Abstract
When an object suspended in fluid moves past a soft substrate it experiences an additional lift force due to the deformability of the substrate. In this work we find this lift force analytically for a general deformable substrate in the limit of small deformations. In particular we employ Lorentz's reciprocal theorem to obtain a general integral relation between the lift force and the linear response function of the soft substrate. We apply these results to an elastic layer, and discuss the behavior of the lift force as a function of Poisson's ratio and the thickness of the layer, obtaining analytic results for thin and thick layers. Then we generalize the theory to a linear viscoelastic response of the substrate. For oscillatory relative motion between the surfaces we find that the resulting lift force is a superposition of steady and oscillating modes whose amplitude and phase contain information about the elastic and viscous components of the material response. Our theory makes transparent the connection between the elastohydrodynamic lift force and the underlying response of the substrate and can be used to characterize the mechanical properties of an arbitrary soft material without solid-to-solid contact via lift force measurements.
