Direct Measurement of the Elastohydrodynamic Lift Force at the Nanoscale

Abstract

Friction in soft and wet contacts is crucial for industry and engineering, but it might also play a central role for the motion of various physiological and biological entities, as well as for the nanorheology of very soft materials. Here, we report on the first direct measurement of the elastohydrodynamic lift force acting on a sphere moving within a viscous liquid, near and along a soft substrate under nanometric confinement. Using atomic force microscopy, the lift force is probed as a function of the gap size, for various driving velocities, viscosities, and stiffnesses. The results are in excellent agreement with scaling arguments and a novel quantitative model developed from the soft lubrication theory, in linear elasticity, and for small compliances. For larger compliances, or equivalently for smaller confinement length scales, a saturation of the lift force is observed and its empirical scaling law is discussed.

Regimes of soft lubrication

“…Indeed, this scaling law was recently recovered experimentally in Zhang et al. (2020). We remark that the scaling will be valid for the three-dimensional case for the entire left column of the table, and the same holds for in the middle column – the reason being that the boundary layers in these cases are always small compared to the contact size.…”

Rotation of a submerged finite cylinder moving down a soft incline

“…Previous theoretical works have studied confined flows in the soft lubrication approximation and accounted for the roles of elasticity [11][12][13][14][15][16], fluid compressibility [17], the inertia of the fluid and the elastic medium [18], and viscoelasticity of the substrate [19]. More recent works have focused on elastohydrodynamic effects for liquids confined at the micro and nano scales [20][21][22], which has important consequences for surface mechanical characterization [23,24]. For symmetrical objects, the results show that elastic deformations lead to a non-symmetric pressure field and to the emergence of a friction-reducing lift force.…”

Lift induced by slip inhomogeneities in lubricated contacts

“…In the presence of small slippage inhomogeneities, our scaling estimate suggests that the lift force, F z,slip , has to be considered alongside other lubrication forces. For instance, using atomic-force microscopy, the elastohydrodynamic force was reported [34] to be F z,EHD ∼ nN. Considering the same experimental setup, but with a rigid substrate exhibiting an ≈1-nm slip inhomogeneity, we obtain F z,slip ∼ nN, i.e., the same order of magnitude as for the soft substrate [35].…”