The quantification of overall mass transfers in gas-liquid systems depends on the spatial evolution of the relevant variables close to the interface of the two phases. When turbulence is present (in the present study the turbulence is considered in the liquid phase), the methods of treating the problem consider the differential form of the momentum and mass conservation equations. The continuous hypothesis that underlies these equations in principle allows verifying the limiting trends very close to the interface. Because the theoretical concepts of turbulence are defined using statistical tools, the mentioned verification depends on the intrinsic definitions used in the statistical approach. In this study the turbulent mass transfer parameters are calculated for the thin region close to the interface based on the tool of random square waves (RSW). Theoretical results are obtained and analyzed in the context of existing experimental data and conceptual discussions of the literature, using a constant 'reduction function', a parameter defined in this methodology. The results of the present analysis show that the RSW method allows obtaining functional trends, as well as indicate the adequacy of using a variable reduction function to better represent reality.

Mean profiles of scalar properties close to moving gas-liquid interfaces subjected to turbulence are quantified using Random Square Waves (RSW). The condition of stationary turbulent transfer allows reducing the third order nonlinear governing equation successively to a second order and to a first order equation, which admits theoretical integration, furnishing the set of solutions analyzed in the present study. It is shown that different solutions may apply to different parts of the calculation domain (physical domain). It is also shown that the stationary problem admits a linear profile close to the gas-liquid interface, while a nonlinear function describes the mean properties apart from the interface.

The one-dimensional turbulent mass transfer was quantified using the nonlinear unclosed statistical governing equations derived from the traditional statistical methods. Further, this study considers the a priori simplifications of the bimodal Random Square Waves (RSW) approximation. This model enables the formulation of parametric equations for the variables of the statistical governing equations, but intrinsic aspects of this method still need to be clarified. In this sense, this study considers details of a version of the RSW equation for turbulent mass transfer which uses a constant reduction function. The mentioned details are related to discontinuities of higher order derivatives of the nondimensional concentration profile in the vicinity of a singular point. Numerical integrations were conducted at the air-water interface in both directions: from the liquid to the gas phase, and from the gas to the liquid phase. The results suggest that the continuity and smoothness of the calculated concentration profile does not depend on the discontinuities of the higher order derivatives, but the behaviour of the higher order derivatives depends strongly on the values of the nondimensional parameters existing in the formulation. Adequate boundary conditions were defined in the liquid phase, involving a new condition for the second derivative of the concentration profile. A fourth order Runge-Kutta method was used. This paper presents the proposed methodology; the comparison between results of calculated and measured concentration profiles,

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