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Noncontinuum drag force on a nanowire vibrating normal to a wall: Simulations and theory
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10.1063/1.3491127
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Affiliations:
1 School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853-5201, USA
2 Department of Mechanical Engineering, University of Victoria, Victoria, British Columbia V8W 3P6, Canada
Phys. Fluids 22, 103101 (2010)
/content/aip/journal/pof2/22/10/10.1063/1.3491127
http://aip.metastore.ingenta.com/content/aip/journal/pof2/22/10/10.1063/1.3491127

## Figures

FIG. 1.

Simulation domain.

FIG. 2.

Convergence of drag force results with simulation box size for a system with .

FIG. 3.

Problem geometry.

FIG. 4.

Dimensionless inverse drag force per unit length as a function of dimensionless distance between nanowire and bottom wall for continuum flow. The solid line is obtained by using Eq. (23), the dotted-dashed line represents lubrication theory results for small given in Eq. (24), and the dashed line represents the approximation for given in Eq. (25).

FIG. 5.

Nondimensionalized slip correction to the drag force, , plotted as a function of dimensionless distance between nanowire and bottom wall.

FIG. 6.

as a function of dimensionless distance between nanowire and bottom wall.

FIG. 7.

Drag force per unit length as a function of Knudsen number for corresponding to dimensions reported in Ref. 7. Legends are as shown in figure. Arrow near the -axis represents the Jeffrey–Onishi predictions in the continuum limit . The inset shows the same data on a linear-linear scale (free molecular flow results omitted for clarity). For simulations, error bars are smaller than symbol size.

FIG. 8.

Normalized drag force per unit length as a function of Kn for different as given in the legend. Lines represent predictions obtained using the semiempirical expression given in Eq. (37) and curve fits for coefficients in that equation. Symbols represent simulation data at . Error bars in simulations are smaller than symbol size.

FIG. 9.

Simulation results for the normalized drag coefficient as a function of nondimensionalized oscillation frequency at different Kn where is the BGK relaxation time defined in Sec. II. The arrows near the -axis represent quasisteady simulation results. Error bars in simulations are smaller than symbol size.

FIG. 10.

Low and high frequency asymptotes for the normalized drag coefficient plotted as a function of Kn. Symbols represent simulation data and the dashed line represents the drag coefficient for an isolated nanowire in the free molecular flow regime. This free molecular flow result is given by Eq. (36) with (Ref. 34). Error bars in simulations are smaller than symbol size.

## Tables

Table I.

Coefficients , , and in Eq. (37) as a function of . The coefficients can be well-fitted by the following equations: , , and .

/content/aip/journal/pof2/22/10/10.1063/1.3491127
2010-10-21
2014-04-18

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