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An experimental study of miscible displacement with gravity-override and viscosity-contrast in a Hele Shaw cell

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Abstract

An experimental investigation of miscible displacements at constant volume flow-rate under the coupled effects of mobility contrast and gravitational segregation has been performed in a Hele Shaw cell having an aspect ratio, width to length, of 1:2. While the viscosity ratio was large (M > 180), the experiments covered both the neutrally buoyant case through to gravity-override-dominated unstable displacements. Dependence of the global displacement properties on the Gravity number (G) and the Peclet number (Pe) were quantified using a flow visualization technique. Within the experiment’s parameter range, no matter how complex the finger patterns became, and independent of G, the area grew linearly in time. As a result, the thickness of the injected less dense and less viscous fluid was almost constant at a value of 0.5–0.58 of the cell thickness with a weak dependence on Peclet number. Based on transversely averaged concentration profiles, the dependence of the average finger length was investigated and it also grew linearly in time. The displacement efficiency and breakthrough time decreased with increase of G, while the longitudinal finger growth rate increased with G. The averaged finger width followed the opposite trend and decreased as G increased. Velocity of the leading fingertip grew linearly with G at fixed Pe. The larger the value of Pe, the faster fingertips spread. As was to be expected, the larger the gravity number, the larger the global tilting of the whole finger pattern. The fractal dimension of the distorted interface at breakthrough was investigated, and it varied from 1.54 for the neutrally buoyant case to 1.08 for the gravity override dominated case.

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Acknowledgments

This work was supported by the US Department of Energy, Office of Basic Energy Sciences under Grant #—DE-FG03-00ER15092—to the University of Southern California.

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  1. Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA, 90089-1191, USA

    Chaoying Jiao & T. Maxworthy

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  1. Chaoying Jiao
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  2. T. Maxworthy
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Correspondence to T. Maxworthy.

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Jiao, C., Maxworthy, T. An experimental study of miscible displacement with gravity-override and viscosity-contrast in a Hele Shaw cell. Exp Fluids 44, 781–794 (2008). https://doi.org/10.1007/s00348-007-0434-8

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  • DOI: https://doi.org/10.1007/s00348-007-0434-8

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