Gas transfer to and across an air-water interface

TLDR

Sea trials show little increase in evaporation and heat transfer coefficients with wind speed between 4–10 m s⁻¹. The transfer velocity is calculated as VL = 0.082 (ρa/ρw)½σ⁻²⁄³u*, based on the viscous sublayer resistance of water for a smooth surface. Reichardt’s velocity‑profile formulation predicts boundary‑layer heat and mass transfer accurately across a wide range of Prandtl/Schmidt numbers, matches laboratory water‑surface data at low air speeds, agrees with sea‑evaporation measurements at ~7 m s⁻¹, and shows that transfer exceeds predictions and scales roughly with the square of wind speed at higher winds.

Abstract

A treatment based on Reichardt's formulation of the velocity profile in turbulent flow over a smooth plane surface is shown to give good agreement with published data on the boundary layer transfer of heat and mass over a wide range of Prandtl (or Schmidt) number, si. Applied to transfer to a water surface, agreement with published laboratory results is also good for low air speeds (smooth water). Comparison with observations for the sea shows there is little difference between the calculated evaporation coefficient and those reported for the sea with winds of ~7 m s-1. This is consistent with sea trials having so far detected little increase of evaporation and heat transfer coefficients with wind speed over the range 4–10 m s-1.The air/water transfer of non-reactive gas is governed by the resistance of the viscous sublayer of water, and the smooth surface treatment gives the transfer velocity (VL) on a liquid phase basis as VL = 0.082 (ρa/ρw)½σ-⅔u* where ρaρw is the density ratio, air/water, and u* = friction velocity of the surface air flow. The agreement between this formula and published wind tunnel results is good for the smooth water condition. At higher wind speeds transfer exceeds the calculated value and appears then to increase roughly in proportion to the square of the wind speed.