Response analysis for the early stages of sedimentation processes

نویسنده

  • Christian Manwart
چکیده

We study correlations between the velocity and the density distribution in non-Brownian particle suspensions at small particle Reynolds numbers Re 1 under the innuence of gravity. If the system is initially at rest, the velocity distribution will soon organize itself into diierent regions of ow mainly moving in and against the direction of gravity. A speciic width is associated with the emerging ngers or \streets" both in bulk suspensions and in unstably stratiied systems, where particle laden uid is placed above pure uid. Whereas for the case of unstable stratiication classical Rayleigh-Taylor theory predicts exponential growth of the arising initial velocity uctuations, we nd that the system is driven by the initial density inhomogeneities that necessarily exist in a particulate suspension. The corresponding velocity modes saturate exponentially. The spatial correlation length of the emerging ngers grows in time until it reaches a limit, which depends either on the system size or for \innnite systems" possibly on the Reynolds number. We study the phenomenon using two and three dimensional linear analysis of model continuum equations. A comparison of our results with two dimensional computer simulations follows the predictions of the analytical approach in a wide parameter range.

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تاریخ انتشار 1998