Evaporation Induced Rayleigh-Taylor Instabilities in Polymer Solutions

Abstract: Understanding the mechanics of detrimental convective instabilities in drying polymer solutions is crucial in many applications such as the production of film coatings. It is well known that solvent evaporation in polymer solutions can lead to Rayleigh-B\'enard or Marangoni-type instabilities. Here we reveal another mechanism, namely that evaporation can cause the interface to display Rayleigh-Taylor instabilities due to the build-up of a dense layer at the air-liquid interface. We study experimentally the onset time ($t_p$) of the instability as a function of the macroscopic properties of aqueous polymer solutions, which we tune by varying the polymer concentration ($c_0$), molecular weight and polymer type. In dilute solutions, $t_p$ shows two limiting behaviors depending on the polymer diffusivity. For high diffusivity polymers (low molecular weight), the pluming time scales as $c_0^{-2/3}$. This result agrees with previous studies on gravitational instabilities in miscible systems where diffusion stabilizes the system. On the other hand, in low diffusivity polymers the pluming time scales as $c_0^{-1}$. The stabilizing effect of an effective interfacial tension, similar to those in immiscible systems, explains this strong concentration dependence. Above a critical concentration, $\hat{c}$, viscosity delays the growth of the instability, allowing time for diffusion to act as the dominant stabilizing mechanism. This results in $t_p$ scaling as $(\nu/c_0)^{2/3}$.