We investigate the viscous fingering instability that arises when air is
injected from the end of an oil-filled, compliant channel. We show that induced
axial and transverse depth gradients foster novel pattern formation. Moreover,
the steady propagation of the interface allows us to elucidate the nonlinear
saturation of a fingering pattern first observed in a time-evolving system
(Pihler-Puzovic et al. PRL 108, 074502, 2012): the wavelength is set by the
viscous fingering mechanism, but the amplitude is inversely proportional to the
tangent of the compliant wall's inclination angle

Ducloue, Lucie

Hazel, Andrew

Juel, Anne

Pihler-Puzovic, Draga

English

arXiv

We present an experimental investigation of interfacial fingering instabilities in a compliant channel, where the interface can adopt a planar front orthogonal to the direction of propagation over most of the channel width. Finite-length fingers develop on that front, similarly to the previously studied radial configuration with injection of air at constant flow rate (Pihler-Puzović et al., Phys. Rev. Lett., vol. 108 (7), 2012, 074502), but, unlike the radial case, the interface propagates steadily. This allows us to present the first quantification of the nonlinearly saturated fingering pattern and to demonstrate that the morphological features of the fingers are selected in a simple way by the local geometry of the compliant cell. In contrast, the local geometry itself is determined from a complex fluid–solid interaction. Furthermore, we find that changes to the geometry of the channel cross-section lead to a rich variety of possible interfacial patterns

The University of Manchester - Institutional Repository

Viscous fingering and dendritic growth under an elastic membrane

We present an experimental investigation of interfacial fingering instabilities in a compliant channel, where the interface can adopt a planar front orthogonal to the direction of propagation over most of the channel width. Finite-length fingers develop on that front, similarly to the previously studied radial configuration with injection of air at constant flow rate (Pihler-Puzović et al., Phys. Rev. Lett., vol. 108 (7), 2012, 074502), but, unlike the radial case, the interface propagates steadily. This allows us to present the first quantification of the nonlinearly saturated fingering pattern and to demonstrate that the morphological features of the fingers are selected in a simple way by the local geometry of the compliant cell. In contrast, the local geometry itself is determined from a complex fluid–solid interaction. Furthermore, we find that changes to the geometry of the channel cross-section lead to a rich variety of possible interfacial patterns.</jats:p

Viscous fingering and dendritic growth under an elastic membrane

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The University of Manchester - Institutional Repository

The University of Manchester - Institutional Repository

The University of Manchester - Institutional Repository

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