Comment on: Macroscopic water vapor diffusion is not enhanced in snow

Abstract. The central thesis of the authors’ paper is that macroscopic water vapor diffusion is not enhanced in snow compared to diffusion through humid air alone. Further, mass diffusion occurs entirely as the result of water vapor diffusion in the humid air at the microscale and the ice phase has no effect other than occupying volume where diffusion cannot occur. The foundation of their conclusion relies on the premise that the synchronous sublimation and deposition of water vapor across ice grains, known as hand-to-hand water vapor transport, does not lead to enhanced mass diffusion. We use a layered microstructure to rigorously show that diffusion is enhanced at all ice volume fractions compared to diffusion through humid air alone, and further, the hand-to-hand model of diffusion correctly predicts this diffusion enhancement.

The authors attempt to dismiss the concept of enhanced mass transfer resulting from hand-to-hand water vapor transport by arguing that there is a “counterflux” of water vapor in the form of downward motion of ice. While the ice phase appears to be propagating downward, all continuum material points of water (either vapor or ice) are moving upward (counter to the temperature gradient) with a monotonically increasing (nonnegative) motion. Specifically, material points of water in vapor form are diffusing upward through the humid air while material points of water in the form of ice are at zero velocity while locked in the ice phase. Material points of water never exhibit downward motion, despite the ice phase appearance of downward motion. Since the motion of all material points of water is monotonically increasing for all time, there is no counterflux of mass due to downward motion of the ice and such apparent motion is a mirage in the context of mass transfer.

This paper presents a rigorous fluid mechanics control volume analysis of mass transfer to demonstrate that the hand-to-hand model of diffusion produces the correct diffusion coefficient for the layered microstructure. Moreover, the control volume analysis shows why the authors’ approach of volume averaging the microscale diffusion coefficient does not capture the complete water vapor mass transport and therefore does not produce the correct macroscale diffusion coefficient.

An entirely fresh perspective on the role of the ice phase in mass diffusion is also presented. In particular, an analysis showing diffusion enhancement is developed without resorting to the hand-to-hand diffusion analogy. In brief, rather than looking at the ice as blocking microscale diffusion, the ice phase should be viewed as a reservoir of water, containing vast amounts of water vapor, ready to be released in the diffusion process.

In conclusion, mass diffusion in a layered microstructure is enhanced at all ice volume fractions compared to diffusion through humid air as a pure substance. The mechanism producing this enhanced diffusion is also on full display in snow under strong temperature gradients. Hence, it is entirely possible, indeed probable, that macroscopic water vapor diffusion is enhanced in snow compared to diffusion in humid air as a pure substance.