# Gas absorption in a thin liquid film flow on a horizontal rotating disk

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## Abstract

An analytical model for the rate of gas absorption into laminar non-wavy film flow on a horizontal rotating disk is obtained assuming short contact times. Literature data for the oxygen mass transfer coefficient in a wavy film is correlated by means of the dimensionless numbers deriving from the model. The rate enhancement due to waves is found to vary from 6 to 13 times. It is established that the absorption process in the film on the disk as compared to that in a gravitational wavy film flow can be intensified up to 14 times by means of a moderate rotation speed.

## Keywords

Mass Transfer Coefficient Sherwood Number Film Flow Short Contact Time Ekman Number## List of symbols

*C*solute concentration, kg m

^{−3}*C*_{n}eigenfunction

*D*diffusivity, m

^{2}s^{−1}*E*Ekman number, \( E = \nu \mathord{\left/{\vphantom {\nu {\omega r^{2}}}} \right.\kern-\nulldelimiterspace} {\omega r^{2}}\)

- \({\overline K} \)
average mass transfer coefficient, Eq. 15, m s

^{−1}*M*(*a*,*b*,*c*)confluent hypergeometric function

*N*local mass transfer rate, kg m

^{−2}s^{−1}- \({\overline N}\)
mean integral mass transfer rate, kg m

^{−2}s^{−1}*Q*volumetric flow rate, m

^{3}s^{−1}*R*radius of the disk, m

*r*radial coordinate, m

*Re*Reynolds number, \(Re = Q \mathord{\left/{\vphantom {Q {2\pi r\nu}}} \right.\kern-\nulldelimiterspace}{2\pi r\nu}\)

- \({\overline{Re}}\)
mean integral Reynolds number on the absorbing film surface, Eq. 22

*Sc*Schmidt number, \({Sc = \nu \mathord{\left/{\vphantom {\nu D}} \right.\kern-\nulldelimiterspace} D}\)

- \({\overline{{Sh}}}\)
*w*fluid velocity, m s

^{−1}*Y*dimensionless axial coordinate, Eq. 4b

*y*axial coordinate, m

*Z*dimensionless complex variable, Eq. 4d

## Greek symbols

## Subscripts

- in
at the entrance

- o
at the film surface

- out
at the exit

- b
bulk (mixed mean)

- s
at the position of sampling

- rot
in the field of rotation

- grav
in the field of gravitation

## References

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