Research Papers: Evaporation, Boiling, and Condensation

Effect of Cutoff Radius on the Surface Tension of Nanoscale Bubbles

[+] Author and Article Information
Ian A. Cosden, Jennifer R. Lukes

 Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104cosden@seas.upenn.edu

J. Heat Transfer 133(10), 101501 (Aug 11, 2011) (8 pages) doi:10.1115/1.4004167 History: Received May 12, 2010; Revised May 03, 2011; Published August 11, 2011; Online August 11, 2011

Molecular dynamics simulations are performed to calculate the surface tension of bubbles formed in a metastable Lennard–Jones (LJ) argon fluid. The calculated normal and transverse pressure components are used to compute a surface tension which is compared to the surface tension computed from the Young–Laplace equation. Curvature effects on surface tension are investigated by performing various sized simulations ranging from 6912 to 256,000 LJ particles. The computed surface tension values differ depending on the calculation method for the smaller systems studied but the methods converge as the system size increases. Surface tension calculations on small bubbles may not be appropriate since the liquid farthest from the interface has yet to achieve the pressure profile of a homogeneous fluid. Density profiles, pressures, and calculated surface tensions are shown to have a strong dependence on the choice of the interaction cutoff radius. A cutoff radius of 8σ, significantly larger than that commonly used in the literature, is recommended for accurate calculations in liquid–vapor systems.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

The metastable liquid state point used in this study

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Figure 2

Snapshots of the bubble nucleation process for L* = 67.5 (202,612 particles). Screenshot generated after time step: (a) 14,700, (b) 32,000, (c) 46,800, (d) 66,500, (e) 80,400, and (f) 110,000. The simulation has been shifted once to ensure the final bubble is centered within the simulation cell. Only the vapor particles are shown.

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Figure 3

Snapshot of bubble showing (a) the entire simulation, i.e., all 202,612 particles and (b) only the 1014 particles tagged as vapor

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Figure 4

Local density, normal pressure, and transverse pressure profiles for L* = 40.2. The radius of the surface of tension, Rs *, and the equimolar dividing radius, Re *, are shown as vertical lines. In this case the Tolman length, δ = Re *  − Rs *, is −1.2.

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Figure 5

Local density profiles from center of bubble for various sized systems ranging from 6912 (L* = 21.9) to 256,000 (L* = 73.0) particles. The slope of the interfacial region for L* = 73.0 is shown and varies between 0.26 and 0.29 for the other bubbles.

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Figure 6

Virial pressure in the liquid region limit (Pl * ) and vapor region limit (Pv * ) as a function of the equimolar dividing radius (Re *). The points at ∞ are calculated from the planar interface simulation.

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Figure 7

Comparison of different methods to calculate surface tension for different bubble sizes. The point at ∞ is calculated from Eq. 17 for the planar interface simulation.

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Figure 8

Radial pressure profiles for different sized bubbles: (a) virial pressure, (b) curve fit to the normal pressure component, (c) transverse pressure component. The radial distance is normalized by half of the simulation box size, L*/2.

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Figure 9

Radial profiles of the virial pressure (P*), normal pressure (P*N ), and transverse pressure (PT *) for (a) Re *  = 7.0, (b) Re *  = 12.0, and (c) Re *  = 20.2. The radial distance is normalized by half of the simulation box size, L*/2.

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Figure 10

The effect of cutoff radius on the local density profile (computed at increments of 0.1r *) for the same starting system configuration, L* = 31.0. Increasing the cutoff radius increases the size of the bubble obtained.

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Figure 11

The effect of the cutoff radius on the liquid region pressure, for L* = 31.0. P *N l is the normal pressure calculated in the region farthest from the center of the bubble, Pl * is the virial pressure calculated in the same region.

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Figure 12

The effect of the cutoff radius on the calculated surface tension of a bubble, for L* = 31.0




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