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Fluid front morphologies in gap-modulated Hele-Shaw cells

Lautaro Díaz-Piola1, Ramon Planet1,2, Otger Campàs3, Jaume Casademunt1,2, and Jordi Ortín1,2,*

  • 1Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
  • 2Universitat de Barcelona Institute of Complex Systems, Barcelona, Spain
  • 3Department of Mechanical Engineering, and California NanoSystems Institute, University of California, Santa Barbara, California 93106, USA

  • *jordi.ortin@ub.edu
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Phys. Rev. Fluids 2, 094006 – Published 25 September, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.094006

Abstract

We consider the displacement of an inviscid fluid (air) by a viscous fluid (oil) in a narrow channel with gap-thickness modulations. The interfacial dynamics of this problem is strongly nonlocal and exhibits competing effects from capillarity and permeability. We derive analytical predictions of steady-state front morphologies, which are exact at linear level in the case of a persistent modulation in the direction of front advancement. The theoretical predictions are in good agreement with experimental measurements of steady-state front morphologies obtained in a Hele-Shaw cell with modulations of the channel depth, consisting on three parallel tracks of reduced depth, for small gap modulations. The relative average distance between theoretical and experimental fronts in the region around the central track is smaller than about 4%, provided that the height of the tracks is less than 13% of the total channel depth and the local distortion of the front height h is small enough (|∇h|<0.8) for the linear approximation to hold.

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Phys. Rev. Fluids 2, 094006– Published 25 September, 2017
  • Received 26 May 2017

©2017 American Physical Society

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