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Solid dissolution in a thin liquid film on a horizontal rotating disk

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Abstract

A model for the rate of dissolution in liquid film on horizontal rotating disk is obtained by the method of Leveque. It as well as models found in the literature are subjected to experimental verification by dissolving disk cast of gypsum in two liquids. Satisfactory agreement with the model predictions is found. The rate with rotation is compared to that in gravitational film. Enhancements up to 2.5 times are established.

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Abbreviations

C :

solute concentration (kg m−3)

C n :

eigenfunction

D :

diffusivity coefficient (m2 s−1)

E :

Ekman number, E=ν/ωr 2

g :

gravity acceleration (m s−2)

J :

local mass transfer rate (kg m−2 s−1)

\(\overline{J}\) :

mean integral mass transfer rate (kg m−2 s−1)

\(\overline{K}\) :

average mass transfer coefficient, Eq. 21 (m s−1)

M(a, b, c):

confluent hypergeometric function

Q :

volumetric flow rate (m3 s−1)

R :

radius of the disk (m)

r :

radial coordinate (m)

Re :

Reynolds number, Re = Q/2πrν

\(\overline{Re}\) :

mean integral Reynolds number on the dissolving disk surface, \(\overline{{Re}}\,=\,Q \mathord{\left/ {\vphantom {Q {\pi \nu }}} \right. \kern-\nulldelimiterspace} {\pi \nu }(R_{{\rm out}} + R_{{\rm in}})\)

Sc:

Schmidt number, Sc = ν/D

\(\overline{\hbox{Sh}}\) :

mean Sherwood number, Eq. 20 or Eq. 23

w :

fluid velocity (m s−1)

Y :

dimensionless axial coordinate, Eq. 5b

y :

axial coordinate (m)

Z :

dimensionless complex variable, Eq. 5d

Γ:

gamma function

δ:

height of the liquid film (m)

η:

dimensionless complex variable, Eq. 12

λ n :

eigenvalue

μ:

dynamic viscosity (Pa s)

ν:

kinematic viscosity (m2 s−1)

ϑ:

dimensionless concentration, Eq. 11

ρ:

fluid density (kg m−3)

ω:

angular disk velocity (rad s−1)

ξ:

dimensionless radial coordinate, Eq. 5c

ψ:

dimensionless concentration, Eq. 5a

in:

at the entrance

w:

at the disk surface

out:

at the exit

b:

bulk (mixed mean)

rot:

in the field of rotation

grav:

in the field of gravitation

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Authors and Affiliations

  1. Department of Chemical Engineering, University of Chemical Technology and Metallurgy, 1756, Sofia, Bulgaria

    G. Peev, A. Nikolova & D. Peshev

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  1. G. Peev
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  2. A. Nikolova
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  3. D. Peshev
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Correspondence to G. Peev.

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Peev, G., Nikolova, A. & Peshev, D. Solid dissolution in a thin liquid film on a horizontal rotating disk. Heat Mass Transfer 43, 397–403 (2007). https://doi.org/10.1007/s00231-006-0111-0

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