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Mass diffusion-controlled bubble behaviour in boiling and electrolysis and effect of bubbles on ohmic resistance

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Abstract

A survey is given of theoretical asymptotic bubble behaviour which is governed by heat or/and mass diffusion towards the bubble boundary. A model has been developed to describe the effect of turbulent forced flow on both bubble behaviour and ohmic resistance. A comparison with experimental results is also made.

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Abbreviations

ga :

liquid thermal diffusivity (m2 s−1)

B :

width of electrode (m)

c :

liquid specific heat at constant pressure (J kg−1 K−1)

ΔC 0 :

initial supersaturation of dissolved gas at the bubble wall (kg m−3)

d :

bubble density at electrode surface (m−2)

D :

diffusion coefficient of dissolved gas (m2 s−1)

D h :

−4S/Z, hydraulic diameter, withS being the cross-sectional area of the flow andZ being the wetted perimeter (m)

e :

base of natural logarithms, 2.718...

f :

local gas fraction

F :

Faraday constant (C kmol−1)

G :

evaporated mass diffusion fraction

h :

height from bottom of the electrode (m)

h w :

total heat transfer coefficient for electrode surface (J s−1 m−2 K−1)

h w,conv :

convective heat transfer coefficient for electrode surface (J s−1 m−2K−1)

H :

total height of electrode (m)

i :

electric current density (A m−2)

j, j * :

number

Jα :

modified Jakob number,ΔC 0/ρ 2

ℒ :

enthalpy of evaportion (J kg−1)

m :

density of activated nuclei generating bubbles at electrode surface (m−2)

n :

product of valency and number of equal ions forming one molecule; for hydrogenn=2, for oxygenn=4

p :

pressure (N m−2)

Δp :

excess pressure (N m−2)

R :

gas constant (J kmol−1 K−1)

R 1 :

bubble departure radius (m)

R 0 :

equilibrium bubble radius (m)

ΔR/R :

relative increase of ohmic resistance due to bubbles, ΔR, in comparison to corresponding value,R, for pure electrolyte

Re :

Reynolds number,νD h/ν

Sc :

Schmidt number,ν/D

Sh :

Sherwood number\({{D_h } \mathord{\left/ {\vphantom {{D_h } {\bar \delta _m }}} \right. \kern-\nulldelimiterspace} {\bar \delta _m }}\)

t :

time (s)

T :

absolute temperature (K)

ΔT :

increase in temperature of liquid at bubble boundary with respect to original liquid in binary mixture (K)

gu :

solution flow velocity (m s−1)

x :

mass fraction of more volatile component in liquid at bubble boundary in binary mixture

x 0 :

mass fraction of more volatile component in original liquid in binary mixture

y :

mass fraction of more volatile component in vapour of binary mixture

α :

contact angle

δ:

local thickness of one phase velocity boundary layer (m)

δm :

local thickness of corresponding mass diffusion layer (m)

δ* :

local thickness of two-phase velocity boundary layer (m)

θ o :

initial liquid superheating (K)

κ :

constant in Henry's law (m2 s−2)

ν :

liquid kinematic viscosity (m2 s−1)

ν * :

bubble frequency at nucleus (s−1)

ρ 1 :

liquid mass density (kg m−3)

ϱ 2 :

gas/vapour mass density (kg m−3)

σ:

surface tension (N m−1)

References

  1. [1]S. J. D. van Stralen, R. Cole, ‘Boiling Phenomena’, Vols. 1 and 2, Hemisphere, Washington/McGraw-Hill, New York (1979).

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  2. L. J. J. Janssenand S. J. D. van Stralen,Electrochim. Acta 26 (1981) 1011.

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  4. H. M. S. Wedershoven, R. M. de Jonge, C. W. M. P. Sillen and S. J. D. van Stralen,Int J. Heat Mass Transfer 25 (1982) 1239.

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Authors and Affiliations

  1. Department of Physics, Eindhoven University of Technology, PO Box 513, 5600, MB Eindhoven, The Netherlands

    S. J. D. Van Stralen & W. M. Sluyter

Authors
  1. S. J. D. Van Stralen
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  2. W. M. Sluyter
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Van Stralen, S.J.D., Sluyter, W.M. Mass diffusion-controlled bubble behaviour in boiling and electrolysis and effect of bubbles on ohmic resistance. J Appl Electrochem 15, 527–536 (1985). https://doi.org/10.1007/BF01059294

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  • DOI: https://doi.org/10.1007/BF01059294

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