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Kinetic roughening in two-phase fluid flow through a random Hele-Shaw cell
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A nonlocal interface equation is derived for two-phase fluid flow, with arbitrary wettability and viscosity contrast,
c
=
(
μ
1
−
μ
2
)
/
(
μ
1
+
μ
2
)
, in a model porous medium defined as a Hele-Shaw cell with random gap
b
0
+
δ
b
. Fluctuations of both capillary and viscous pressure are explicitly related to the microscopic quenched disorder, yielding conserved, nonconserved, and power-law correlated noise terms. Two length scales are identified that control the possible scaling regimes and which scale with capillary number Ca as
ℓ
1
∼
b
0
(
c
C
a
)
−
1
/
2
and
ℓ
2
∼
b
0
C
a
−
1
. Exponents for forced fluid invasion are obtained from numerical simulation and compared with recent experiments.
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PAUNÉ I XURIGUERA, Eduard and CASADEMUNT I VIADER, Jaume. Kinetic roughening in two-phase fluid flow through a random Hele-Shaw cell. Physical Review Letters. 2003. Vol. 90, num. 14, pags. 144504-1-144504-4. ISSN 0031-9007. [consulted: 20 of August of 2026]. Available at: https://hdl.handle.net/2445/12830