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Capillary Interaction Between Micron-Sized Ce2O3 Inclusions at the Ar Gas/Liquid Steel Interface

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Abstract

The agglomeration behavior of Ce2O3 inclusions was observed in situ on a 20 pct Cr liquid steel surface (i.e., the argon gas/liquid steel interface) using high temperature confocal scanning laser microscopy (CSLM). The inclusions are electrolytically extracted from the steel sample. These inclusions are heterogeneous in chemical composition and are shaped irregularly with a rough surface, suggesting pinning (undulating) three-phase contact lines around the inclusion particles on the liquid steel surface. To understand the interactions between Ce2O3 inclusions deeply, the particles are treated either as capillary ‘charges’ with planar contact lines or as capillary ‘multipoles’ with undulating contact lines through the analogy with 2D electrostatics. These capillary interactions include ‘charge’–‘charge’, ‘charge’–‘quadrupole’, ‘charge’–‘hexapole’, ‘quadrupole’–‘quadrupole’ and ‘hexapole’–‘hexapole’. It is found that the interaction between capillary ‘quadrupoles’ performs best in interpreting the strong pairwise attractive force between Ce2O3 inclusions. However, there are apparent deviations between the attractive force derived from the CSLM test and that predicted from the capillary ‘quadrupoles’ model. These deviations might be caused by the more complex undulation of the real contact lines rather than the rotational symmetry assumption in the capillary ‘quadrupole’ model. Based on the present analysis, the resistive drag force is larger compared to the inertial force by 3 or 4 orders of magnitude.

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Abbreviations

A Y :

Projected area of particle ‘Y’ (m2)

b Y :

Immersion depth of particle ‘Y’ (m)

C:

Coulomb (A s)

D Y :

Density ratio of particle ‘Y’ and liquid phase

f :

Drag coefficient

F Chrg–Chrg :

Capillary force between capillary ‘charges’ (N)

F Chrg–MP :

Capillary force between a capillary ‘charge’ and a capillary ‘multipole’ (N)

F cap :

Capillary force on particles (N)

F inert :

Inertial force on particles (N)

g :

Gravity acceleration vector (m/s2)

G −1 :

Hydrodynamic resistance coefficient

G 0 :

A constant for the interaction between capillary ‘multipoles’

H Y :

Undulation amplitude of particle ‘Y’ (m)

h QP :

Meniscus profile around a capillary ‘quadrupole’ (m)

h HP :

Meniscus profile around a capillary ‘hexapole’ (m)

K 0 :

Modified Bessel function of zeroth order

L :

Distance between particle mass centers (m)

n Y :

Multipole order of particle ‘Y’

m Y :

Mass of particle ‘Y’ (kg)

q −1 :

Capillary length (m)

Q Y :

Capillary ‘charge’ of particle ‘Y’ (m)

r c,Y :

Radius of contact line of particle ‘Y’ (m)

R eq,Y :

Equivalent radius of particle ‘Y’ (m)

t :

Time (s)

T :

Temperature (K)

v :

Velocity (m/s)

ΔW Chrg –Chrg :

Capillary interaction energy between two ‘charges’ (J)

ΔW Chrg–MP :

Capillary interaction energy between a ‘charge’ and a ‘multipole’ (J)

ΔW MP–MP :

Capillary interaction energy between ‘multipoles’ (J)

α :

Contact angle between liquid and solid particle

Δα :

Contact angle deviation

μ :

Dynamic viscosity (Pa s)

γ :

Interfacial tension of fluid interfaces (N/m)

φ Y :

Rotation angle of particle ‘Y’ around a vertical axis

ρ I, ρ II :

Densities of the fluid phases (kg/m3)

ρ Y :

Density of particle ‘Y’ (kg/m3)

ψ Y :

Meniscus slope angle of particle ‘Y’

κ B :

Boltzmann constant (J/K)

Drag:

Drag resistance

Chrg:

Capillary ‘charge’

QP:

Capillary ‘quadrupole’

HP:

Capillary ‘hexapole’

Chrg–Chrg:

Interaction between capillary ‘charges’

Chrg–MP:

Interaction between a capillary ‘charge’ and a ‘multipole’

MP:

Capillary ‘multipoles’

tot:

Total

Y:

Particle index, A or B

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Acknowledgments

The authors thank the China Scholarship Council (CSC) for financial support (File No. 201706080018).

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On behalf of all authors, the corresponding author states that there is no conflict of interest.

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  1. Department of Materials Engineering, KU Leuven, Kasteelpark Arenberg 44, Box 2450, 3001, Leuven, Belgium

    Zilong Qiu, Annelies Malfliet, Bart Blanpain & Muxing Guo

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  1. Zilong Qiu
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  2. Annelies Malfliet
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Qiu, Z., Malfliet, A., Blanpain, B. et al. Capillary Interaction Between Micron-Sized Ce2O3 Inclusions at the Ar Gas/Liquid Steel Interface. Metall Mater Trans B 53, 1775–1791 (2022). https://doi.org/10.1007/s11663-022-02486-6

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