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Wall effects on the thermocapillary migration of single gas bubbles in stagnant liquids

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Abstract

In this paper, the governing continuum conservation equations for two-phase flow are solved using the commercial software package (Ansys-Fluent 1) to investigate the thermocapillary movement of a single bubble in stagnant liquid under zero-gravity condition. The current results show that different temperature gradients lead to different bubble migration velocities, and bubble migration velocity varies linearly with the temperature gradient for the given conditions. Furthermore the inside column diameter was found to have a significant influence on the thermocapillary migration of the bubble. Calculation were made in columns with inside diameters Dr 15, 20, 30, 40, 60, 80, 100 and 120 mm. Reduction on bubble migration velocity only occurred when the ratio of the bubble diameter to the column diameter, db/Dr, is greater than 0.267 due to column wall effect. On the other hand, the influence of the column diameter on the rise velocity is negligible when db/Dr is equal to or smaller than 0.267. No bubble shape deformation were observed and the bubble were spherical in shape for all column width. Present investigation of the shape and trajectory of bubble motion driven by surface tension-gradient in different column width is a new area of study and aims to support research into space applications which can help to determine the new migration time and speed.

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Abbreviations

UDF:

User-defined functions

VOF:

Volume of fluid

CFD:

Computational fluid dynamics

CP :

Specific heat at constant pressure (KJ/ Kg). K

D:

Columns inside diameter (m)

d:

Bubble diameter (m)

g:

Gravitational acceleration (m s−2)

YGP:

Young, Block, and Goldstein

k:

Thermal conductivity (W m−1 K−1)

keff :

Effective thermal conductivity (W m−1 K−1)

kf :

Thermal conductivity of the fluid (W m−1 K−1)

L:

Length of the cavity (m)

\(\mu\) :

Dynamic viscosity for continuous phase (N/m2)

\(\mu '\) :

Dynamic viscosity for gas phase (N/m2)

\(\lambda\) :

Thermal conductivity for continuous phase (W m−1 K−1)

\(\lambda '\) :

Thermal conductivity for gas phase (W m−1 K−1)

\(\sigma\) :

Interfacial tension (N/m)

r:

Bubble radius (m)

ρ:

Density (kg m−3)

p:

Pressure (kg m−1 s−2)

CSF:

Continuum Surface Force

Pr:

Prandtl number ( \(Pr = {\nu \mathord{\left/ {\vphantom {\nu \alpha }} \right. \kern-0pt} \alpha }\, )\)

Rr:

Reynolds number (\(Re_{T} = r_{b} V_{T} /v )\)

Ma:

Marangoni number (\(Ma_{T} = r_{b} V_{T} /\alpha\) = \(Ma_{T} = Re_{T} .Pr\))

\(\vec{F}\) :

Volumetric forces at the interface

T:

Liquid temperature

AR:

Aspect ratio

mm:

Millimeter (mm)

Sec:

Second (S)

t:

Time (s)

T:

Temperature (K)

V:

Thermal velocity (\(V_{T} = \sigma_{b} (dT/dx) r_{b} /\mu\)) m/s

x:

x coordinates (m)

y:

y coordinates (m)

2D:

Two dimension

Axis:

Axisymmetric

UDF:

User-defined functions

\(\alpha\) :

Volume fraction

ν:

Kinematic viscosity (m2 s−1)

ρ:

Density (kg m−3)

\(\mu\) :

Dynamic viscosity for continuous phase (N/m2)

\(\mu '\) :

Dynamic viscosity for gas phase (N/m2)

\(\lambda\) :

Thermal conductivity for continuous phase (W m−1 K−1)

\(\lambda '\) :

Thermal conductivity for gas phase (W m−1 K−1)

\(\sigma\) :

Interfacial tension (N/m)

n :

Surface normal

K :

Local surface curvature

c:

cold

h:

hot

f:

fluid

eff:

effective

Top:

Top walls

Bottom:

Bottom walls

YGP:

Young, Block, and Goldstein

T:

Thermal

G:

Gas phase

L:

Liquid phase

o :

Reference temperature

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Author information

Authors and Affiliations

  1. College of Technological Studies (CTS), Public Authority for Applied Education and Training (PAAET), P. O. Box 5351, 32084, Hawally, Kuwait

    Yousuf Alhendal & Abdulrahim Kalendar

  2. School of Mechanical, Aerospace and Civil Engineering, The University of Manchester, George Begg Building, Sackville Street, Manchester, M13 9PL, UK

    Ali Turan

Authors
  1. Yousuf Alhendal
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  2. Ali Turan
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  3. Abdulrahim Kalendar
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Corresponding author

Correspondence to Yousuf Alhendal.

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We wish to confirm that there are no known conflicts of interest associated with this publication: Wall Effects on the Thermocapillary Migration of Single Gas Bubbles in Stagnant Liquids and there has been no significant financial support for this work that could have influenced its outcome.

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Alhendal, Y., Turan, A. & Kalendar, A. Wall effects on the thermocapillary migration of single gas bubbles in stagnant liquids. Heat Mass Transfer 53, 1315–1326 (2017). https://doi.org/10.1007/s00231-016-1903-5

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  • DOI: https://doi.org/10.1007/s00231-016-1903-5

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