Selection in the Saffman-Taylor finger problem and the Taylor-Saffman bubble problem without surface tension
نویسندگان
چکیده
منابع مشابه
Selection of the Saffman-Taylor Finger Width in the Absence of Surface Tension: an Exact Result
We solve the Saffman-Taylor finger selection problem in the absence of surface tension by showing that an arbitrary interface in a Hele-Shaw cell evolves to a single uniformly advancing finger occupying one half of the channel width. This result contradicts all previous work in this field and the generally accepted belief that surface tension is indispensable for the selection of the 1 2 -width...
متن کاملSaffman-Taylor problem on a sphere.
The Saffman-Taylor problem addresses the morphological instability of an interface separating two immiscible, viscous fluids when they move in a narrow gap between two flat parallel plates (Hele-Shaw cell). In this work, we extend the classic Saffman-Taylor situation, by considering the flow between two curved, closely spaced, concentric spheres (spherical Hele-Shaw cell). We derive the mode-co...
متن کاملSelection of the Taylor-Saffman bubble does not require surface tension.
A new general class of exact solutions is presented for the time evolution of a bubble of arbitrary initial shape in a Hele-Shaw cell when surface tension effects are neglected. These solutions are obtained by conformal mapping the viscous flow domain to an annulus in an auxiliary complex plane. It is then demonstrated that the only stable fixed point (attractor) of the nonsingular bubble dynam...
متن کاملComment on "Two-finger selection theory in the Saffman-Taylor problem".
It is pointed out that the two-parameter family of solutions for the Saffman-Taylor problem recently studied by Magdaleno and Casademunt [Phys. Rev. E 60, R5013 (1999)] does not correspond to two fingers moving in a Hele-Shaw cell with the channel geometry, as was implied in their paper. It is thus clarified that their solution, while correctly describing a periodic array of axisymmetric finger...
متن کاملNonlinear Saffman-Taylor instability.
We show, both theoretically and experimentally, that the interface between two viscous fluids in a Hele-Shaw cell can be nonlinearly unstable before the Saffman-Taylor linear instability point is reached. We identify the family of exact elastica solutions [Nye et al., Eur. J. Phys. 5, 73 (1984)]] as the unstable branch of the corresponding subcritical bifurcation which ends up at a topological ...
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 1998
ISSN: 0893-9659
DOI: 10.1016/s0893-9659(98)00103-7