Ice wicking

Liquid-ice interactions are becoming increasingly relevant for many applications including hydraulic fracturing, arctic drilling, and liquid-impregnated surfaces. It is therefore surprising that the capillary action of a liquid wicking across the surface of ice has never been characterized. We observe silicone oil as it wicks up sheets of frost grown on vertically oriented aluminum surfaces of varying wettability. Superhydrophilic and hydrophilic surfaces promote the growth of continuous frost sheets which displace oil with a power-law slope of 1/3 with respect to time. While in contrast to the 1/2 slope of Washburn's law governing most porous media, the 1/3 slope can be rationalized by considering the dendritic frost structure as an array of vertical wedges incapable of supporting the liquid's weight. Nonwetting surfaces grow frost from a more dilute distribution of frozen dropwise condensate, resulting in lower slopes of 1/4 for hydrophobic surfaces and nearly zero for superhydrophobic surfaces promoting jumping-droplet condensation. When switching to a near-horizontal orientation, Washburn's law is obtained for continuous frost sheets. The spreading rate of a liquid across frost can therefore be controlled by tuning the underlying surface wettability or surface orientation. Finally, we show that oils cannot wick inside of a bulk volume of frozen water due to the small pore size of the hexagonal lattice structure.

Figure 1

(a) Liquid-ice interactions are relevant to a myriad of systems such as oil spills (pictured above), arctic drilling, rain impacting icy ground, or liquid-impregnated surfaces. (b) An unexplored mechanism driving liquid transport across dendritic ice structures is capillary action.

Figure 2

Frost wicking setup. (a) Side view of the experimental setup in an environmental chamber. (b) Depiction of dipping a vertically oriented sheet of frost into an oil bath to observe ice wicking.

Figure 3

(a) Side-view imaging of individual ice dendrites after $t\sim 10\mathrm{s}$ of frost growth. The surface temperature was $T_w=-30{}^{\circ }\mathrm{C}$ with ambient conditions of $T_{\infty }\approx 23{}^{\circ }\mathrm{C}$ and $H_{\text{rel}}\approx 54\%$. (b) For 3-mm-thick frost sheets, top-down imaging reveals that the overall frost morphology varies dramatically for HPL, HPB, and SHPB surfaces.

Figure 4

Wicking rates of silicone oils up frost sheets grown on vertically oriented aluminum plates held to $T_w=-5{}^{\circ }\mathrm{C}$. (a) 10-cSt silicone oil wicking up 3-mm-thick frost sheets, for wettabilities ranging from SHPL to SHPB. (b) Silicone oil wicking across frost grown on a HPL aluminum plate, where the oil viscosity and frost thickness were varied. See movies 1 and 2 in [30] for the wicking dynamics corresponding to (a) and (b). (c) Time-lapse thermographic images of 10-cSt silicone oil wicking up a HPL surface covered with 3 mm of frost. The substrate was chilled to $T_w=-10{}^{\circ }\mathrm{C}$, while the ambient conditions were $T_{\infty }\approx 23{}^{\circ }\mathrm{C}$ and $H_{\text{rel}}\approx 65.6\%$. The emissivity coefficient of ice was calibrated to $\epsilon =0.98$. White arrows were added digitally to (b) and (c) to help visualize the location of the wicking front.

Figure 5

Displacement vs time for silicone oils wicking up vertically oriented frost sheets. The oil displacement for frost grown on (a) SHPL and (b) HPL surfaces follows a 1/3 power-law slope, in agreement with Eq. (3), which models wicking up vertical arrays of corners. (c) The oil displacement for frost grown on HPB aluminum decays beneath this 1/3 power law, due to the nonuniform coverage of the frozen dropwise condensation. (d) For frost grown on SHPB surfaces, the oil either did not wick at all or only in slow increments due to the dilute coverage of jumping-droplet condensation. Dashed lines in (a)–(c) all correspond to Eq. (3) for $\beta =0.4$.

Figure 6

(a) Radial spreading of a $50\text{−}\mu \mathrm{L}$ droplet of 10-cSt silicone oil on a horizontally oriented SHPL substrate covered with a 1-mm-tall frost sheet. (b) The radial spreading of the droplet was measured every 5 s for 30 s by averaging the radial displacement on all four sides of the droplets. Error bars are one standard deviation of the average of the four measurements. The data obey the $t^{1/3}$ power law predicted by Eq. (4) (dotted line).

Figure 7

(a) Experimental setup for connecting the bottom of a slightly inclined frosted substrate to an oil reservoir. (b) The displacement of 10-cSt silicone oil was measured every 30 s for over 2 h by averaging three points (left, right, and middle) of the oil-frost interface. The data obey the $t^{1/2}$ power law predicted by Eq. (1) (dashed line).

Figure 8

Setup for bulk ice wicking experiments. (a) Schematic of the aluminum chamber containing frozen water. After freezing is complete, the bottom and side panels are removed to expose the bottom of the ice column to an oil bath and a sidewall of the ice column for imaging any resulting wicking. (b) Photograph of the chamber full of ice and submerged in oil. The top of the ice column visible in the viewing window is outlined in the red inset.