hypothetically explains the observed delays of approxi-

1 (*z *+ *z*p )*k*i kp

(

)

φ∆*z*

∇*p *+ ρlg

=-

mately three and seven days in Figure 11. We recall

(10)

*k*p z + *k*i zp

resaturation on the wetting cycle for runs 1 of both

where is the viscosity of water (1.789 103), g the

samples. In these cases, water continued to enter the

gravitational constant (9.8 m s2), ρl the density of water

ice after the next drying cycle was initiated (e.g., dry-

(1000 kg m3), and ∇*p *the pressure gradient. The quan-

ing curve in Fig. 10). Solution of eq 11, subject to the

tity in the brackets is the mean harmonic permeability,

observed delay times and a rise height *z *of *h*i, yields

extremely low ice permeabilities of around 4 1019

where *k*i is the ice permeability, *z*p the thickness of the

and 1 1018, respectively, for runs 2 and 3. Corre-

porous plate, and *k*p the plate permeability. Pressures

at the top of the rise *z *and at the bottom of the porous

sponding air entry values are 4.3 and 3.4 kPa. Appen-

plate are respectively the nodal entry tension, *P*Wn,

dix A provides details on the solution.

and the gravitational pressure, ρlg(*h*0 *z*′). These act

Once the sample is saturated, water rises rapidly to

over the combined distance *h*p + *z*. Integrating eq 10

fill the air gap. Tension at the top of the rise (*P*Wn) is

we obtain an implicit equation of rise height in terms

now 0 and the porosity is 1. We determine the thick-

of time

ness of the air gap *t*g from the observed volumes of

water re-entry during phase 2. Note that the area ratio

*P *- ρlg zc

=*t*

- 2 log 0

(11)

Solution of eq 11 for a rise height of *h*i and for the

observed times to complete phase 2 yields

permeabilities of 1 1015 and 3 1015 m2. Thus, the

where

-*c *ρlg

predicted permeability of the newly frozen ice in the

φ

air gap is much larger than that for the central core.

In order to not "over-fit" the data, we use the same

permeabilities for phase 3 that were determined for the

(12)

central core in phase 1. These *k*i values slightly

φ *k*i

overpredict the flow rates for runs 2 and 3. With *b *= 4,

a middle *k*i value of 7 1019 m2 corresponds to vein

and where *P*0 = *P*Wn + ρlg*h*0 , and *c *= (1 + φ*A*r). With

doublet widths of 31 and 8 m. These widths are in

varying parameters and boundary conditions (Table 2),

line with values suggested by the MC runs.

eq 11 describes the three flow phases observed in Fig-

The higher permeabilities for phase 2 are consistent

ure 11. We explain the three phases as follows: 1) water

with greater vein dilation in ice at the sides of the

rises under tension within the central ice core until the

sample, but also suggest that by comparison ice in the

veins are saturated, 2) water rises under a gravitational

central core underwent structural changes during the

head to fill the air gap, and 3) water flows to a seepage

experiments. All four runs with sufficient data for analy-

face at the top of the ice sample.

sis showed long equilibrium times, on the order of

The hypothesis of unsaturated flow in phase 1 is the

weeks, for the wetting curve. We speculate that vein-

most speculative of the three scenarios. Flow under ten-

wall melting during the desaturation process may have

sion prevents entry of water into the side air gap and

Phase 1

Phase 2

Phase 3

0.00635

0.043

0.043

6.35 1016

0.25 0.29

0.25 0.29

0.21 0.25

58.1

0.837

0.884

58.1

0.0003

0.0003

0

4 1019 1 1018

1 1015 3 1015

4 1019 1 1018

4.0 4.0

na

na

Φ

0.001 0.001

1.0

1.0

4.3 3.4

0

0