^{1,a)}, Vincent K. Shen

^{1,b)}, Jeffrey R. Errington

^{2,c)}and Thomas M. Truskett

^{3,4,d)}

### Abstract

Using event-driven molecular dynamics simulations, we quantify how the self diffusivity of confined hard-sphere fluids depends on the nature of the confining boundaries. We explore systems with featureless confining boundaries that treat particle-boundary collisions in different ways and also various types of physically (i.e., geometrically) rough boundaries. We show that, for moderately dense fluids, the ratio of the self diffusivity of a rough wall system to that of an appropriate smooth-wall reference system is a linear function of the reciprocal wall separation, with the slope depending on the nature of the roughness. We also discuss some simple practical ways to use this information to predict confined hard-sphere fluid behavior in different rough-wall systems.

W.P.K. gratefully acknowledges financial support from a National Research Council postdoctoral research associateship at the National Institute of Standards and Technology (NIST). T.M.T. acknowledges support of the Welch Foundation (F-1696) and the National Science Foundation (NSF) (CBET 1065357). J.R.E. acknowledges financial support of the NSF (CBET 0828979). The Biowulf Cluster at the National Institutes of Health (NIH) provided computational resources for this paper.

I. INTRODUCTION

II. MODEL FLUID

III. SURFACE ROUGHNESS AND BOUNDARY CONDITIONS

A. Featureless walls

B. Physically rough walls

IV. RESULTS

A. Featureless flat walls

B. Thermal walls

C. Rotational walls

D. Physically rough walls

V. CONCLUSIONS

### Key Topics

- Self diffusion
- 33.0
- Surface measurements
- 26.0
- Surface collisions
- 12.0
- Boundary value problems
- 10.0
- Thermodynamic properties
- 9.0

## Figures

Schematics of the geometries of the confined fluid system, as described in the text. (a) Featureless walls and (b) physically rough walls.

Schematics of the geometries of the confined fluid system, as described in the text. (a) Featureless walls and (b) physically rough walls.

Self diffusivity *D* versus total density ρ = *N*/(*AH*) for the hard-sphere fluid confined between smooth walls in slit-pore geometry.

Self diffusivity *D* versus total density ρ = *N*/(*AH*) for the hard-sphere fluid confined between smooth walls in slit-pore geometry.

Self diffusivity *D* versus total density ρ for the hard-sphere fluid confined between thermal walls, for various wall separations *H*.

Self diffusivity *D* versus total density ρ for the hard-sphere fluid confined between thermal walls, for various wall separations *H*.

Fraction of collisions in the system involving the wall surface *f* _{ w } for the hard-sphere fluid confined to a slit-pore geometry. Symbols have the same meaning as in Fig. 3.

Fraction of collisions in the system involving the wall surface *f* _{ w } for the hard-sphere fluid confined to a slit-pore geometry. Symbols have the same meaning as in Fig. 3.

Ratio of the self-diffusivity between thermal walls *D* ^{TW} to its value when confined between smooth walls *D* ^{SW} at the same ρ and *H* versus (a) ρ and (b) *H* ^{−1}. Symbols in (a) are the same as those in Fig. 3. In (b), all data is for ρσ^{3} > 0.2, and dashed line is a fit to the form *D* ^{TW}/*D* ^{SW} = 1.0–1.44σ/*H*.

Ratio of the self-diffusivity between thermal walls *D* ^{TW} to its value when confined between smooth walls *D* ^{SW} at the same ρ and *H* versus (a) ρ and (b) *H* ^{−1}. Symbols in (a) are the same as those in Fig. 3. In (b), all data is for ρσ^{3} > 0.2, and dashed line is a fit to the form *D* ^{TW}/*D* ^{SW} = 1.0–1.44σ/*H*.

Ratio of predicted to observed self diffusivity (see text) for the thermal wall system. Dotted blue and red dashed lines provide 5% and 25% error bounds, respectively. Symbols are the same as those in Fig. 3.

Ratio of predicted to observed self diffusivity (see text) for the thermal wall system. Dotted blue and red dashed lines provide 5% and 25% error bounds, respectively. Symbols are the same as those in Fig. 3.

Self diffusivity *D* ^{RW} versus density ρ for the hard-sphere fluid confined between rotational walls at (a) θ = π/2 and various wall separations *H* and (b) *H*/σ = 7 and various values of θ.

Self diffusivity *D* ^{RW} versus density ρ for the hard-sphere fluid confined between rotational walls at (a) θ = π/2 and various wall separations *H* and (b) *H*/σ = 7 and various values of θ.

Ratio of self diffusivity between rotational walls *D* ^{RW} to that between smooth walls *D* ^{SW} at the same ρ and *H* versus ρ at (a) θ = π/2 and various *H* and (b) *H*/σ = 7 and various θ, and versus (c) *H* ^{−1} at various θ. Symbols in (a), and (b) and (c) are the same as those in Figs. 7(a) and 7(b), respectively. In (c), all data points are for ρσ^{3} > 0.2; lines are linear fits of the form *D* ^{RW}/*D* ^{SW} = 1 − *C*(*H*/σ)^{−1}; the inset to (c) shows the value of *C* as a function of θ from linear fits in main panel of (c).

Ratio of self diffusivity between rotational walls *D* ^{RW} to that between smooth walls *D* ^{SW} at the same ρ and *H* versus ρ at (a) θ = π/2 and various *H* and (b) *H*/σ = 7 and various θ, and versus (c) *H* ^{−1} at various θ. Symbols in (a), and (b) and (c) are the same as those in Figs. 7(a) and 7(b), respectively. In (c), all data points are for ρσ^{3} > 0.2; lines are linear fits of the form *D* ^{RW}/*D* ^{SW} = 1 − *C*(*H*/σ)^{−1}; the inset to (c) shows the value of *C* as a function of θ from linear fits in main panel of (c).

Ratio of predicted to observed self diffusivity (discussed in text) versus the observed self diffusivity for the rotational wall system with the value of θ denoted in each figure. Dotted blue and red dashed lines provide 10% and 25% error bounds, respectively. Symbols have the same meaning as in Fig. 7(a).

Ratio of predicted to observed self diffusivity (discussed in text) versus the observed self diffusivity for the rotational wall system with the value of θ denoted in each figure. Dotted blue and red dashed lines provide 10% and 25% error bounds, respectively. Symbols have the same meaning as in Fig. 7(a).

Self diffusivity in ((a) and (c)) smooth *x* and ((b) and (d)) rough *y* directions versus density for the hard-sphere fluid confined between physically rough walls (see Fig. 1) with λ/σ = 3.0 and ((a) and (b)) *a* _{ w }/σ = 1.0 and various *H* and ((c) and (d)) *H*/σ = 7.5 and various *a* _{ w }.

Self diffusivity in ((a) and (c)) smooth *x* and ((b) and (d)) rough *y* directions versus density for the hard-sphere fluid confined between physically rough walls (see Fig. 1) with λ/σ = 3.0 and ((a) and (b)) *a* _{ w }/σ = 1.0 and various *H* and ((c) and (d)) *H*/σ = 7.5 and various *a* _{ w }.

Fraction of particle collisions that involve the wall *f* _{ w } for the hard-sphere fluid confined between physically rough walls versus density. (a) *a* _{ w }/σ = 1.0 at various *H* and (b) *H*/σ = 7.5 and various *a* _{ w }. Symbols have the same meaning as in Fig. 10.

Fraction of particle collisions that involve the wall *f* _{ w } for the hard-sphere fluid confined between physically rough walls versus density. (a) *a* _{ w }/σ = 1.0 at various *H* and (b) *H*/σ = 7.5 and various *a* _{ w }. Symbols have the same meaning as in Fig. 10.

Ratio of self diffusivity in rough direction *D* _{ y } and smooth direction *D* _{ x } with λ/σ = 3.0 versus ((a) and (b)) ρ and (c) *H* ^{−1} for the hard-sphere fluid confined between physically rough walls. Symbols in (a) and (c) are the same as in Fig. 10. In (c) all data points are for ρσ^{3} > 0.2 and lines are fits to the form *D* _{ y }/*D* _{ x } = 1 − *C*(*H*/σ)^{−1}. Panel (d) displays the values of *C* versus *a* _{ w } at all the wavelengths studied.

Ratio of self diffusivity in rough direction *D* _{ y } and smooth direction *D* _{ x } with λ/σ = 3.0 versus ((a) and (b)) ρ and (c) *H* ^{−1} for the hard-sphere fluid confined between physically rough walls. Symbols in (a) and (c) are the same as in Fig. 10. In (c) all data points are for ρσ^{3} > 0.2 and lines are fits to the form *D* _{ y }/*D* _{ x } = 1 − *C*(*H*/σ)^{−1}. Panel (d) displays the values of *C* versus *a* _{ w } at all the wavelengths studied.

Ratio of predicted (see text) to observed value of *D* _{ y } plotted versus *D* _{ y } for the hard-sphere fluid confined between physically rough walls with λ/σ = 3.0 and ((a) and (b)) *a* _{ w }/σ = 1 and various *H* and ((c) and (d)) *H*/σ = 7.5 and various *a* _{ w }. Symbols in (a) and (b), and (c) and (d) correspond to those in Figs. 10(a) and 10(c), respectively. In (a) and (c) we use values of *C* obtained from the fits in Fig. 12(c), while in (b) and (d) we use *C* = 2.12*a* _{ w }/σ (see Fig. 12(d)). The dotted green and dashed red lines correspond to 10% and 25% error bounds, respectively.

Ratio of predicted (see text) to observed value of *D* _{ y } plotted versus *D* _{ y } for the hard-sphere fluid confined between physically rough walls with λ/σ = 3.0 and ((a) and (b)) *a* _{ w }/σ = 1 and various *H* and ((c) and (d)) *H*/σ = 7.5 and various *a* _{ w }. Symbols in (a) and (b), and (c) and (d) correspond to those in Figs. 10(a) and 10(c), respectively. In (a) and (c) we use values of *C* obtained from the fits in Fig. 12(c), while in (b) and (d) we use *C* = 2.12*a* _{ w }/σ (see Fig. 12(d)). The dotted green and dashed red lines correspond to 10% and 25% error bounds, respectively.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content