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Thermocapillary Convection in a Binary Mixture with Moderate Prandtl Number in a Shallow Annular Pool

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Abstract

This paper presented a series of numerical simulations on thermocapillary convection for mixed toluene/hexane solution with mass fraction of \(c_{0}= 26.27\)% in a shallow annular pool. The Prandtl number of the binary solution is 5.54. Results indicate that when the annular pool subjects to a radial temperature gradient, the solute shifts toward the inner wall under the Soret effect, which leads to a concentration gradient with the opposite direction to the temperature gradient. With the increase of surface heat dissipation, thermocapillary convection is enhanced and the flow is more prone to destabilization. Therefore, the critical thermocapillary Reynolds number of the flow destabilization and the corresponding critical oscillation frequency all decrease, but the critical wave number increases. After flow destabilization, the concentration fluctuation similar to the temperature fluctuation on the free surface appears. No matter the free surface is adiabatic or not, the flow always undergoes a transition from two-dimensional steady axisymmetric flow to the hydrothermal waves, and then to chaos with the increase of thermocapillary Reynolds number.

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Abbreviations

Bi :

Biot number

C :

Mass fraction

d :

Depth, m

D :

Mass diffusivity of species, m2/s

F :

Dimensionless oscillation frequency

h :

Convective heat-transfer coefficient, W/(m2 ⋅K)

m :

Azimuthal wave number

p :

Pressure, Pa

P :

Dimensionless pressure

Pr :

Prandtl number

r :

Radius, m

R :

Dimensionless radius

R e C :

Solutalcapillary Reynolds number

R e T :

Thermocapillary Reynolds number

R σ :

Capillary ratio

S T :

Soret coefficient, 1/K

t :

Time, s

T :

Temperature, K

v :

Velocity, m/s

V :

Dimensionless velocity

V :

Dimensionless velocity vector

z :

Axial coordinate, m

Z :

Dimensionless axial coordinate

α :

Thermal diffusivity, m2/s

ε :

Aspect ratio

γ C :

Solutal coefficient of surface tension, N/m

γ T :

Temperature coefficient of surface tension, N/(m⋅K)

η :

Radius ratio

μ :

Dynamic viscosity, kg/(m⋅s)

ν :

Kinematic viscosity, m2/s

𝜃 :

Azimuthal coordinate, rad

ρ :

Density, kg/m3

τ :

Dimensionless time

ψ :

Dimensionless stream function

c:

Critical

i:

Inner

o:

Outer

R:

Radial

Z:

Axial

𝜃 :

Azimuthal

0:

Initial

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Acknowledgements

We are grateful for the support of the National Natural Science Foundation of China (Grant No. 51406019). We are also grateful to Dr. Aaron H. Persad from University of Toronto for his helpful grammatical edits.

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Authors and Affiliations

  1. Key Laboratory of Low-Grade Energy Utilization Technologies and Systems of Ministry of Education, College of Power Engineering, Chongqing University, Chongqing, 400044, China

    Li Zhang, Jia-Qian Luo, Chun-Mei Wu, Jia-Jia Yu & You-Rong Li

  2. Nanfang Translators College of Sichuan International Studies University, Chongqing, 401120, China

    Li Zhang

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  1. Li Zhang
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  2. Jia-Qian Luo
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Correspondence to Chun-Mei Wu.

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Zhang, L., Luo, JQ., Wu, CM. et al. Thermocapillary Convection in a Binary Mixture with Moderate Prandtl Number in a Shallow Annular Pool. Microgravity Sci. Technol. 30, 33–42 (2018). https://doi.org/10.1007/s12217-017-9572-7

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