کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10481983 | 933249 | 2012 | 28 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On the thinning of films (I)
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
فیزیک ریاضی
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
We investigate, from a mathematical perspective, the problem of a layer of fluid attracted to a horizontal plate when the layer is in equilibrium with a bulk reservoir. It is assumed that as the temperature varies, the bulk undergoes a continuous phase transition. On the basis of free energetics, this initially causes thinning of the layer but, at lower temperatures, the layer recovers and rebuilds. We provide a mathematical framework with which to investigate these problems. As an approximation, we model the layered system by a mean-field Ising magnet. The layered system is first studied in isolation (fixed thickness) and then as a system in contact with the bulk (variable thickness) with general results established. Finally, we investigate the limit of large thickness. Here, a well defined continuum theory emerges which provides an approximation to the discrete systems. In the context of the limiting theory, it is established that discontinuities in the layer thickness (as a function of temperature) or the derivative thereof are inevitable. By comparison with actual data from Garcia and Chan (1998) [1] and Ganshin et al. (2006) [2] the discontinuities may indeed be present but they are not quite in the form predicted by the theory. Finally-still in the context of the limiting theory-it is shown that at low temperatures, the layer may be lost altogether; the nature of the critical binding force is elucidated.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica A: Statistical Mechanics and its Applications - Volume 391, Issue 7, 1 April 2012, Pages 2353-2380
Journal: Physica A: Statistical Mechanics and its Applications - Volume 391, Issue 7, 1 April 2012, Pages 2353-2380
نویسندگان
Lincoln Chayes, Joseph Rudnick, Aviva Shackell, Roya Zandi,