  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.
