Turbulence aspects of mass transfer in the thin interfacial region of the concentration boundary layer in gas–liquid systems

Abstract

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.

Mass Transfer Through Free Surface Boundary Layers Using a Statistical Approach

“…3, A also increases with z/ in the boundary layer, following experimental data obtained by [9] and shown in [16]. This result extends the discussion of [27], in which the focus was the stationary solution of RSW for constant A, showing now a wider range of application. A=0.0 is characteristic for damping (attenuation) of fluctuations due to molecular diffusivity near the interface.…”

“…A=0.0 is characteristic for damping (attenuation) of fluctuations due to molecular diffusivity near the interface. Because molecular diffusion is important in the so called "outer diffusive layer" (see the BOKVS interfacial structure in [22] and [27], for example), low values of A also occur in this layer.…”

“…5(a) shows the comparison between measured and calculated concentration fluctuation intensities, given as the root mean square c' of the concentration fluctuations c, ′ , and the RSW equation ′ 1 (see [16]). The experimental data were obtained by [9] and discussed by [16] and [27]. The z axis is normalized with the position of the peak of c' in order to facilitate comparisons with measurements.…”

“…Because divergence considers the turbulent movement of the superficial velocity components, it points to the importance of elucidating how the structure of turbulence combines with the molecular diffusion to control the mass exchange in the adjacent region of the gas-liquid interface. In a study of long maturation, Schulz and co-workers [9], [15], [16], [25][26][27] progressively presented the tool "Random Square Waves", which was applied to an interface boundary layer. The starting equation is the Reynolds averaged mass conservation equation, where the Reynolds decomposition of variables, given by a mean parcel and a fluctuating parcel, is the main assumption.…”

Turbulent One-dimensional Interfacial Scalar Transport: Statistical Random Square Waves Solution

“…Theoretical improvements (Janzen 2006;Schulz et al 2010;Lopes Jr 2012) gradually empowered the formulation, so that the statistical functions defined in the RSW method could be adequately used in the scalar advection-diffusion equation. Normalized analytical solutions were then obtained for the interfacial mass transport (Gonçalves and Schulz 2013;Gonçalves 2014;Schulz et al 2018), firstly for the stationary regime (steady state) and a constant reduction function (a basic statistical element of the RSW method). In the sequence, for more general situations (transient flows with variable reduction function), the possibility of using Taylor series to obtain adequate concentration profiles and related statistical parameters was introduced (Lavín and Schulz 2019; Lavín 2020).…”