Quantifying Hydrodynamic Slip:  A Comprehensive Analysis of Dewetting Profiles

Abstract

To characterize nontrivial boundary conditions of a liquid flowing past a solid, the slip length is commonly used as a measure. From the profile of a retracting liquid front (e.g., measured with atomic force microscopy), the slip length can be extracted with the help of a Stokes model for a thin liquid film dewetting from a solid substrate. Specifically, we use a lubrication model derived from the Stokes model for strong slippage and linearize the film profile around the flat, unperturbed film. For small slip lengths, we expand the linearized full Stokes model for small slopes up to third order. Using the respective model, we obtain, in addition to the slip length, the capillary number, from which we can estimate the viscosity of the fluid film. We compare numerical and experimental results, test the consistency and the validity of the models/approximations, and give an easy-to-follow guide of how they can be used to analyze experiments.

Stability and Dewetting of Thin Liquid Films

“…From the dynamics of hole growth 27,28,34-40 as well as from the shape of the liquid rim surrounding the hole one can get information about the slip or no-slip boundary condition of the liquid close to the solid substrate. 17,41,42 In the late stage, the straight ribbons that separate two coalescing holes decay into droplets due to the Rayleigh-Plateau instability, 43 c.f. Fig.…”

Reduced Interfacial Entanglement Density Affects the Boundary Conditions of Polymer Flow

“…According to our previous studies on OTS and DTS concerning nonentangled PS melts, asymmetric rims are related to slippage [13][14][15]. For DTS, slip lengths b of up to 5 m were obtained, for OTS, values are about 1 order of magnitude smaller.…”

“…These previous studies, however, lack one facet, which by now has been identified as one of the major issues influencing dewetting dynamics and profiles: hydrodynamic slippage [13][14][15]. In this Letter, we study the very nature of slippage in a molecular weight regime where chain entanglements can make an impact on the solidliquid interface friction.…”

“…As shown recently, lubrication models for Newtonian flow and different slip conditions (no-slip, weak-slip, intermediate-slip, and strong-slip [21]) and a more generalized model based on the full Stokes equations [14] can be applied to thin dewetting films with the important result that values for the slip length b can be obtained.…”

“…The theoretical description of the model for Newtonian liquids presented in [14] is derived from the full Stokes equations in two dimensions for a viscous, incompressible liquid including the Navier slip-boundary condition b ¼ u x =@ z u x j z¼0 , where u x denotes the velocity in the direction of dewetting (x direction) and z the vertical scale with the substrate at z ¼ 0. This leads to the equations of motion for a flat liquid film.…”