Differential Colorimetry Measurements of Fluctuation Growth in Nanofilms Exposed to Large Surface Thermal Gradients

TL;DR

This study uses differential colorimetry to measure early out-of-plane growth of nanofilm protrusions caused by thermocapillary instabilities, confirming the linear instability model with quantitative growth rate agreement.

Contribution

It provides the first quantitative validation of the thermocapillary model for nanofilm protrusion growth using differential colorimetry measurements.

Findings

Exponential growth of protrusions confirmed.

Good agreement between measured growth rates and the thermocapillary model.

Material parameters fitted with a single constant.

Abstract

Slender liquid nanofilms exposed to large surface thermal gradients are known to undergo thickness fluctuations which rapidly self-organize into arrays of nanoprotrusions with a separation distance of tens of microns. We previously reported good agreement between measurements of the characteristic spacing and the wavelength of the most unstable mode predicted by a linear stability analysis based on a long wavelength thermocapillary model. Here we focus on differential colorimetry measurements to quantify early time out-of-plane growth of protrusions for peak heights spanning 20 to 200 nm. Analysis of peak heights based on shape reconstruction reveals robust exponential growth. Good quantitative agreement of the growth rates with the thermocapillary model is obtained using a single fit constant to account for material parameters of nanofilms that could not be measured directly. These findings lend further support to the conjecture that the array protrusions uncovered almost two decades ago stem from a linear instability whose growth rate is controlled by thermocapillary forces counterbalanced by capillary forces.