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									          A general correlation for mass transfer in isotropic and anisotropic solid foams
                     G. Incera Garrido, S. Lang, F. Patcas, B. Kraushaar-Czarnetzki,
              Institute of Chemical Process Engineering, University of Karlsruhe, Germany

   The aim of this research was the analysis of mass transfer from the gas phase to the outer
   surface of foams in a wide hydrodynamic range. We investigated ceramic and metallic foams with
   three different porosities and four pore densities as well as a honeycomb and packings of
   spheres for comparison. The catalytic oxidation of CO was chosen as a diagnostic tool. This
   reaction was carried out at 220 °C, at which temperature external mass transfer is rate limiting.
   The reaction unit was a plug flow system with external recycle allowing for the variation of fluid
   velocity. The first step was a detailed analysis of the network structures of the various foams
   because any further property, be it mass (or heat) transfer or pressure drop is related to the
   morphology. Finally, mass transfer and pressure drop data were assessed from all types of
   carriers, and a dimensional analysis was performed to obtain relations between mass transfer
   and hydrodynamic properties.
   A dimensional analysis was performed, aiming at the development of general quantitative
   relations between the mass transfer properties in foams and the related dimensionless products
   of the phenomenon-influencing variables. The Sh-values of all structures were compared at equal
   fluid properties (Sc) by plotting over Re. The data for packed beds and honeycombs were in good
   agreement with literature correlations and served as a validation of the experimental method used
   (Fig. 1). The Sh-values of the foams increase with the size of the pores. In contrast to particle
   packings, who's Sh-numbers can be generally described with Re and Sc alone, an additional
   geometric parameter is effective in foams. The reason for this phenomenon is the anisotropy of
   the cells, i.e. the deformation of the strut network caused upon fabrication of the foams by
   replication which includes squeezing of the greenbodies.
   With the additional characterization of pore diameters in the x-z and y-z planes, the anisotropy of
   the pores in space could be quantified. A pore anisotropy ratio was defined by dividing the
   longest pore length by the two shorter ones, a2/(b∙c) and included in the dimensionless
   description of the mass transfer properties of the sponges (Fig. 2).
     100                                         Dwivedi &                                100
                  3,9 mm beads                                                                      Correlation
                  10ppi_0.85                     Upadhyay                                           CI Upper L
                  20ppi_0.85                                                                        CI Lower L
                                                             Shsponges/(Sc1/3*Fg,A) [-]

                  30ppi_0.85                                                                        45PPI_0.85
                  45ppi_0.85                                                                        30PPI_0.85
                  10ppi_0.8                                                                         10PPI_0.85
                  20ppi_0.8                                                                         45PPI_0.8
Sh [-]

         10       30ppi_0.8                                                               10        30PPI_0.8
                  45ppi_0.8                                                                         20PPI_0.8
                  20ppi_0.75                     Hawthorn                                           10PPI_0.8
                                                                                                    20PPI_0.75                anisotropy function
                  400CPSI HC
                                                                                                                                a2 
                                                                                                                        Fg,A  
                                                                                                                                bc            εh 
                                                                                                                                    
          1                                                                                 1
              1           10     100      1000          10000                                   1          10         100           1000                  10000
                                 Re [-]                                                                              Re [-]

   Fig. 1. Experimental Sh and Re data of all analyzed                                              Fig.2. General correlation for the prediction
   structures and literature correlations.                                                          of mass transfer properties of foams
                                                                                                    including an anisotropy function
   Based on the Lévêque-analogy, mass transfer data could be correlated with the experimental
   pressure drop of the structures within  20 %, confirming the possibility to use this analogy for a
   first estimation of mass transfer coefficients from pressure drop data. However, more accurate
   values of mass transfer coefficients are determined with the correlation presented above.

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