Tube-side mass transfer for hollow fibre membrane contactors operated in the low Graetz range.
Transformation of the tube-side mass transfer coefficient derived in hollow fibre membrane contactors (HFMC) of different characteristic length scales (equivalent diameter and fibre length) has been studied when operated in the low Graetz range (Gz<10). Within the lowGzrange, mass transfer is generally described by the Graetz problem (Sh=3.67) which assumes that the concentration profile comprises a constant shape over the fibre radius. In this study, it is experimentally evidenced that this assumption over predicts mass transfer within the low Graetz range. Furthermore, within the lowGzrange (below 2), a proportional relationship between the experimentally determined mass transfer coefficient (Kov) and the Graetz number has been identified. ForGznumbers below 2, the experimentalShnumber approached unity, which suggests that mass transfer is strongly dependent upon diffusion. However, within this diffusion controlled region of mass transfer, tube-side fluid velocity remained important. ForGznumbers above 2,Shcould be satisfactorily described by extension to the Lévêque solution, which can be ascribed to the constrained growth of the concentration boundary layer adjacent to the fibre wall. Importantly this study demonstrates that whilst mass transfer in the low Graetz range does not explicitly conform to either the Graetz problem or classical Lévêque solution, it is possible to transform the experimentally derived overall mass transfer coefficient (Kov) between characteristic length scales (dhandL). This was corroborated by comparison of the empirical relationship determined in this study (Sh=0.36Gz) with previously published studies operated in the lowGzrange. This analysis provides important insight for process design when slow tube-side flows, or low Schmidt numbers (coincident with gases) constrain operation of hollow fibre membrane contactors to the lowGzrange.
Cranfield Water Science Institute, Vincent Building, Cranfield University, Bedfordshire MK43 0AL, UK.
C Y
CY
Wang
Cranfield Water Science Institute, Vincent Building, Cranfield University, Bedfordshire MK43 0AL, UK.
E
E
Mercer
Cranfield Water Science Institute, Vincent Building, Cranfield University, Bedfordshire MK43 0AL, UK.
F
F
Kamranvand
Cranfield Water Science Institute, Vincent Building, Cranfield University, Bedfordshire MK43 0AL, UK.
L
L
Williams
Cranfield Water Science Institute, Vincent Building, Cranfield University, Bedfordshire MK43 0AL, UK.
A
A
Kolios
Cranfield Water Science Institute, Vincent Building, Cranfield University, Bedfordshire MK43 0AL, UK.
A
A
Parker
Cranfield Water Science Institute, Vincent Building, Cranfield University, Bedfordshire MK43 0AL, UK.
S
S
Tyrrel
Cranfield Water Science Institute, Vincent Building, Cranfield University, Bedfordshire MK43 0AL, UK.
E
E
Cartmell
Cranfield Water Science Institute, Vincent Building, Cranfield University, Bedfordshire MK43 0AL, UK.
E J
EJ
McAdam
Entrance region; Graetz problem; Graetz-Lévêque; Low Reynolds number; Lumen