Slip Flow Over Structured Surfaces with Entrapped Microbubbles

On hydrophobic surfaces, roughness may lead to a transition to a superhydrophobic state, where gas bubbles at the surface can have a strong impact on a detected slip. We present two-phase lattice Boltzmann simulations of a Couette flow over structured surfaces with attached gas bubbles. Even though the bubbles add slippery surfaces to the channel, they can cause negative slip to appear due to the increased roughness. The simulation method used allows the bubbles to deform due to viscous stresses. We find a decrease of the detected slip with increasing shear rate which is in contrast to some recent experimental results implicating that bubble deformation cannot account for these experiments. Possible applications of bubble surfaces in microfluidic devices are discussed.

Figure 1

Slip length $b$ as a function of protrusion angle $\phi$. A unit cell of each array is shown in insets and corresponding results are given by triangles (rhombic array), diamonds (rectangular array), and circles (square array). The inset in the top-left corner shows the definition of $\phi$.

Figure 2

Snapshots of simulations of bubbles on structured surfaces. Shown are a square array of bubbles with Capillary number (a) $\mathrm{Ca}=0.02$ and (b) $\mathrm{Ca}=0.4$, and (c) a slot with a cylindrical bubble. In each case a unit cell is shown.

Figure 3

(a) Slip length as a function of capillary number for a square array of bubbles with three different protrusion angles, $\phi =63°$, 68°, and 71° (from uppermost to lowermost). In the inset cross sections of liquid-gas interfaces for four capillary numbers are shown. (b) Taylor deformation as a function of Capillary number for the bubble with $\phi =71°$. These Ca values correspond to shear rates of the order of ${10}^{-6}–{10}^{-7}{\mathrm{s}}^{-1}$.

Figure 4

Slip length as a function of hole area fraction. Filled circles denote values for the flow parallel to the slots and triangles relate to the perpendicular direction. Corresponding open symbols are for a surface with rectangular holes ($\phi =72°$). The inset shows the normalized slip length as a function of the solid-area fraction, where the dashed line is the theoretical prediction for small solid-area fractions.