Effects of surface roughness on shear viscosity

This paper investigates the effect of surface roughness on fluid viscosity using molecular dynamics simulations. The three-dimensional model consists of liquid argon flowing between two solid walls whose surface roughness was modeled using fractal theory. In tandem with previously published experimental work, our results show that, while the viscosity in smooth channels remains constant across the channel width, in the presence of surface roughness it increases close to the walls. The increase of the boundary viscosity is further accentuated by an increase in the depth of surface roughness. We attribute this behavior to the increased momentum transfer at the boundary, a result of the irregular distribution of fluid particles near rough surfaces. Furthermore, although the viscosity in smooth channels has previously been shown to be independent of the strength of the solid-liquid interaction, here we show that in the presence of surface roughness, the boundary viscosity increases with the solid's wettability. The paper concludes with an analytical description of the viscosity as a function of the distance from the channel walls, the walls’ surface roughness, and the solid's wetting properties. The relation can potentially be used to adjust the fluid dynamics equations for a more accurate description of microfluidic systems.

Figure 1

MD model illustrating liquid argon (cyan) confined by two solid walls (pink). The surfaces to the right show walls of different values of the roughness parameter corresponding to (a) $G=0$, (b) $G=0.75$, and (c) $G=1.5$, respectively.

Figure 2

Velocity profiles in the $x$ and $y$ channel directions.

Figure 3

Density isosurfaces for $\rho =1.525\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$ for (a) smooth and (b) rough channel walls.

Figure 4

Mean square displacement in the (a) $x$ and (b) $y$ directions. The MSD in the $z$ direction is identical to that in the $x$ direction and was omitted.

Figure 5

(a) Strain rate and (b) shear stress of the liquid across the channel width for different values of the average depth of roughness.

Figure 6

Viscosity profiles for different values of the roughness parameter $G$.

Figure 7

Viscosity profiles for different values of the roughness parameter $G$ for (a) ${\varepsilon }_{\mathrm{wf}}=0.002\mathrm{eV}$, (b) ${\varepsilon }_{\mathrm{wf}}=0.002\mathrm{eV}$, (c) ${\varepsilon }_{\mathrm{wf}}=0.010\mathrm{eV}$, and (d) ${\varepsilon }_{\mathrm{wf}}=0.010\mathrm{eV}$ (Couette flow).