Exponential Growth of Fingering Instabilities of Spreading Films Under Horizontal Thermal Gradients

Abstract

A thin liquid ribbon deposited on a wettable surface and subjected to a horizontal thermal gradient develops periodic fingers towards the cold region. We present an observation of the exponential growth regime, expected at early times, but not accessible in other driven fingering patterns induced by gravitational flows, spinning drops, or vertical thermal gradients. We have monitored the wavelength λ and the raising time τ of the unstable mode of undulation of the contact line; we find that λτ2 is independent of the ribbon thickness, in agreement with a linear stability analysis.