Differential colorimetry measurements of fluctuation growth in nanofilms exposed to large surface thermal gradients

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. I. BACKGROUNDExperiments designed to elicit the physical mechanisms generating linear instabilities in macroscale fluid systems normally rely on early time measurements of an emergent length or time scale signalling the growth of the most unstable wavelength. This is common to measurements in many large scale systems which manifest stationary periodic, oscillatory uniform or oscillatory periodic phenomena. At the macroscale, such measurements can often be obtained by direct visualization. With growing interest in small scale fluidic phenomena, similar measurements pose more challenges -not only do films easily rupture or are otherwise compromised by defects but measurements must often rely on indirect techniques from which key parameter value are inferred. At microscale or nanoscale dimensions, matching system size and materials properties to the appropriate measurement technique often severely restricts the options available. For films whose thickness is of the order of tens of microns or more, laser or white light interferometry, sometimes coupled with shadowgraphy, is often the tool of choice [1][2][3].For more than a decade now, there has been interest in identifying the source of various runaway instabilities in even thinner films, which undergo spontaneous transition from an initially flat and uniform layer to microarrays containing nanoprotusions. In these systems, fluid elongations tend to grow without bound unless prematurely terminated by direct contact with an opposing substrate * Current address: or by fluid depletion effects. Early time measurements of the fastest growing wavelength in polymeric nanofilms subject either to large surface electric field gradients [4][5][6][7] or large surface thermal gradients [8][9][10][11] have yielded a characteristic in-plane separation distance of the order of tens of microns. Current understanding of these systems is that capillary forces, which suppress ...

Self-similar cuspidal formation by runaway thermocapillary forces in thin liquid films

“…All else equal, a larger difference in temperature ΔT causes undulations of smaller wavelength. Recent [36][37][38] and ongoing experiments to confirm the mechanism leading to instability so far indicate good agreement with predictions for the fastest growing mode and its growth rate. In what follows, λ max is selected as the characteristic lateral scale L used to non-dimensionalize lateral scales in the governing equation of motion.…”

“…We have previously shown [30,[36][37][38] that the evolution process leading to rounded lenslet microarrays can be terminated on demand and the liquid shapes affixed in place by dropping the temperature of both substrates below the solidification point. Rapid solidification of these liquid structures is made possible by two advantageous features: the large surface to volume ratios intrinsic to microscale or nanoscale films which facilitates rapid cooling, and digital control over the temperature of the confining substrates.…”

Mathematical modelling of thermocapillary patterning in thin liquid film: an equilibrium study

“…The thermophysical properties used are: the reference surface tension γ 0 = 31.53 mN m −1 , thermocapillary coefficient α = 88.5 μN (°C) −1 , thermal conductivity k a = 0.036 W (m °C) −1 and k p = 0.13 W (m °C) −1 (Mark 2009; Fiedler et al. 2019). The structure height of the template was not measured in the experiments, and we assume it equals the film thickness d = h 0 .…”

“…Integrating twice, one obtains the horizontal velocity u (Nazaripoor et al. 2018; Fiedler, McLeod & Troian 2019), that is, the velocity profile in the y -direction is described by a parabolic function. For the film flow, conservation of mass requires that …”

“…Integrating twice, one obtains the horizontal velocity u (Nazaripoor et al 2018;Fiedler, McLeod & Troian 2019),…”