Particle-fluid mass transfer in multiparticle systems at low Reynolds numbers

Abstract

The problem of mass transfer between active solid particles and a fluid in multiparticle systems is examined with a focus on the stagnant and the low Reynolds number cases. This problem has attracted significant attention with regard to operation of fixed and fluidized beds. It is recognized that different Sherwood numbers can be defined depending on the choice of the reference concentration difference (driving force). An effective Sh has often been used to analyze experimental data based on an overall concentration difference across the bed. A local Sh can also be introduced based on a concentration difference close to the active particle. However, the use of these two different Sherwood numbers implies a different implementation of the mass balance equations.The mass balance equations are here analytically solved both under stagnant and non-stagnant conditions in a multiparticle system under suitable simplifying assumptions. Equations for the effective and local Sherwood numbers are derived for the general case and for the asymptotic limits. Allowance is given for the variation of bed voidage and volume fraction of active particles in the bed. It is shown that the local Sh only depends on geometrical and fluid-dynamics considerations and accordingly has a general validity. On the contrary, the effective Sh also depends on the assumptions made in deriving the mass balance equations across the bed (e.g., fluid plug flow). The use of the local Sh is therefore suggested.Results show that for Re→0 the limiting value of the local Sh is always a finite number, while the effective Sh tends to zero linearly with Re. It is shown that this result is simply a consequence of the plug flow assumption made in the bed mass balance. The general expressions derived here compare very well to experimental trends for the cases of large Reynolds numbers and of few isolated active spheres immersed in a bed of inert particles, where most of the reported experimental data gather. Unfortunately, for the most controversial case of very low Re in beds made entirely of active particles no reliable data appears to be available to check the accuracy of the expressions.