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Hydrodynamic force measurements under precisely controlled conditions: Correlation of slip parameters with the mean free path
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Figures

Image of FIG. 1.

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FIG. 1.

Schematic view of the AFM setup.

Image of FIG. 2.

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FIG. 2.

Linear dependence of / on Δ in Kr, at two distances. The error bars represent the standard deviations obtained by averaging over more than 10 sweeps. Data can be fitted with very good agreement to the linear relation / = ωΔ + , where and are free parameters.

Image of FIG. 3.

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FIG. 3.

Casimir force gradient (normalized by the nominal radius) (1/)∂ /∂ as a function of separation for all investigated gases. The generally good qualitative agreement of the measured amplitudes with the theoretical expectation rules out phase calibration errors (see the Appendix). All runs show a Gaussian distribution of their errors. The inset contains a zoom in the distance regime of lowest experimental uncertainty.

Image of FIG. 4.

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FIG. 4.

AFM tapping mode images taken on the sphere and the plate after completion of the measurements. On both images, polynomial backgrounds up to second order have been removed.

Image of FIG. 5.

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FIG. 5.

Inverse of the damping coefficients γ = /(). The best fits of Eq. (5) to experimental data (left scales) within {80 nm, λ} < < 5 μm (corresponding to the central range, which is limited by the vertical dashed lines) are given together with the normalized residuals of the fit (right scales). The error bars represent standard deviations obtained by averaging over at least 10 sweeps.

Image of FIG. 6.

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FIG. 6.

Dependence of the fitted radii for = 0 in Table II on the mean free path. The dashed line represents a fit to the equation , with and being free parameters. Note that the uncertainty in the mean free path is smaller than the size of the symbols for all data.

Image of FIG. 7.

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FIG. 7.

Ratio λ in dependence of the mean free path. A fit (dashed line) of data at to the generic exponential with , , being free parameters has been added as a guide to the eye.

Image of FIG. 8.

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FIG. 8.

No clear correlation between the TMAC and the mean free path.

Image of FIG. 9.

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FIG. 9.

Dependence of the VSC (a) and the TMAC (b) on the mean free path. The dashed curves in (a) represent least square fits of the data at to the generic form , and are intended as a guide to the eye only. Data obtained at are indicated by “II.” Note that the error bars contain contributions from the uncertainties in λ as well as λ.

Tables

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Table I.

Thermodynamic properties of the gases used in the present work, as obtained from Refs. and the hard sphere model stated in Eq. (6) .

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Table II.

Results for the slip length λ, , and the effective radius obtained by fitting the Vinogradova model Eq. (5) to experimental data. For convenience, we also include the slip length on the sphere, λ.

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Table III.

Results for the dimensionless parameters VSC and TMAC extracted from data on the slip lengths in Table II and the mean free path of the gases under consideration of temporal variations in the ambient pressure.

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/content/aip/journal/pof2/25/4/10.1063/1.4801096
2013-04-23
2014-04-20

Abstract

A customized atomic force microscope has been utilized in dynamic mode to measure hydrodynamic forces between a sphere and a flat plate, both coated with gold. In order to study the influence of the mean free path on slippage without systematic errors due to varying surface properties, all data have been acquired at precisely the same spot on the plate. Local accommodation coefficients and slip lengths have been extracted from experimental data for He, Ne, Ar, Kr, as well as N, CO, and CH, at Knudsen numbers between 3 × 10 and 3. We found that slippage is effectively suppressed if the mean free path of the fluid is lower than the roughness amplitude on the surface, while we could not observe a clear correlation between the accommodation coefficient and the molecular mass.

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Scitation: Hydrodynamic force measurements under precisely controlled conditions: Correlation of slip parameters with the mean free path
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/4/10.1063/1.4801096
10.1063/1.4801096
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