Coupled instability modes at a solvent/non-solvent interface to decorate cellulose acetate flowers

Abstract

Dispensing a water drop on the thin film of a solution composed of cellulose acetate (CA) in dimethyl formamide (DMF) forms a thin and porous CA layer at the water–DMF interface. While a denser water drop on a rarer CA–DMF film manifests a Rayleigh–Taylor instability—RTI, the dynamically forming porous layer at the water–DMF interface triggers a Saffman–Taylor instability—STI. The combined effects of RTI and STI enable the formation, growth, coalescence, and branching of an array of periodic finger patterns to finally develop into a flower-like morphology. A general linear stability analysis (GLSA) of a thin bilayer composed of a Newtonian and incompressible water layer resting on a Darcy–Brinkman porous medium could predict the length and the time scales of such a finger formation phenomenon. The GLSA uncovers the crucial roles of pressure gradients originating from the gravitational effects, osmotic forces, the Marangoni effect, and capillary forces on the dynamics of the finger formation. While the density difference between water and CA–DMF layer plays a crucial role in deciding the initial finger spacing, the osmotic pressure dictates the formation, growth, branching, and coalescence of fingers. The length-FL and number-Navg of fingers are found to scale as FL∼We0.33Re−0.25 and Navg∼We0.33Re0.25. Further, an inverse relationship of the concentration of CA (C) with ∼We−0.3 and ∼Re−0.7 highlights its role in the formation and growth of fingers. The loading of CA in DMF, the viscosity and density of the CA–DMF film, and the curvature of the fingers are found to be other parameters that decide morphologies.