Comment 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 fingers in an unbounded Hele-Shaw cell, gives rather a central finger flanked by two half-fingers when restricted to a channel with impermeable rectilinear walls. The correct four-parameter family of exact solutions for two unequal fingers in such a channel is presented for the zero surface tension case.
Vasconcelos
G L
GL
Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, Brazil.