Multiscale deformation of a liquid surface in interaction with a nanoprobe

The interaction between a nanoprobe and a liquid surface is studied. The surface deformation depends on physical and geometric parameters, which are depicted by employing three dimensionless parameters: Bond number B_{o}, modified Hamaker number H_{a}, and dimensionless separation distance D. The evolution of the deformation is described by a strongly nonlinear partial differential equation, which is solved by means of numerical methods. The dynamic analysis of the liquid profile points out the existence of a critical distance D_{min}, below which the irreversible wetting process of the nanoprobe happens. For D ≥ D_{min}, the numerical results show the existence of two deformation profiles, one stable and another unstable from the energetic point of view. Different deformation length-scales, characterizing the stable liquid equilibrium interface, define the near- and the far-field deformation zones, where self-similar profiles are found. Finally, our results allow us to provide simple relationships between the parameters, which leads to determine the optimal conditions when performing atomic force microscope measurements over liquids.