Scalar transport across the turbulent
gas-liquid interface
The interest in turbulent scalar transport across the
gas-liquid interface can be traced back to the 1930’s when Higbie (1935) tried to present a universal model to explain
the phenomenon irrespective of the means of turbulence generation, whether
originating from the gaseous or liquid sides. Many researchers followed on have
made attempts to derive such a universal model but most models invariably
involved parameters which are apparatus specific and hence are not simple or
able to extend to more general applications. My interest follows that of my PhD
work in our effort to relate the more generic turbulence on the liquid side to
the bulk flow velocity and macro length scale and correlate it the associated
scalar mass/heat transport across the interface [Khoo
& Sonin (1992), Int. J. Heat Mass Trans., Vol.
35, pp 2233; Brown et al (1990), Int. J. Heat Mass Trans., Vol. 33, pp 2001].
This was met with limited success. Though the scalar transport is a function of
the turbulence at/near the interface, it becomes apparent that the turbulence
quantities taken w.r.t the fluctuating interface
controls the transport rate. In the early 1990’s there is no commercial
instrumentation that is able to measure the flow field and the fluctuating
interface simultaneously, and PIV is
still in its developmental stage. At NUS, we embarked to develop a PIV-based
system including the necessary software routines to track and measure the
liquid velocity field and the fluctuating interface velocity leading to two
papers published [Khoo et al (1993), Exps Fluids, Vol. 13, pp 350; Law et al (1999), Exps Fluids, Vol. 27, pp 321]. (Even now, commercially
available PIV system has to be modified to measure both fields simultaneously
and the cost is rather high.)
Only with the required instrumentation problem solved, we
were able to measure the linear vertical velocity gradient w.r.t.
the interface (brms) and obtained a relation which correlates
very well the scalar transport rate and brms
for two vastly different flow conditions; one generated by turbulence solely
from beneath the liquid via a submerged jet and the other via wind shear from
above the interface [Law and Khoo (2002) (AIChE J., Vol. 48, pp 1856-1868]. Further experiments with
gaseous stream above and liquid stream below in both co-current and
counter-current directions performed confirmed the mentioned correlation
obtained [Xu et al, 2006, AIChE
J., Vol. 52, pp 3363-3374]. Because brms and related
parameters describing the near-surface turbulence are not directly dependent on
the particular means of generation, this gives the possibility that the said
parameters identified in the relation are applicable to any other flows and
hence the universality. In addition, as the said parameters are found in a very
small region residing next to the interface, it further lends support to the
small eddy model [first proposed by Lamont & Scott (1970), AIChE J., Vol. 16, pp 513] as opposed to the large eddy
model and others. It may just be noted the relation is obtained from
experiments without wave-breaking and generation of bubbles which can lead to
two-regime behavior [Khoo & Sonin
(1992), J. Geophy. Res., Vol. 97, pp 14413]; strictly
if one can measure the variation of brms in entrained
gas bubbles in the liquid, then there exists the possibility that the relation
obtained for the scalar transport rate may yet be applicable. All these latter
works were carried out at NUS and independent of my former thesis advisor at
MIT who had moved on to pursue other research interest.
The importance and significance of the work are further
supported by the following evidences:
(a) Invited to present a public seminar on “Turbulence
structure at the air-water interface and its relationship to air-water mass
transfer” at TUB (Technical University of Berlin) on
(b) BP International Limited (subsequently named as BP
Amoco) has awarded a research grant in 1995 amounting to £38000 on
“Transport across the turbulent air-sea interface” for a PhD
scholarship tenable for a period of 3 years at NUS. This is a competitive grant
application and is the first time awarded outside of the
(c) Related to application
of the research work is the invitation to present and publish a paper on
“Coastal sediment transport and chemical spill modeling” at the
International Chemical and Oil Pollution Conference & Exhibition 2001, held
in Singapore in September 2001. (In this regard, the turbulent transport model
is incorporated into the 3D POM on the water circulation to study the effect of
an accidental chemical spills on the regional seas and
(d) The national A*STAR research institute ICES (Institute
of Chemical Engineering Sciences) has awarded a PhD scholarship to Mr. Xu Zhifeng tenable at NUS
starting 2003 to carry on work to further ascertain the general applicability
of brms with other different means of
turbulence generation.
Future work:
(a) The incorporation of the rate of scalar transport into
the 3D water circulation model to study the effect of (passive) chemical spill
(whether accidental or otherwise) in the regional seas in
(b) The
establishment of (brms) as the dominant factor controlling the
scalar transport across the turbulent gas-liquid interface provides for the
motivation to extend it to the falling film which is very prevalent in the
chemical industries.
List of
relevant publications
Brown, J S, B C Khoo*
and A A Sonin,
"Correlation for Condensation of Pure Vapor on Turbulent, Subcooled Liquid". International
Journal of Heat & Mass Transfer, 33, part. 9 (1990): 2001‑2018.
(
Khoo*, B C and A A
Sonin, "Scalar rate correlation at a turbulent
liquid free surface: A two‑regime correlation for high Schmidt
numbers". International Journal of Heat & Mass
Transfer, 35, part. 9 (1992): 2233‑2244. (
Khoo*, B C and A A
Sonin, "Augmented gas exchange across wind‑sheared
and shear‑free air‑water interface". Journal
of Geophysical Research, 97, part. C9 (1992): 14413‑14415. (
Khoo*, B C, T C Chew, P S Heng
and H K Kong, "Turbulence characterisation of a
confined jet using PIV". Experiments
in Fluids, 13 (1992): 350‑356. (
Chen, M, B C Khoo* and E S Chan, “Three dimensional circulation
model of
Law, C N S, B C Khoo* and T C Chew, "Turbulence structure in the
immediate vicinity of the shear‑free air‑water interface induced by
a deeply submerged jet". Experiments
in Fluids, 27 (1999): 321‑331. (
Khoo*, B C and J. Lou, “Coastal
sediment transport and chemical spill modeling”. International
Chemical and Oil Pollution Conference & Exhibition (ICOPCE) 2001.
Compiler: IBC
Khoo*, B C, J Lou and K Kumar, “A
quasi-3D convention dispersion model for coastal sediment transport and
chemical spill”.
Law, N S and B C Khoo*,
"Transport across a turbulent air‑water interface". AIChE Journal, 48, no. 9 (2002): 1856‑1868. (
Chen, M, K Murali, B C Khoo*, J Lou and K
Kumar, "Circulation modelling in the
Xu, Z.F., B C Khoo*
and K. Carpenter, "Mass transfer across the turbulent gas‑water
interface". AIChE
Journal, 52, no. 10 (2006): 3363‑3374. (