Frictional force on sliding drops

The dynamic frictional force between solid surfaces in relative motion differs from the static force needed to initiate motion, but this distinction is not usually thought to occur for liquid drops moving on a solid. Recent experiments [Gao et al., Nat. Phys. 14, 191 (2018)] have challenged this view and claim to observe an analog of solid-on-solid friction for sliding drops. We use molecular dynamics simulations to investigate the forces that moving liquids exert on solids in several situations. In contrast to the indirect techniques required in laboratory experiments, the forces involved in friction are directly accessible in these calculations. We find that, aside from possible inertial effects due to the abrupt initiation of motion and aging effects for unconfined drops, the frictional forces are constant in time.

Figure 1

Couette flow velocity profile at $10\tau$ and $200\tau$. The MD results (20 realization average) are in green $(*)$, the Newtonian Navier-Stokes solution in red (+), and the shear-thinning model in blue $(\circ )$.

Figure 2

Average wall forces in Couette flow. For the bottom wall the MD results in red (+) and the Navier-Stokes solution is in blue $(\times )$; for the top wall the MD results are in green $(*)$ and the Navier-Stokes solution if in magenta $(\times )$.

Figure 3

Sessile drop driven across an atomically smooth homogeneous substrate at times (a) 0, (b) $500\tau$, and (c) $2500\tau$.

Figure 4

Sessile drop driven across a substrate with a chemical step, pinned at (a) $f=0.0005$ and in motion for $f=0.001$ at (b) times $500\tau$ and (c) $2500\tau$.

Figure 5

(a) Center of mass and (b) lateral force vs time for a sessile drop forced across the various substrates at $f=0.001$, averaged over 20 realizations: smooth, red (+); chemical step, green $(*)$; and physical step, blue $(\circ )$.

Figure 6

Flow inside the drop on a homogeneous substrate: (a) two-dimensional velocity field in the moving center of the mass frame and (b) average lateral velocity profile in the center of the drop in the substrate frame.

Figure 7

Local fields for a drop on a homogeneous substrate, (a) at rest and (b) in motion after $250\tau$, in a single realization: density, red (+); $x$ velocity, green $(*)$; $x$ force, orange $(\times )$; and $y$ force, blue $(\circ )$.

Figure 8

Drop driven into a corner by motion of the bottom wall to the right, at times (a) 0, (b) $200\tau$, and (c) $600\tau$. The translation of the wall is shown by the red dot, which indicates the location of an atom fixed in the wall,

Figure 9

(a) Streamlines and (b) local fields for a drop squeezed into a corner at $u=0.1$: density, red (+); $x$ velocity, green $(*)$; $x$ force, orange $(\times )$; and $y$ force, blue $(\circ )$.

Figure 10

Time variation of the (a) $x$ and (b) $y$ forces on the sliding wall for various velocities: $u=0.1$, red (+); $u=0.25$, green $(*)$; $u=0.5$, orange $(\circ )$; and $u=1.0\sigma /\tau$, blue $(\times )$.

Figure 11

Time decay of fluid density and velocity near the wall, and the $x$ and $y$ forces on the drop at $u=1.0\sigma /\tau$; the color code is as in Fig. 7.

Figure 12

Simulation of the experiment of Gao et al. [4]. Shown on top are the (a) side and (b) top views of the equilibrated system and on bottom the effects of sliding the substrate to the left at times (c) 1000 and (d) $5000\tau$.

Figure 13

Force on the pin in the simulation shown in Fig. 12.