Fingering instability in Marangoni spreading on a deep layer of polymer solution

Abstract

Spreading on the free surface of a complex fluid is ubiquitous in nature and industry, such as drug delivery, oil spill, and surface treatment with patterns. Here, we report on a fingering instability that develops during Marangoni spreading on a deep layer of the polymer solution. In particular, the wavelength depends on the molecular weight and concentration of the polymer solution. We use the transmission lattice method to characterize the free surface morphology during spreading and the finger height at the micron scale. We use the Maxwell model to explain the spreading radius, which is dominated by elasticity at small time scales and by viscous dissipation at large time scales. In a viscous regime, with consideration of shear thinning, the spreading radius follows the universal 3/4 power law. Our model suggests a more generalized law of the spreading radius than the previous laws for Newtonian fluids. Furthermore, we give a physical explanation on the origin of the fingering instability as due to normal stresses at high shear rates generating a high contact angle, providing a necessary condition for the fingering instability. The normal stress also generates the elastic deformation at the leading edge and so selects the wavelength of the fingering instability. Understanding the spreading mechanism on a layer of viscoelastic fluid has a particular implication in airway drug delivery and surface coating.