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Transient and stationary axial dispersion in vortex array flows—II. Decoupling of inter- and intra-vortex transport phenomena

Chemical Engineering Science
Publication Date
DOI: 10.1016/s0009-2509(97)00049-3
  • Dispersion
  • Vortex
  • Flow
  • Tracer
  • Axial Scan
  • Mass Transfer
  • Mathematics


Abstract In flows consisting of arrays of vortex units, the transient dispersion regime is of a very complex nature: the effective dispersion coefficient varies strongly with time, comprises both inter- and intra-vortex phenomena and depends heavily upon the injection condition. However, in an infinite array of identical vortices, it is found that when the cross-section of a vortex is injected homogeneously, the effective dispersion coefficient remains strictly constant and is independent of all intra-vortex transport phenomena. In other words, regardless of the presence of strong intra-vortex concentration gradients, the second-order moment of the tracer distribution varies with the time as if all the vortices are perfectly mixed. A mathematical proof for this phenomenon is given. A measurement method based upon this feature allows the separate and direct determination of the inter-vortex exchange coefficient in laminar Couette-Taylor flow, without the need to quantify the intra-vortex transport phenomena, or without the need to wait until all intra-vortex concentration gradients have disappeared. The obtained experimental correlation validates recently performed theoretical calculations and shows that the mass transfer occurs by means of a continuous, strictly ordered surface renewal mechanism. For the transient dispersion effects which are obtained when nonhomogeneous injections are applied, an approximate expression for the variation of the effective dispersion coefficient with the time is established. Within the (very good) accuracy of this expression, the effect of the inter- and intra-vortex transport upon the tracer dispersion rates could also be decoupled.

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