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Title: Fractal structures in freezing brine
Authors: Alyaev, Sergey
Keilegavlen, Eirik
Nordbotten, Jan Martin
Pop, Sorin
Issue Date: 2017
Citation: JOURNAL OF FLUID MECHANICS, 826, p. 975-995
Abstract: The process of initial ice formation in brine is a highly complex problem. In this paper, we propose a mathematical model that captures the dynamics of nucleation and development of ice inclusions in brine. The primary emphasis is on the interaction between ice growth and salt diffusion, subject to external forcing provided by temperature. Within this setting two freezing regimes are identified, depending on the rate of change of the temperature: a slow freezing regime where a continuous ice domain is formed; and a fast freezing regime where recurrent nucleation appears within the fluid domain. The second regime is of primary interest, as it leads to fractal-like ice structures. We analyse the critical threshold between the slow and fast regimes by identifying the explicit rates of external temperature control that lead to self-similar salt-concentration profiles in the fluid domains. Subsequent heuristic analysis provides estimates of the characteristic length scales of the fluid domains depending on the time-variation of the temperature. The analysis is confirmed by numerical simulations.
Notes: [Alyaev, Sergey; Keilegavlen, Eirik; Nordbotten, Jan Martin; Pop, Iuliu Sorin] Univ Bergen, Dept Math, Postboks 7803, N-5020 Bergen, Norway. [Alyaev, Sergey] IRIS, Thormoehlensgt 55, N-5008 Bergen, Norway. [Nordbotten, Jan Martin] Princeton Univ, Dept Civil & Environm Engn, Princeton, NJ 08544 USA. [Pop, Iuliu Sorin] Univ Hasselt, Fac Sci, Campus Diepenbeek,Agoralaan Bldg D, BE-3590 Diepenbeek, Belgium.
URI: http://hdl.handle.net/1942/24842
DOI: 10.1017/jfm.2017.472
ISI #: 000407896700006
ISSN: 0022-1120
Category: A1
Type: Journal Contribution
Validation: ecoom, 2018
Appears in Collections: Research publications

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