Based on the notion of a construction process consisting of the stepwise addition of particles to the pure fluid, a discrete model for the apparent viscosity as well as for the maximum packing fraction of polydisperse suspensions of spherical, non-colloidal particles is derived. The model connects the approaches by Bruggeman and Farris and is valid for large size ratios of consecutive particle classes during the construction process, appearing to be the first model consistently describing polydisperse volume fractions and maximum packing fraction within a single approach. In that context, the consistent inclusion of the maximum packing fraction into effective medium models is discussed. Furthermore, new generalized forms of the well-known Quemada and Krieger-Dougherty equations allowing for the choice of a second-order Taylor coefficient for the volume fraction (φ 2 -coefficient), found by asymptotic matching, are proposed. The model for the maximum packing fraction as well as the complete viscosity model are compared to experimental data from the literature showing good agreement. As a result, the new model is shown to replace the empirical Sudduth model for large diameter ratios. The extension of the model to the case of small size ratios is left for future work.

Transport of heat and mass and the thermodynamics of porous microreactors with thermal diffusion and radiation effects are investigated analytically. The examined configuration includes an axisymmetric, thickwall microchannel with an iso-flux thermal boundary condition imposed on the external surfaces. The microchannel is filled with porous materials and accommodates a zeroth order homogenous chemical reaction. Internal radiative heat transfer is modelled in addition to heat convection and conduction, while the local thermal non-equilibrium approach is taken within the porous section of the system. The transport of species is coupled with that of heat via the inclusion of thermodiffusion or Soret effect. Two-dimensional heat and mass transfer differential equations are solved analytically. The results are subsequently used to predict the thermodynamic irreversibilities inside the reactor and a thorough analysis of local and total entropy generation rates is performed. Also, the changes in Nusselt number, calculated on the internal walls of the microreactor, versus various parameters are reported. It is shown that the radiation effects can impact the temperature of the solid phase of the porous medium and lead to alteration of Nusselt number. It is further observed that the transfer of mass is the main source of irreversibility in the system. The findings are of particular use for the design and analysis of the microreactors with homogenous chemical reactions and can be also used for the validation of computational models.

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