In an attempt to improve the poor prediction of our previous theory, we examine corrections from the small region in a Hele-Shaw cell near the meniscus where the flow is three dimensional. At larger Reynolds numbers, we find an O(1) change to the effective boundary condition for mass conservation which is to be applied to the large scale flow outside the small region.

1.
P.
Gondret
and
M.
Rabaud
, “
Shear instability of two-fluid parallel flow in a Hele-Shaw cell
,”
Phys. Fluids
9
,
3267
(
1997
).
2.
P.
Plouraboué
and
E. J.
Hinch
, “
Kelvin–Helmholtz instability in a Hele-Shaw cell
,”
Phys. Fluids
14
,
922
(
2002
).
3.
L.
Meignin
,
P.
Ern
,
P.
Gondret
, and
M.
Rabaud
, “
Gap size effects for the Kelvin–Helmholtz instability in a Hele-Shaw cell
,”
Phys. Rev. E
64
,
026308
(
2001
).
4.
C.-W.
Park
and
G. M.
Homsy
, “
Two-phase displacement in Hele-Shaw cells: Theory
,”
J. Fluid Mech.
139
,
291
(
1984
).
5.
L.
Meignin
,
P.
Gondret
,
C.
Ruyer-Quil
, and
M.
Rabaud
, “
Subcritical Kelvin–Helmholtz instability in a Hele-Shaw cell
,”
Phys. Rev. Lett.
90
,
234502
(
2003
).
You do not currently have access to this content.