Viscous banding instabilities: non-porous viscous fingering

We demonstrate a novel instability found within unconfined viscous bands/rims, or free-surface flows involving longitudinal viscosity contrast. Such instabilities may be described as banding instabilities, non-porous fingering of the intrusion less fluid into band more fluid. A consequence this work is that widely known to occur in porous media following seminal Saffman & Taylor ( Proc. R. Soc. Lond. A, vol. 245, 1958, pp. 312–329), also environments. Although mechanism characteristically different from Saffman–Taylor instability, there are important similarities between two. The main similarity contrast leads instability. distinguishing feature confinement, such rigid walls Hele-Shaw cell, not necessary for occur. More precisely, driven by jump dynamic pressure gradient, whereas hydrostatic directly related slope discontinuity across front. examine onset bands down an inclined plane, determine conditions under which and map out range behaviours parameter space terms two dimensionless parameters: ratio volume ahead