کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1898090 1534070 2007 8 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Self-similar asymptotics for a class of Hele–Shaw flows driven solely by surface tension
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Self-similar asymptotics for a class of Hele–Shaw flows driven solely by surface tension
چکیده انگلیسی

We investigate the dynamics of relaxation, by surface tension, of a family of curved interfaces between an inviscid and viscous fluids in a Hele–Shaw cell. At t=0t=0, the interface is assumed to be of the form |y|=Axm|y|=Axm, where A>0A>0, m≥0m≥0, and x>0x>0. The case of 01m>1 corresponds to a cusp, whereas m=1m=1 corresponds to a wedge. The inviscid fluid tip retreats in the process of relaxation, forming a lobe which size increases with time. Combining analytical and numerical methods we find that, for any mm, the relaxation dynamics exhibits self-similar behavior. For m≠1m≠1 this behavior arises as an intermediate asymptotics: at late times for 0≤m<10≤m<1, and at early times for m>1m>1. In both cases the retreat distance and the lobe size exhibit power-law behaviors in time with different dynamic exponents, uniquely determined by the value of mm. In the special case of m=1m=1 (the wedge) the similarity is exact and holds for the whole interface at all times t>0t>0, while the two dynamic exponents merge to become 1/3. Surprisingly, when m≠1m≠1, the interface shape, rescaled to the local maximum elevation of the interface, turns out to be universal (that is, independent of mm) in the similarity region. Even more remarkably, the same rescaled interface shape emerges in the case of m=1m=1 in the limit of zero wedge angle.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica D: Nonlinear Phenomena - Volume 235, Issues 1–2, November 2007, Pages 48–55
نویسندگان
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