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RESEARCH PAPERS: Bubbles, Particles and Droplets

Surface Deformation and Convection in Electrostatically-Positioned Droplets of Immiscible Liquids Under Microgravity

[+] Author and Article Information
Y. Huo

School of Mechanical and Materials Engineering,  Washington State University, Pullman, WA 99164

B. Q. Li1

School of Mechanical and Materials Engineering,  Washington State University, Pullman, WA 99164li@mme.wsu.edu

1

To whom correspondence should be addressed.

J. Heat Transfer 128(6), 520-529 (Nov 30, 2005) (10 pages) doi:10.1115/1.2188460 History: Received December 03, 2004; Revised November 30, 2005

A numerical study is presented of the free surface deformation and Marangoni convection in immiscible droplets positioned by an electrostatic field and heated by laser beams under microgravity. The boundary element and the weighted residuals methods are applied to iteratively solve for the electric field distribution and for the unknown free surface shapes, while the Galerkin finite element method for the thermal and fluid flow field in both the transient and steady states. Results show that the inner interface demarking the two immiscible fluids in an electrically conducting droplet maintains its sphericity in microgravity. The free surface of the droplet, however, deforms into an oval shape in an electric field, owing to the pulling action of the normal component of the Maxwell stress. The thermal and fluid flow distributions are rather complex in an immiscible droplet, with conduction being the main mechanism for the thermal transport. The non-uniform temperature along the free surface induces the flow in the outer layer, whereas the competition between the interfacial surface tension gradient and the inertia force in the outer layer is responsible for the flows in the inner core and near the immiscible interface. As the droplet cools into an undercooled state, surface radiation causes a reversal of the surface temperature gradients along the free surface, which in turn reverses the surface tension driven flow in the outer layer. The flow near the interfacial region, on the other hand, is driven by a complimentary mechanism between the interfacial and the inertia forces during the time when the thermal gradient on the free surface has been reversed while that on the interface has not yet. After the completion of the interfacial thermal gradient reversal, however, the interfacial flows are largely driven by the inertia forces of the outer layer fluid.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic representation of a positively charged melt droplet levitated in an electrostatic field: (a) levitation mechanism, (b) a two-laser-beam heating arrangement, and (c) two-fluid structure under the heat arrangement in (b)

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Figure 2

Boundary element and finite element mesh for numerical computation

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Figure 3

Computation of free and interfacial surface of an Al-Pb droplet in microgravity: (a) interfacial surface shape (ri∕r0=0.6); (b) undeformed free surface of liquid sphere; (c) E0=1.5×106(V∕m) and Q=0 (C); (d) E0=2.5×106(V∕m) and Q=0 (C)

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Figure 4

Steady-state fluid flow and temperature distribution in the droplet (ri∕ro=0.6) for some immiscible materials

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Figure 5

Steady state temperature distribution (ΔT=T−Tsmin, where Tsmin is the minimum surface temperature) along the free surface (a) and the interface between the two immiscible liquid metals (b). The surface is measured from south (θ=−π∕2) to north (θ=π∕2) pole.

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Figure 6

Steady state fluid flow distribution along the free surface boundary (a) and the interface between the two immiscible liquid metals (b). The angle θ is measured from (θ=−π∕2) to (θ=π∕2). The velocity is positive in the clockwise direction and negative in the counter clockwise direction.

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Figure 7

Steady-state fluid flow and temperature distribution in the Si-Co droplet with different radius ratios

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Figure 8

Transient fluid flow and temperature distributions in a Pb-Fe droplet after the heating lasers are turned off

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Figure 9

Transient temperature distribution (ΔT=T−Tmin) along the surface from (θ=−π∕2) to (θ=π∕2): (a) free surface and (b) the immiscible interface (Pb-Fe)

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Figure 10

Transient fluid flow distribution along the surface from (θ=−π∕2) to (θ=π∕2): (a) free surface and (b) the immiscible interface (Pb-Fe). The velocity is positive in the clockwise direction and negative in the counter clockwise direction.

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