We report on the numerical implementation of thin film equations that describe the capillary-driven evolution of viscous films, in two-dimensional configurations. After recalling the general forms ...and features of these equations, we focus on two particular cases inspired by experiments: the leveling of a step at the free surface of a polymer film, and the leveling of a polymer droplet over an identical film. In each case, we first discuss the long-term self-similar regime reached by the numerical solution before comparing it to the experimental profile. The agreement between theory and experiment is excellent, thus providing a versatile probe for nanorheology of viscous liquids in thin film geometries.
Thin viscous liquid films driven by capillarity are well described in the lubrication theory through the thin film equation. In this article, we present an analytical solution of this equation for a ...particular initial profile: a stepped perturbation. This initial condition allows a linearization of the problem making it amenable to Fourier analysis. The solution is obtained and characterized. As for a temperature step in the heat equation, self-similarity of the first kind of the full evolution is demonstrated and a long-term expression for the excess free energy is derived. In addition, hydrodynamical fields are described. The solution is then compared to experimental profiles from a model system: a polystyrene nanostep above the glass transition temperature which flows due to capillarity. The excellent agreement enables a precise measurement of the capillary velocity for this polymeric liquid, without involving any numerical simulation. More generally, as these results hold for any viscous system driven by capillarity, the present solution may provide a useful tool in hydrodynamics of thin viscous films.
We present results on the leveling of polymer microdroplets on thin films prepared from the same material. In particular, we explore the crossover from a droplet spreading on an infinitesimally thin ...film (Tanner's law regime) to that of a droplet leveling on a film thicker than the droplet itself. In both regimes, the droplet's excess surface area decreases towards the equilibrium configuration of a flat liquid film, but with a different power law in time. Additionally, the characteristic leveling time depends on molecular properties, the size of the droplet, and the thickness of the underlying film. Flow within the film makes this system fundamentally different from a droplet spreading on a solid surface. We thus develop a theoretical model based on thin film hydrodynamics that quantitatively describes the observed crossover between the two leveling regimes.
The surface molecular motion of monodisperse polystyrene (PS) with various chain end groups was investigated on the basis of temperature‐dependent scanning viscoelasticity microscope (TDSVM). The ...surface glass transition temperatures, Tgss for the proton‐terminated PS (PS‐H) films with number‐average molecular weight, Mn of 4.9k–1,450k measured by TDSVM measurement were smaller than those for the bulk one, with corresponding Mns, and the Tgss for Mn smaller than ca. 50k were lower than room temperature (293 K). In the case of Mn = ca. 50k, the Tgss for the α,ω‐diamino‐terminated PS (α,ω‐PS(NH2)2) and α,ω‐dicarboxy‐terminated PS (α,ω‐PS(COOH)2) films were higher than that of the PS‐H film. On the other hand, the Tgs for the α,ω‐perfluoroalkylsilyl‐terminated PS (α,ω‐PS(SiC2CF6)2) film with the same Mn was much lower than those for the PS films with all other chain ends. The change of Tgs for the PS film with various chain end groups can be explained in terms of the depth distribution of chain end groups at the surface region.
