Lift induced by slip inhomogeneities in lubricated contacts

Lubrication forces depend to a high degree on elasticity, texture, charge, chemistry, and temperature of the interacting surfaces. Therefore, by appropriately designing surface properties, we may tailor lubrication forces to reduce friction, adhesion, and wear between sliding surfaces and control repulsion, assembly, and collision of interacting particles. Here, we show that variations of slippage on one of the contacting surfaces induce a lift force. We demonstrate the consequences of this force on the mobility of a cylinder traveling near a wall and show the emergence of particle oscillation and migration that would not otherwise occur in the Stokes flow regime. Our study has implications for understanding how inhomogeneous biological interfaces interact with their environment; we also propose a method of patterning surfaces for controlling the motion of nearby particles.

Figure 1

Two lubrication models. (a) 2D solid cylinder moving near a flat wall with a transition from slip (blue) to no slip (gray). (b) 2D cylinder half-coated with a slip region and moving near a wall. [(c), (d)] Sketches of cylinder trajectories for the two systems with ${\delta }_0=0.05r, \ell =1.79{\delta }_0$ and cylinder density ${\rho }_{\text{c}}=8.77\rho$. The particle experiences a small rotation that is not visually observable. (e) Gap thickness vs the transverse displacement of the cylinder. Inset shows the trajectory over a larger spatial extent.

Figure 2

Cylinder trajectories induced by variation of slippage. (a) Cylinder with density ratio ${\rho }_c/\rho =8.77$ falling near a wall that alternates between slip (blue) and no slip (gray). (b) Neutrally buoyant cylinder (${\rho }_c/\rho =1$) rotating above a slip-to-no-slip transition. (c) Neutrally buoyant Janus cylinder (${\rho }_c/\rho =1$) rotating next to a wall. Right column (ii) shows the gap thickness as a function of the transverse displacement. For all configurations, ${\delta }_0/r=0.05$ and $L=1.79$.

Figure 3

Analytical resistance coefficients for both model systems ($\varepsilon =0.05$). In the inset (i), the coefficients with no $\widehat{}$ refer to configuration (ii) and the ones with $\widehat{}$ refer to (iii).

Figure 4

Pressure distributions in four configurations and for three slip lengths, $L=0$ (red), $L=1$ (blue), and $L=\infty$ (black).