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Premelting, Pressure Melting, and Regelation of Ice Revisited

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Premelting, Pressure Melting, and Regelation of Ice Revisited Journal of Applied Mathematics and Physics, 2018, 6, 2181-2191 http://www.scirp.org/journal/jamp ISSN Online: 2327-4379 ISSN Print: 2327-4352 Premelting, Pressure Melting, and Regelation of Ice Revisited Chloe T. Calderon, Pirooz Mohazzabi Department of Mathematics and Physics, University of Wisconsin-Parkside, Kenosha, WI, USA How to cite this paper: Calderon, C.T. and Mohazzabi, P. (2018) Premelting, Pres- Abstract sure Melting, and Regelation of Ice Revisited. Journal of Applied Mathematics and Physics, In this article we review some of the most important and relevant 6, 2181-2191. literature on the properties of ice. We focus on three of its surface https://dx.doi.org/10.4236/jamp.2018.611183 properties, namely, the slipperiness of ice, the phenomena of a string under load passing through a block of ice without cutting the block Received: September 26, 2018 in half, and pressure melting and adhesion of blocks of ice. We then Accepted: November 4, 2018 provide an argument for the most plausible factor responsible for Published: November 7, 2018 each of these effects. Copyright c 2018 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Com- Keywords mons Attribution International License (CC BY 4.0). Ice Regelation, Pressure Melting, Quasi-Liquid http://creativecommons.org/licenses/by/4.0/ 1. Introduction Lorem ipsum dolor sit amet, consectetuer Perhaps the most interesting solid that we encounter in our everyday adipiscing elit. Ut purus elit, vestibulum ut, life is ice. Ice is one of the few materials in nature with the property placerat ac, adipiscing vitae, felis. Curabitur dictum gravida mauris. Nam arcu libero, of expansion when its liquid form freezes. The cause of this expan- nonummy eget, consectetuer id, vulputate a, sion is the formation of a hexagonal ring structure. However, none of magna. Donec vehicula augue eu neque. Pel- the other materials with this property (such as bismuth) are nearly lentesque habitant morbi tristique senectus et as important in life as water is. Another interesting property of ice netus et malesuada fames ac turpis egestas. Mauris ut leo. Cras viverra metus rhoncus is its unusual slipperiness. At the macroscopic level, the coefficient of sem. Nulla et lectus vestibulum urna fringilla friction on ice is about one order of magnitude lower than other solid- ultrices. Phasellus eu tellus sit amet tortor s; however, it is not constant and varies with factors such as sliding gravida placerat. Integer sapien est, iaculis in, speed, temperature, and the normal force [1]. This small coefficien- pretium quis, viverra ac, nunc. Praesent eget sem vel leo ultrices bibendum. Aenean fau- t of friction makes ice even more distinct from other materials since cibus. Morbi dolor nulla, malesuada eu, pulv- generally the coefficient of kinetic friction increases with temperature, inar at, mollis ac, nulla. Curabitur auctor sem- whereas the coefficient of kinetic friction of ice decreases with an in- per nulla. Donec varius orci eget risus. Duis crease in temperature [2]. Therefore, one should really compare the nibh mi, congue eu, accumsan eleifend, sagit- tis quis, diam. Duis eget orci sit amet orci coefficient of friction of ice at a few degrees below its melting point to dignissim rutrum. that of other materials when they are also a few degrees below their Nam dui ligula, fringilla a, euismod sodales, melting points. The difference would certainly be greater than just sollicitudin vel, wisi. Morbi auctor lorem non one order of magnitude. justo. Nam lacus libero, pretium at, lobortis vitae, ultricies et, tellus. Donec aliquet, tor- Yet another uncommon property that makes ice distinct from other tor sed accumsan bibendum, erat ligula aliquet materials is regelation, where two pieces of ice bond when pushed magna, vitae ornare odio metus a mi. Morbi ac orci et nisl hendrerit mollis. Suspendisse DOI:ut massa. 10.4236/jamp.2018.611183 Cras nec ante. Pellentesque Nov. a nul- 7, 2018 2181 Journal of Applied Mathematics and Physics la. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Aliquam tincidunt urna. Nulla ullamcorper vestibulum turpis. Pellentesque cursus luctus mauris. Nulla malesuada porttitor diam. Donec felis erat, congue non, volutpat at, tincidunt tris- tique, libero. Vivamus viverra fermentum felis. Donec nonummy pellentesque ante. Phasellus adipiscing semper elit. Proin fermentum mas- sa ac quam. Sed diam turpis, molestie vitae, placerat a, molestie nec, leo. Maecenas lacinia. Nam ipsum ligula, eleifend at, accumsan nec, suscipit a, ipsum. Morbi blandit ligula feu- giat magna. Nunc eleifend consequat lorem. Sed lacinia nulla vitae enim. Pellentesque t- incidunt purus vel magna. Integer non en- im. Praesent euismod nunc eu purus. Donec bibendum quam in tellus. Nullam cursus pul- vinar lectus. Donec et mi. Nam vulputate metus eu enim. Vestibulum pellentesque felis eu massa. Quisque ullamcorper placerat ipsum. Cras nibh. Morbi vel justo vitae lacus tincidun- t ultrices. Lorem ipsum dolor sit amet, con- sectetuer adipiscing elit. In hac habitasse platea dictumst. Integer tempus convallis au- gue. Etiam facilisis. Nunc elementum fermen- tum wisi. Aenean placerat. Ut imperdiet, en- im sed gravida sollicitudin, felis odio placerat quam, ac pulvinar elit purus eget enim. Nunc vitae tortor. Proin tempus nibh sit amet nisl. Vivamus quis tortor vitae risus porta vehicula. Fusce mauris. Vestibulum luctus nibh at lec- tus. Sed bibendum, nulla a faucibus semper, leo velit ultricies tellus, ac venenatis arcu wisi vel nisl. Vestibulum diam. Aliquam pellen- tesque, augue quis sagittis posuere, turpis la- cus congue quam, in hendrerit risus eros eget felis. Maecenas eget erat in sapien mattis port- titor. Vestibulum porttitor. Nulla facilisi. Sed a turpis eu lacus commodo facilisis. Morbi fringilla, wisi in dignissim interdum, justo lec- tus sagittis dui, et vehicula libero dui cursus dui. Mauris tempor ligula sed lacus. Duis cur- sus enim ut augue. Cras ac magna. Cras nulla. Nulla egestas. Curabitur a leo. Quisque eges- tas wisi eget nunc. Nam feugiat lacus vel est. Curabitur consectetuer. Suspendisse vel felis. Ut lorem lorem, inter- dum eu, tincidunt sit amet, laoreet vitae, ar- cu. Aenean faucibus pede eu ante. Praesent enim elit, rutrum at, molestie non, nonummy vel, nisl. Ut lectus eros, malesuada sit amet, fermentum eu, sodales cursus, magna. Donec eu purus. Quisque vehicula, urna sed ultricies auctor, pede lorem egestas dui, et convallis elit erat sed nulla. Donec luctus. Curabitur et nunc. Aliquam dolor odio, commodo pretium, ultricies non, pharetra in, velit. Integer arcu est, nonummy in, fermentum faucibus, egestas vel, odio. Sed commodo posuere pede. Mauris ut est. Ut quis purus. Sed ac odio. Sed vehicula hen- drerit sem. Duis non odio. Morbi ut dui. Sed accumsan risus eget odio. In hac habitasse platea dictumst. Pellentesque non elit. Fusce sed justo eu urna porta tincidunt. Mauris felis odio, sollicitudin sed, volutpat a, ornare ac, er- at. Morbi quis dolor. Donec pellentesque, er- at ac sagittis semper, nunc dui lobortis purus, quis congue purus metus ultricies tellus. Proin et quam. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos hy- menaeos. Praesent sapien turpis, fermentum vel, eleifend faucibus, vehicula eu, lacus. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis eges- tas. Donec odio elit, dictum in, hendrerit sit amet, egestas sed, leo. Praesent feugiat sapi- en aliquet odio. Integer vitae justo. Aliquam vestibulum fringilla lorem. Sed neque lectus, consectetuer at, consectetuer sed, eleifend ac, lectus. Nulla facilisi. Pellentesque eget lec- tus. Proin eu metus. Sed porttitor. In hac habitasse platea dictumst. Suspendisse eu lec- tus. Ut mi mi, lacinia sit amet, placerat et, mollis vitae, dui. Sed ante tellus, tristique ut, iaculis eu, malesuada ac, dui. Mauris nibh leo, facilisis non, adipiscing quis, ultrices a, dui. Morbi luctus, wisi viverra faucibus pretium, nibh est placerat odio, nec commodo wisi enim eget quam. Quisque libero justo, consectetuer a, feugiat vitae, porttitor eu, libero. Sus- pendisse sed mauris vitae elit sollicitudin male- suada. Maecenas ultricies eros sit amet ante. Ut venenatis velit. Maecenas sed mi eget dui varius euismod. Phasellus aliquet volutpat o- dio. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Pellentesque sit amet pede ac sem eleifend con- sectetuer. Nullam elementum, urna vel im- perdiet sodales, elit ipsum pharetra ligula, ac pretium ante justo a nulla. Curabitur tristique arcu eu metus. Vestibulum lectus. Proin mau- ris. Proin eu nunc eu urna hendrerit faucibus. Aliquam auctor, pede consequat laoreet var- ius, eros tellus scelerisque quam, pellentesque hendrerit ipsum dolor sed augue. Nulla nec lacus. Suspendisse vitae elit. Aliquam arcu neque, ornare in, ullamcorper quis, commodo eu, libero. Fusce sagittis erat at erat tristique mollis. Maecenas sapien libero, molestie et, lobortis in, sodales eget, dui. Morbi ultrices rutrum lorem. Nam elementum ullamcorper leo. Morbi dui. Aliquam sagittis. Nunc plac- erat. Pellentesque tristique sodales est. Mae- cenas imperdiet lacinia velit. Cras non urna. Morbi eros pede, suscipit ac, varius vel, eges- tas non, eros. Praesent malesuada, diam id pretium elementum, eros sem dictum tortor, vel consectetuer odio sem sed wisi. Sed feugiat. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Ut pellentesque
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