Research Papers

Modeling Alkaline Liquid Metal (Na) Evaporating Thin Films Using Both Retarded Dispersion and Electronic Force Components

[+] Author and Article Information
Joseph B. Tipton

Department of Mechanical, Aerospace and Biomedical Engineering, University of Tennessee, Knoxville, TN 37996-2210

Kenneth D. Kihm1

Department of Mechanical, Aerospace and Biomedical Engineering, University of Tennessee, Knoxville, TN 37996-2210kkihm@utk.edu

David M. Pratt

Structures Division, Air Vehicles Directorate, United States Air Force Research Laboratory, Wright-Patterson AFB, OH 45433-7542


Corresponding author.

J. Heat Transfer 131(12), 121015 (Oct 15, 2009) (9 pages) doi:10.1115/1.4000022 History: Received January 09, 2009; Revised April 07, 2009; Published October 15, 2009

A new thin-film evaporation model is presented that captures the unsimplified dispersion force along with an electronic disjoining pressure component that is unique to liquid metals. The resulting nonlinear fourth-order ordinary differential equation (ODE) is solved using implicit orthogonal collocation along with the Levenberg–Marquardt method. The electronic component of the disjoining pressure should be considered when modeling liquid metal extended meniscus evaporation for a wide range of work function boundary values, which represent physical properties of different liquid metals. For liquid sodium, as an example test material, variation in the work function produces order-of-magnitude differences in the film thickness and evaporation profile.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

Schematic of a cylindrical capillary geometry identifying the distinct regions of the extended evaporating meniscus. The majority of heat and mass transfer occurs in the transition thin-film region.

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Figure 2

A comparison of the retarded DLP theory and nonretarded (Hamaker approximation) London dispersion component of the disjoining pressure for the case of type 304 stainless steel (Medium 1) and vapor (Medium 2) interacting across liquid sodium (Medium 3)

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Figure 3

Dependence of χ(κn) on the work function related parameter, κn, as related via Eq. 6. This function determines the boundary condition for Derjaguin’s electronic component of the disjoining pressure.

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Figure 4

Steady thin-film evaporation solutions as functions of x measured from the absorption thickness H0 over the range of possible disjoining pressures: (a) thin-film thickness, (b) evaporative mass flux, and (c) liquid pressure gradient. Cases A–G represent the effects of varying strengths of the electron degeneracy component of the disjoining pressure depending upon the electronic work function boundary condition (R=200 μm and ΔT=0.0005 K).

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Figure 5

(a) Spatial convergence and (b) iterative convergence for R=200 μm, ΔT=0.0005 K, and χ(κ)=0.001650 (Case E: ΠB/ΠA=1.0)



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