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Hydrodynamics and mass exchange in gas-liquid slug flow in microchannels

  • Supplement: Rossiiskii Khimicheskii Zhurnal-Zhurnal Rossiiskogo Khimicheskogo Obshchestva im. D.I. Mendeleeva (Russian Chemistry Journal)
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Abstract

The present state of hydrodynamics and mass transfer studies in segmented gas-liquid flow in microchannels has been analyzed. It has been shown that such parameters as gas bubble velocity, gas hold-up, relative gas bubble length, pressure drop, mass transfer coefficients from gas bubbles to liquid slugs and to liquid film, as well as mass transfer coefficient from liquid to channel wall can be satisfactorily predicted. Nevertheless, some correlations were obtained under definite conditions and should be summarized. The purpose of further research is to develop reliable methods for calculation of mass transfer coefficients as functions of channel geometry, phase properties, and phase velocities in mini- and microchannels.

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Abbreviations

a :

phase contact surface area, m2/m3

A b :

cross-sectional area of a bubble, m2

A c :

cross-sectional area of a capillary, m2

A f :

cross-sectional area of a film, m2

C 1 :

dimensionless constant

C 0 :

dimensionless constant of the slipp model

d c :

capillary diameter, m

D :

diffusion coefficient, m2 s−1

g :

gravity, m s−1

J :

dimensionless constant of the motion of the fastest-moving liquid elements relative to a bubble, reduced to the mean velocity of liquid slug

k :

mass-transfer coefficient, m s−1

L :

capillary length, m

L f :

liquid film length, m

L s :

reduced length of liquid slug, m

L UC :

cell length, m

n :

dimensionless coefficient

N UC :

number of cells along the capillary, rel. units

p :

pressure, Pa

Δp trans :

pressure drop in a capillary, associated with change of liquid slug velocity profile, Pa

ΔpΔF :

pressure drop associated with new surface formation on bubble motion, Pa

Q f :

liquid film mean volumetric flow rate, m3 s−1

q b :

gas volumetric flow rate due to bubble motion (local), m3 s−1

q f :

liquid film volumetric flow rate (local), m3 s−1

q s :

liquid slug volumetric flow rate (local), m3 s−1

R :

capillary radius, m

R b :

bubble radius, m

t f :

contact time of gas bubble with liquid film s

u 1 :

local medium velocity, m s−1

U b :

bubble velocity, m s−1

U f :

liquid film velocity, m s−1

U G :

gas velocity reduced to the total capillary cross-sectional area, m s−1

U L :

liquid velocity reduced to the total capillary cross-sectional area, m s−1

U s :

liquid slug velocity, reduced to the total capillary cross-sectional area (two-phase flow velocity), m s−1

w :

relative bubble velocity, m s−1

w b :

slip velocity between bubbles and the stagnant liquid, m s-1

x :

axial coordinate, m

β:

gas volumetric flow fraction, rel. units

γ:

angle between the vector of two-phase flow velocity in a capillary U s and the vector of gravity g

γ m :

roots of the second-order Bessel function: J 2(γ) = 0

δ:

film thickness surrounding a bubble, m

ɛA :

relative bubble surface area, rel. units

ɛL :

relative bubble length, rel. units

ɛV :

gas void fraction, rel. units

η:

ratio of bubble velocity to two-phase flow velocity, η = U b/U s, rel. units

μ:

dynamic viscosity, Pa s

ν:

kinematic viscosity coefficient, m2 s−1

ρ:

dencity, kg m−3

σ:

interfacial tension, N m−1

\( Ca = \frac{{\mu _1 U_b }} {\sigma } \) :

modified Bond number

\(Ca = \frac{{\mu _1 U_b }} {\sigma }\) :

capillary number

\( Ca_s = \frac{{\mu _1 U_s }} {\sigma } \) :

capillary number calculated from U s

Ca*:

critical capillary number

\( Fo = \frac{{Dt_f }} {{\delta ^2 }} \) :

Fourier criterion reduced to liquid film thickness

\( Gr = \frac{L} {{d_c }}\frac{1} {{\operatorname{Re} Sc}} = \frac{L} {{d_c }}\frac{1} {{Pe}} \) :

Gretz criterion

\( Pe = \operatorname{Re} Sc = \frac{{U_s d_c }} {D} \) :

Peclet number

\( Re = \frac{{\rho _1 U_s d_c }} {{\mu _1 }} \) :

Reynolds number

\( Sh = \frac{{kd_c }} {D} \) :

Sherwood number

\( Sc = \frac{{\nu _1 }} {D} \) :

Schmidt number

\( We = \frac{{\rho _1 U_s^2 d_c }} {\sigma } \) :

Weber number

1:

continuous medium (liquid)

2:

disperse medium (gas)

a:

gas-liquid system used to obtain Eq. (17)

b:

bubble

c:

capillary

d:

gas-liquid system different from that used to obtain Eq. (17)

f:

film

fs:

liquid-solid film

gl:

gas-liquid

gf:

gas-liquid film

gs:

gas-solid

g, G:

gas

ls:

liquid-solid

s:

liquid slug

tot:

total

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Authors and Affiliations

  1. St. Petersburg State Technological Institute (Technical University), Moskovskii pr. 26, St. Petersburg, 190013, Russia

    R. Sh. Abiev & I. V. Lavretsov

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  1. R. Sh. Abiev
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Original Russian Text © R.Sh. Abiev, I.V. Lavretsov, 2011, published in Rossiiskii Khimicheskii Zhurnal, 2011, Vol. 55, No. 2, pp. 60–70.

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Abiev, R.S., Lavretsov, I.V. Hydrodynamics and mass exchange in gas-liquid slug flow in microchannels. Russ J Gen Chem 82, 2088–2099 (2012). https://doi.org/10.1134/S1070363212120298

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