THOSE ICICLES THAT WERE drooping from eaves and telephone lines not long ago may have appeared to be simple constructions, but in fact their shapes and the way they develop have long perplexed people who investigate them. Why is an icicle usually cone-shaped, with a tip no wider than a few millimeters? Why does a narrow, liquid-filled tube of ice extend several centimeters up the center of the icicle from the tip? (You can probe the tube with a toothpick.) What accounts for the white line that traces the central axis of the column? Why do horizontal ribs spaced about a centimeter apart develop along the sides of the column? Why is the ice solid in some places but spongy in others? What bends and twists some icicles?

The physics involved in any freezing of water is always richly complex. In a simple model the freezing interface between liquid and ice consists of dendritic fingers of ice that stretch into the liquid. Along the fingers molecules in the liquid gradually join the crystal structure of the ice by giving up part of their energy and becoming immobile. The lost energy, called heat, is conducted to some region colder than the freezing interface-often to nearby cold air.

Icicles grow by such a process. One way they begin to grow has been studied by Norikazu Maeno and Tsuneya Takahashi of Hokkaido University. Picture a slowly melting blanket of snow on a rooftop. When water first trickles over the edge of the roof, it forms a pendent drop in the cold air. As the sides of the drop begin to freeze, forming a thin shell of ice, the heat released by the freezing is transferred to the air and to the roof edge.

As more meltwater runs down the ice shell, part of it freezes on the way, widening the fledgling icicle. The rest joins the drop dangling at the bottom of the structure [see Figure 2]. The gradual freezing of the sides of the drop lengthens the icicle. If the drop ever becomes too large-somewhat wider than five millimeters-it falls, but additional meltwater soon adds a new drop. As long as the supply of meltwater continues, the icicle grows wider and longer. The tip, whose width is set by the diameter of the pendent drop, remains narrow.

H. Hatakeyama of the Tokyo District Meteorological Observatory and S. Nemoto of the Meteorological Research Institute in Tokyo reported another way an icicle might be initiated [see Figure 3]. The top part of the initial drop may freeze uniformly, creating a horizontal freezing interface that moves downward. If the water supply is feeble and the roof edge is cold, all the water may freeze rather than just a thin shell. The structure may then lengthen in steps as successive meltwater drops develop at the bottom and freeze solid. If, however, there is enough water to maintain a pendent drop, at some stage in the growth of the icicle the sides of the drop will freeze and form an ice shell, as in Maeno and Takahashi's scheme.

Whenever an ice shell forms, the liquid inside the shell from then on freezes only slowly. According to Lasse Makkonen of the Technical Research Center in Espoo, Finland, the heat released by the internal freezing is conducted through the ice to the top of the icicle (called the "root") and then to the edge of the roof. The conduction is so gradual that the internal freezing interface may move down the central axis of the icicle very slowly; if the interface is well separated from the root, as it is in the case of a mature icicle, it may even be stationary.

From the interface to the tip of the icicle, liquid is trapped in a narrow ice tube. In spite of its weight the liquid is stable, in part because of the surface tension between it and the tube's walls. In addition the tube is so narrow that chance disturbances along the bottom of the water column or in the pendent drop are usually insufficient to allow air to seep up into the tube to drain the liquid. In typical winter temperatures the interior freezing interface can reach the tip leaving a completely frozen icicle only if the meltwater supply is cut off and growth at the tip ceases.

The external surface of the ice is sheathed by a thin layer of liquid [see Figure 5]. Freezing at the external ice-liquid interface is rapid, because the heat released by the freezing is quickly conducted through the liquid and lost to the air. (Maeno and Takahashi find that the liquid sheath on active icicles is no thicker than .1 millimeter.) The temperature at the freezing interface is the freezing point of water, which is zero degrees Celsius for pure water but may be lower if the water is impure. The temperature in the rest of the water layer is slightly lower than the freezing point, a condition known as supercooling. The coldest water borders the air, which may of course be considerably colder than the water.

Charles A. Knight of the National Center for Atmospheric Research in Boulder, Colo., points out that icicles can grow in air warmer than the freezing point provided the air has little water vapor. The scarcity of water vapor promotes the evaporation of water from the external surface of the water sheath. As water molecules escape from the liquid, they carry away energy, supercooling the water surface. The chilled water acts as a heat dump, into which water freezing along the ice surface sends its heat.

Why is the heat released along the internal freezing interface not conducted horizontally through the thin layer of ice separating it from the air? The reason is that both the internal and the external freezing interface are at the freezing point of water. With no temperature difference, conduction is eliminated. If the internal interface is to advance, the released heat must be conducted to the root of the icicle.

When the water in or on an icicle freezes, air is driven out of solution, forming bubbles imprisoned in the ice. The most striking bubbles are the tiny ones that develop along the central axis as the internal freezing interface descends. When the icicle is illuminated by white light, some of the light scatters from the bubbles, giving the appearance of a white line along the central axis.

According to Maeno and Takahashi, an icicle lengthens between eight and 32 times faster than it widens. I think one reason for the dissimilar growth rates is that more water collects at the tip than at any place along the sides. Another reason may have to do with the way ice crystals grow. The basic geometry of an ice crystal is a thin hexagonal plate. The central axis perpendicular to the plane of the plate (the basal plane) is called the c axis. As molecules join the plate, it grows more rapidly in the basal plane than along the c axis. If crystals in an icicle are oriented with the c axis pointed radially outward, perpendicular to the freezing interface and thus approximately perpendicular to the central axis of the icicle, then the icicle should be expected to lengthen faster than it widens.

Early research about the dominant orientation of icicle crystals was often contradictory. Some investigators even argued that there is no dominant orientation-that an icicle is a hodgepodge of small, randomly oriented crystals. In an attempt to settle the matter, Robert A. Laudise and Robert L. Barns of the AT&T Bell Laboratories in Murray Hill, N.J., set out with a group of young volunteers to examine icicles collected from nearby houses. Icicles with diameters larger than about an inch were sawed from their perch. The specimens were then sawed again to provide both horizontal and vertical cross sections. Working in a cold room, the investigators reduced each slice to a thickness of about an eighth of an inch by rubbing it on a thick plate of aluminum that had been warmed with hot water.

Inspection involved two "crossed" polarizing filters mounted on a platform that had a glass top. (The arrangement was described in this department in July, 1986.) In this procedure one filter is laid on the glass and a specimen slice is placed on it; a second filter is laid over the slice and is rotated so that its direction of polarization is perpendicular to that of the first filter. Lamplight scattered from white cardboard under the platform becomes polarized when it passes through the lower filter.

In the absence of the icicle specimen, the light could not pass through the second filter. When, however, the light passes through an ice crystal, its polarization is rotated and so depending on the extent of the rotation-all or some of the light does pass through the second filter. When you peer down through the arrangement, the individual ice crystals differ in brightness depending on how much each one rotates the polarization of the light passing through it. If the slice is thin enough, the regions are even colored differently. If the slice is rotated about the vertical, the brightness of each crystal changes unless it happens to have its c axis approximately along your line of sight, in which case it remains dark throughout the rotation. By thus inspecting an icicle slice with polarized light, you can detect both the size of the crystals and the orientation of their c axis.

When Laudise and Barns examined specimens from some 60 icicles, they found that the width of the crystals varied from less than .8 millimeter to more than 20 centimeters. Some icicles consisted of a multitude of small crystals randomly oriented; others had large single crystals whose c axis seemed never to be aligned with the icicle's central axis.

Knight later added the idea that the orientation of the c axis of the large crystals may result from recrystallization as the icicle grows. As heat is supplied from the freezing, initially small and randomly oriented crystals may change their boundaries and merge, becoming oriented as Laudise and Barns observed. Variations in the air temperature or the supply of sunlight and meltwater may also play a role. Knight cautions, however, that crystal orientation may actually have little influence on the shape of an icicle. Instead the dissimilar growth rates may be due to the way heat is removed from an icicle, somewhat as modeled by Makkonen.

The relation between the growth rate of an icicle and the rate at which meltwater is supplied is surprising. According to Maeno and Takahashi, the rate of widening is largely independent of the supply rate; the rate of lengthening, on the other hand, is actually slowed by an increase in the supply rate. The first finding suggests that the liquid sheath maintains a constant thickness, thereby regulating the rate of heat conduction through it and the rate of freezing on the ice surface. The second finding is more difficult to understand. Is the lengthening slowed by heat that is released when a larger supply of water arrives at the drop and then is supercooled? Does the more frequent detachment of drops reduce the chance that drops at the tip will freeze, or does it somehow disrupt the ice growth?

Ira W. Geer of the State University College at Brockport in New York found that an icicle tip is sometimes so irregular that air spurts up into the ice tube, dumping the liquid. The tube is soon refilled by liquid that has drained to the tip along the exterior of the icicle and then is drawn up the tube by surface tension. Usually a large air bubble remains trapped in the upper reaches of the tube, later becoming buried in ice as the interior freezing interface descends.

Geer investigated the growth of an icicle by photographing it every five minutes for about 90 minutes. From the negatives he constructed a composite drawing to learn whether the horizontal ribs along the sides of the icicle migrate vertically in the course of growth. He found that the ribs are approximately stationary; they are regions that grow outward faster than the intermediate hollows do. Maeno and Takahashi offer two explanations for the fast growth of the ribs. The liquid layer is thinner on a rib than it is in the adjacent hollows, allowing the heat from the freezing on the ice surface to be conducted quickly to the external surface of the water. The rib is also more exposed, enhancing heat transfer to the air and perhaps the evaporation of water.

Evidence for the rapid growth of the ribs can be seen in horizontal sections cut from an icicle. A section from a rib region displays abundant air bubbles collected in bands that resemble the growth rings in a cross section cut from a tree. Each band in the icicle is created when the rib grows outward, trapping air bubbles in ice before they can escape. Presumably the bands are linked to variations in air temperature and water supply.

Knight found that the ribs are usually solid ice, whereas the hollows are often spongy: they consist of liquid separating sheets of ice that are extensions of the basal planes of the crystals. He reports that he could insert a knife blade a centimeter or more into the spongy sections, forcing out some of the liquid. Knight suggests that the spongy sections develop during periods when heat loss by the icicle is rapid and the water supply is abundant, but he thinks more study is needed.

Mature icicles also develop vertical ridges, which are often complex and branched. They may be due to wind that increases the removal of heat, and therefore the rate of freezing, on one side of an icicle. Another factor is the possible asymmetry of the water supply. On a wide icicle water may flow along a narrow trail instead of wetting the icicle uniformly. Geer noticed that water draining along a dormant icicle tends to follow one track as long as the track remains wet. The ridge it produces may grow outward five millimeters or more before the water veers off onto a new track. A drop of water may follow a wet track because it encounters less surface tension there than it encounters on a dry, icy region.

Icicles are sometimes decorated with tiny spikes extending from the surface. Maeno and Takahashi measured spikes about a millimeter wide and as much as 20 millimeters long. The spikes are created when the water sheath freezes during a meltwater drought. When liquid water trapped under a skin of ice begins to freeze, its expansion can rupture the skin, ejecting the remaining liquid outward from the surface; the ejected liquid freezes to form a spike. Are the spikes more likely to form in the initially spongy ice where liquid is slow to freeze?

I noticed a different kind of spike on an icicle tip. The collapse of the liquid bridge between a detaching drop and the liquid remaining on the tip frequently left a thread of water that immediately froze. The ice thread, less than a millimeter thick and only two or three millimeters long, was twisted-evidence of the rapid freezing. A touch of my bare finger would melt the thread, and so would the formation of the next pendent drop.

Icicles are often crooked, asymmetric or misaligned from the vertical. Maeno and Takahashi offer several reasons for such growth. Complex shaping can develop from an asymmetric supply of water, particularly on wide icicles. A steady wind can also bias the growth by pushing the pendent drops leeward and by increasing the heat loss on the windward side of the icicle. If the icicle grows on a branch, the gradual addition of weight bends the branch, curving the icicle as the fresh growth at the tip continues to follow the vertical. Similarly, if the icicle grows on the edge of a roof, partial melting of the ice and snow on the roof may allow the layer to creep and curve over the edge, changing the direction of the icicle's growth. To this list of explanations one should add the possibility that wind-driven snow may accumulate on the icicle and distort its shape.

Several helpful suggestions for the study of icicles are available [see "Bibliography"]. For example, Geer wonders how icicle growth might be influenced if an impurity such as salt, soap, alcohol or food coloring were added to the water supply. What would the bubbles be like in an icicle grown with unsalted carbonated water? When a natural icicle becomes dormant, how does sublimation gradually smooth its surface?

More projects can be added to the list. How might a nail embedded in the ice tube at the tip alter the icicle's later growth? What is the temperature distribution inside a mature icicle? What factors determine the length of the ice tube and the size and spacing of the horizontal ribs? Does infrared radiation from nearby warm objects or air turbulence on the leeward side of an icicle bias its shape? How do icicles grow from seawater or freshwater spray? If you are prepared for painstaking work, you might try to correlate the growth rate of an icicle with the ambient air temperature and the wind speed. I shall be interested to hear about your observations of these often ignored sculptures of ice.

Bibliography

ARE ICICLES SINGLE CRYSTALS? R. A. Laudise and R. L. Barns in Journal of Crystal Growth, Vol. 46, No. 3, pages 379-386; March, 1979.

ICICLES AS CRYSTALLIZATION PHENOMENA. Charles A. Knight in Journal of Crystal Growth, Vol. 49, No. 1, pages 193-198; May, 1980.

THE NOT-SO-ORDINARY ICICLE. Ira W. Geer in Weatherwise, Vol. 34, No. 6, pages 257-259; December, 1981.

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