Air Permeability and Capillary Rise as Measures of the Pore Structure of Snow

Air Permeability and Capillary Rise as Measures

of the Pore Structure of Snow:

An Experimental and Theoretical Study

Rachel E. Jordan1, Janet P. Hardy1, Frank E. Perron, Jr. 1, and David J. Fisk1

Air permeability and capillary tension are macroscopic snow properties that are influenced by the

pore structure of the snow cover. Formulas for predicting fluid transport, species elution, and acous-

tic wave propagation require parameterization of one or both of these properties. We report paired

measurements of permeability K and capillary rise h from snow samples at field sites in Hanover,

New Hampshire, and Sleepers River, Vermont. We augment these data with laboratory tests on

sieved snow and glass beads. Our measurements demonstrate a linear relationship between K and Φ/

h2, which we corroborate theoretically using a simple conduit model of the pore space, where Φ is

the snow porosity. We propose that scatter in the data results, in part, from the effect of crystal shape

on air flow and imbibition contact angle. We also show that grain size D can be estimated from

capillary rise, through inversion of Shimizu's equation.

Since the early measurements and classification schemes of Bader in 1939, many investigators have

expanded the permeability database to include observations of a wide range of snow types. We

summarize these data and report our own recent observations from the New England sites and from

an additional site in Manitoba, Canada. We note that filter velocities are high in the CRREL perme-

ameters and are likely beyond the range of Darcy's Law when they exceed 1.3104 (1 φ)/D m s1.

In this case, data can be corrected either with the Ergun equation or with a multiple regression of the

pressure gradient on velocity and velocity-squared. Our measurements are in the high range of re-

ported values. However, after normalizing our data by the square of grain size, they follow the

empirical function of Shimizu fairly closely. This agreement supports our measurements, and dem-

onstrates the usefulness of Shimizu's function for snow types other than the relatively dense, fine-

grained snow used in his analysis.

Our normalized permeability data for low-density snow, as well as the Shimizu function, are below

Happel and Brenner's (1965) cell model predictions for suspensions of spheres and infinite cylin-

ders. By extending their cell model to oblate spheroids and discs, we estimate permeability that is in

closer agreement with our data. Theoretically determined K from these models is reduced mainly

because of the higher surface-to-volume ratio of more asymmetric particles. We suggest that a de-

crease in surface-to-volume ratio as snow ages accounts for a relative increase in normalized perme-

ability.

U.S. Army Cold Regions Research and Engineering Laboratory, 72 Lyme Road, Hanover, New Hampshire

03755-1290, USA