Local rates of mass transfer from spheres in ordered arrays

Abstract

The local mass transfer rates from a sphere in a regular packing array have been determined by measuring the local radius change of a slightly soluble 1.500-in. diameter benzoic acid test sphere after having been immersed in a water stream. Results in the form of typical local Sherwood number profiles are reported for single spheres over a particle Reynolds number range of 166 to 1,560, and for spheres in simple cubic packing and rhombohedral packing over particle Reynolds number ranges of 488 to 2,409 and 1,680 to 3,410, respectively. All runs were made a t room temperature. An idealized flow pattern around spheres in simple cubic packing is presented.Although extensive work has been done on various overall transport phenomena, such as the overall mass and heat transport from randomly packed beds to flowing fluids (1, 6, 9, 10, 12, 16,18,20) and from single particles such as single spheres (8, 10) or cylinders to flowing fluids, only limited references to previous investigations of the local transport phenomena from spheres in packed beds to flowing fluids are known. It was the objective of this work to investigate the local rates of mass transfer from slightly soluble spheres in a packed bed to a flowing fluid. By application of an appropriate analogy between heat and mass transfer and the local heat and mass transfer, the local heat transfer characteristics in a packed bed of spheres can be predicted from corresponding local mass transfer characteristics that can be more readily investigated in the laboratory. The present work was limited to investigation of two ordered arrays of spheres, the simple cubic packing having a void fraction of 0.47 and the rhombohedral packing having a void fraction of 0.26. These two arrays are the limiting packings expected in a bed of randomly packed spheres that has an average void fraction of 0.38 to 0.40. THEORYIn the investigation of the local rates of mass transfer from slightly soluble spheres in a packed bed molecular diffusion, natural convection mass transfer and forced convection mass transfer may be of importance at a given location on a sphere. Of course, with a fluid flowing through the packed bed, it would be expected that the primary mechanism of mass transfer would be by forced convection. However, in regions on a sphere adjacent to a point of contact between spheres, the theory of real fluids indicates that fluid velocities are very low. Hence, one would expect that mass transfer would be due primarily to the mechanisms of molecular diffusion and natural convection in these regions. Since the mass transfer coefficients for molecular diffusion are orders of magnitude less than those for forced convection, one would expect a large variation in the local mass transfer rates from a slightly soluble sphere in a packed bed. It is this variation of local mass transfer rates that is the subject of this investigation.For the present case of a slightly soluble sphere, the time-average rate of mass transfer from the sphere surface to the flowing stream could be determined ...

Solid-Liquid Mass Transfer in Concurrent Two-Phase Flow through Packed Beds

“…In a packed column, there are liquid zones with different local hydrodynamic conditions, so that the local solid-liquid mass transfer coefficient may be rather different from the average. This was ascertained for single phase flow in a packed bed (Rhodes and Peebles, 1965; Jolls and Hanratty, 1969), and is probably true for two-phase flow also.…”

Local and Over-All Mass Transfer Rates around Solid Spheres with First-Order Homogeneous Chemical Reactions

“…The problem of pure physical mass transfer from a single solid sphere into a fluid flowing past it has been studied by many investigators both analytically (Acrivos and Taylor, 1962;Baird and Hamielec, 1962;Friedlander, 1957Friedlander, , 1961; Pfeffer, 1964; Pfeffer and Happel, 1964;Yuge, 1956) and experimentally (Garner and Grafton, 1954; Garner and Hoffman, 1960; Garner and Keey, 1958; Garner and Suckling, 1958; Peltzman ; Rhodes and Peebles, 1965; Rowe et ah, 1965; Steinberger and Treybal, 1960). For flow at high Reynolds numbers, boundary layer theory as well as experimental data have shown that the over-all Sherwood number is dependent on the parameter NRell2Nsclls and can be expressed by the relation ArSh" = -Re''Wsc1'3…”