquid interface in gas-liquid slug flow is suggested. Under the assumption of perfect mixing in liquid plugs, the recurrent relations for temperature in then-th liquid plug and heat and mass fluxes from then-th gas slug are derived. Total mass and heat fluxes in gas-liquid slug flow during gas hydrate formation are determined.ZusammenfassungEs wird ein Modell zur Berechnung des Wärmeübergangs bei der Gashydratbildung an Gas/Flüssigkeit-Grenzflächen einer Pfropfenströmung vorgeschlagen. Unter der Voraussetzung vollständiger Durchmischung in den Flüssigkeitspfropfen werden die Rekursivbeziehungen für die Temperatur imn-ten Flüssigkeitspfropfen und die Wärme-und Stoffströme vomn-ten Gaspfropfen hergeleitet. Schließlich erfolgt die Ermittlung des Gesamtmassen- und Wärmeflusses in der Gas/Flüssigkeit-Pfropfenströmung bei Gashydratbildung.

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.