An eddy cell model of mass transfer into the surface of a turbulent liquid

TLDR: In this paper, a model of the hydrodynamic behavior near the surface of a turbulent pipe flow of water is proposed to provide a link between the observed mass transfer behavior and the state of the turbulent field.

Abstract: Experimental gas absorption studies for bubbles transported in turbulent pipe flow of water strongly indicate that liquid phase controlled mass transfer is due to surface renewal by turbulent eddies. Predictions of transport behavior from the conditions of turbulent flow cannot be made in support of this mechanism because no satisfactory theory of turbulent transport near a gas-liquid interface is available. This work considers a model of the hydrodynamic behavior near the surface which provides a link between the observed mass transfer behavior and the state of the turbulent field. In this model, the very small scales of turbulent motion are considered to be controlling. These motions are idealized, and their flow and mass transfer behavior are solved analytically. The overall result for eddies of various sizes is related to the turbulent energy spectrum by using only the easily accessible parameter ϵ, the energy dissipation rate. This model gives quantitative agreement to within a factor of 2 for three widely different experimental situations including gas-liquid and liquid-solid interfaces. However, the predicted Reynolds number dependence is somewhat higher than the experimental result. The model attempts to clearly define the basic physical process at the interface. Therefore, it indicates the direction for further experimentation needed to clarify the basic relationship between the mass transfer rates in the liquid phase and the hydrodynamic behavior of the turbulent liquid.