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Received March 27, 2012
Accepted June 7, 2012
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Onset of radial viscous fingering in a Hele-Shaw cell
Department of Chemical Engineering, Jeju National University, Jeju 690-756, Korea
kim.minchan@gmail.com
Korean Journal of Chemical Engineering, December 2012, 29(12), 1688-1694(7), 10.1007/s11814-012-0091-3
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Abstract
The onset of viscous fingering in a radial Hele-Shaw cell was analyzed by using linear theory. In the selfsimilar domain, the stability equations were derived under the normal mode analysis. The resulting stability equations were solved analytically by expanding the disturbances as a series of orthogonal functions and also numerically by employing the shooting method. It was found that the long wave mode of disturbances has a negative growth rate and the related system is always stable. For the limiting case of the infinite Peclet number, Pe→∞, the analytically obtained critical conditions are Rc=11.10/√Pe and nc=0.87√Pe . For Pe≥100, these stability conditions explain the system quite_x000D_
well.
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