Selection of the Saffman-Taylor Finger Width in the Absence of Surface Tension: An Exact Result

Journal Article · Sat Feb 28 23:00:00 EST 1998 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.80.2113· OSTI ID:578102

Mineev-Weinstein, M ^[1]

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1. Theoretical Division, MS-B213, LANL, Los Alamos, New Mexico 87545 (United States)

Using exact time-dependent nonsingular solutions [Mineev-Weinstein and Dawson, Phys.Rev.E {bold 50}, R24 (1994); Dawson and Mineev-Weinstein, Physica (Amsterdam) {bold 73D}, 373 (1994)], we solve the Saffman-Taylor finger selection problem in the absence of surface tension. We show that a generic interface in a Hele-Shaw cell evolves to a nonlinearly stable single uniformly advancing finger occupying one-half of the channel width. This result contradicts the generally accepted belief that surface tension is indispensable for the selection of the 1/2-width finger. {copyright} {ital 1998} {ital The American Physical Society}

• OSTI ID: 578102
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 10 Vol. 80; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
FINGERS
INTERFACES
STABILITY
SURFACE TENSION
TIME DEPENDENCE
WIDTH