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Dynamic behavior of an ellipsoidal bubble contaminated by surfactant near a vertical wall

  • Transport Phenomena
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Abstract

Adding a small amount of surfactant to gas-liquid two-phase flow can markedly change bubble behavior, which has crucial application value in nuclear energy, petrochemical, chemical, and environmental engineering. In this paper, the dynamic behavior of a single ellipsoidal bubble (Re∼800) contaminated by surfactant rising near a vertical wall in stagnant liquid is studied using the shadow method. The effects of different concentrations of sodium dodecyl sulfate solution (100 ppm, 400 ppm, 800 ppm) and initial dimensionless distances on bubble dynamics were compared. The dynamic parameters, shape oscillation, force, and energy of the bubble were analyzed. The results show that the critical initial dimensionless distance at which the collision occurs is decreased due to a dimensionless distance change from 3.3 to 0.23, accelerating the transition from zigzag to spiral movement. Transverse movement of the contaminated bubble is restrained. Because of the Marangoni effect caused by the surfactant, the boundary condition changes from zero shear to non-zero shear, resulting in a decrease in velocity and an increase in the drag coefficient. As the surfactant concentration increases, the lift coefficient does not significantly change with concentration variations. The influences of the wall effect on velocity and drag gradually weaken. Comparing free-rising and collision conditions, the aspect ratio of the contaminated bubble is distinct from the regularity of a clean bubble. The surfactant also changes the wall-normal velocity frequency and symmetrical shape frequency and inhibits energy conversion during collision.

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Abbreviations

Eo:

Eötvös number, Eo=gd2eq(ρl−ρg)σ−1 [-]

Mo:

Morton number, Mo=(ρl−ρg)gμl4σ}−3ρ−2 [-]

Re:

Reynolds number, Re=ρlUdeqμ−1 [-]

St:

Strouhal number, \({\rm{St}} = {\rm{f}}{{\rm{d}}_{eq}}/\overline {\rm{U}} \,[ - ]\)

We:

Weber number, We=ρ

A:

surface area [mm2]

A ij :

added mass tensor [-]

C:

surfactant concentration [ppm]

CD :

drag coefficient [-]

CL :

lift coefficient [-]

CM :

added mass coefficient [-]

deq :

equivalent diameter [mm]

dh :

horizontal axis of in a plane of the bubble [mm]

dv :

vertical axis of in a plane of the bubble [mm]

dD :

major axis of the bubble (y-z) [mm]

dM :

major axis of the bubble (x-y) [mm]

D ij :

rotational inertia tensor [-]

e:

minor axis of the bubble [mm]

Ek :

kinetic energy [μJ]

Es :

surface energy [μJ]

Et :

total energy [μJ]

f:

frequency of trajectory [Hz]

f(2, 0):

frequency of shape oscillation (2, 0) [Hz]

f(2, 2):

frequency of shape oscillation (2, 2) [Hz]

g:

gravity acceleration [ms−2]

h:

amplitude [mm]

FB :

buoyancy [N]

FD :

drag force [N]

FL :

liftforce [N]

l :

elevation [mm]

r:

horizontal shift of the periodic trajectory [mm]

req :

equivalent radius [mm]

S:

initial wall distance [-]

S*:

initial dimensionless wall distance, S*=S/req [-]

t:

time interval between two frames of a photograph [s]

u:

wall-normal velocity [ms−1]

U:

instantaneous velocity of bubble [ms−1]

\(\overline {\rm{U}} \) :

mean velocity of bubble [ms−1]

v:

vertical velocity [ms−1]

V:

volume of bubble [mm3]

w:

spanwise velocity [ms−1]

x, y, z:

Cartesian co-ordinates [mm]

ρ :

density [kgm−3]

σ :

surface tension [Nm−1]

μ :

dynamic viscosity [Nsm−2]

λ :

wavelength [mm]

τ :

ellipticity of the bubble [-]

χ :

aspect ratio [-]

θ :

the polar angle of the bubble rising path [rad]

φ :

azimuth angle of the bubble rising path [rad]

Ω :

rotation velocity [rad/s]

Γ :

torque [Nm]

ε :

Levi-Civita symbol [-]

g:

gas phase

i:

corresponding components on the coordinate axis

l :

liquid phase

u, v, w:

corresponding components to the direction of velocity

x, y, z:

corresponding components in x, y, z-direction

0:

free-rising bubble

*:

dimensionless quantity

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Acknowledgements

This research is supported by the National Natural Science Foundation of China (11572357, 11602077) and Natural Science Foundation of Hebei Province, China (A2021202009).

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Authors and Affiliations

  1. Department of Process Equipment and Control Engineering, Hebei University of Technology, Tianjin, 300130, China

    Enbo Ju, Runze Cai, Haopeng Sun, Ying Fan, Wenyi Chen & Jiao Sun

  2. National-Local Joint Engineering Laboratory for Energy Conservation in Chemical Process Integration and Resources Utilization, School of Chemical Engineering, Hebei University of Technology, Tianjin, 300130, China

    Enbo Ju, Runze Cai, Haopeng Sun, Ying Fan, Wenyi Chen & Jiao Sun

  3. Department of Mechanics, School of Mechanical Engineering, Tianjin University, Tianjin, 300350, China

    Jiao Sun

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  1. Enbo Ju
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Correspondence to Wenyi Chen or Jiao Sun.

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Ju, E., Cai, R., Sun, H. et al. Dynamic behavior of an ellipsoidal bubble contaminated by surfactant near a vertical wall. Korean J. Chem. Eng. 39, 1165–1181 (2022). https://doi.org/10.1007/s11814-021-1035-6

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  • DOI: https://doi.org/10.1007/s11814-021-1035-6

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