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Spreading melts with basal solidification
Author(s) -
Bunk M.A.,
King J.R.
Publication year - 2003
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200310058
Subject(s) - isothermal process , mechanics , lubrication theory , flow (mathematics) , thermal , materials science , thermodynamics , gravitation , range (aeronautics) , substrate (aquarium) , lubrication , geology , physics , composite material , classical mechanics , oceanography
Spreading of melts under the influence of solidification has a wide range of applications in engineering and nature. The isothermal spreading process of a viscous melt under the influence of gravity has been well studied in the literature. Features of many practical spreading flows, however, cannot be described with an isothermal model, non‐isothermal effects often being non‐negligible. Due to the range of properties of the melt and possible thermal boundary conditions, many different problems suggest themselves; this paper concerns the spreading of melts on a horizontal substrate under the influence of basal solidification. Using lubrication theory for spreading flows in the viscous/gravitational regime the influence of solidification on the spreading flow is considered for melts with a large release of latent heat. We consider two‐dimensional melts with cross‐sectional area be proportional to t α . The results show different spreading regimes, depending on the parameter α. We get complete solidification for α = 0, retreating contact lines for 0 < α < 1/2, stagnating contact lines for α = 1/2, and advancing contact lines for α > 1/2. The asymptotic behaviour for short and large times is discussed, clarifying the various regimes.