The membrane module is a core component of the toilet, allowing us to get clean water from faecally contaminated urine. Experimental work has defined the tube-side mass transfer coefficient derived in hollow fibre membrane contactors of different characteristic length scales (equivalent diameter and fibre length) under the slow flow conditions that are expected in the toilet.
The work is described in detail in a paper in the Journal of Membrane Science, which is free to download:
Yang, C.Y., E. Mercer, F.
Kamranvand, L. Williams, A. Kolios, A. Parker, S. Tyrrel, E. Cartmell, E.J.
McAdam Tube-side mass transfer forhollow fibre membrane contactors operated in the low Graetz range, Journal of Membrane Science 523, 235–246
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 low Gz range, 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 low Gz range (below 2), a proportional relationship between the experimentally determined mass transfer coefficient (Kov) and the Graetz number has been identified. For Gz numbers below 2, the experimental Sh
number 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.
For Gz numbers above 2, Sh could 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 (dh and L). This was corroborated by comparison of the empirical relationship determined in this study (Sh=0.36Gz) with previously published studies operated in the low Gz
range. 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 low Gz range.