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Dean vortices with wall flux in a curved channel membrane system: 2. The velocity field

Authors

  • Kun Yong Chung,

    1. Bioseparations Research Center, Howard P. Isermann Dept. of Chemical Engineering, Rennselaer Polytechnic Institute, Troy, NY 12180
    Current affiliation:
    1. CFC Alternatives Technology Center, KIST, P.O. Box 131, Cheongryang, Seoul 130–650, Korea
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  • Mary E. Brewster,

    1. Bioseparations Research Center, Howard P. Isermann Dept. of Chemical Engineering, Rennselaer Polytechnic Institute, Troy, NY 12180
    Current affiliation:
    1. Battelle Pacific Northwest Labs., P.O. Box 999, Richland, WA 99352
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  • Georges Belfort

    Corresponding author
    1. Bioseparations Research Center, Howard P. Isermann Dept. of Chemical Engineering, Rennselaer Polytechnic Institute, Troy, NY 12180
    • Bioseparations Research Center, Howard P. Isermann Dept. of Chemical Engineering, Rennselaer Polytechnic Institute, Troy, NY 12180
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Abstract

The velocity and pressure fields and the effect of wall flux on these fields in a spiral channel are presented. As fluid flows inward through a spiral channel with constant gap and permeable walls, the streamwise flux decreases while the curvature increases. Thus, by balancing the stabilizing effect of wall suction with the destabilizing effect of increasing curvature, established vortices can be maintained along the spiral channel. This approach is used to prescribe spiral geometries with different wall fluxes. Using a weakly nonlinear stability analysis, the influence of wall flux on the characteristics of Dean vortices is obtained. The critical Dean number is reduced when suction is through the inner wall only, is slightly reduced when suction is equal through both walls, and is increased when suction is through the outer wall only. The magnitude of change is proportional to a ratio of small numbers that measures the importance of the effect of curvature. In membrane filtration applications the wall flux is typically 2 to 5 orders of magnitude less than the streamwise flow. If the radius of curvature of the channel is of the order of 100 times the channel gap, the effect on the critical Dean number is within 2% of the no-wall flux case. If the radius of curvature is sufficiently large, however, it is possible to observe effects on the critical Dean number that approach O(1) in magnitude for certain parameter ranges.

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