Early time instability in nanofilms exposed to a large transverse thermal gradient: Improved image and thermal analysis

Fiedler, Kevin; Troian, Sandra M.

doi:10.1063/1.4968575

Cited by 8 publications

(16 citation statements)

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“…In these systems, fluid elongations tend to grow without bound unless prematurely terminated by direct contact with an opposing substrate 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 development of regions of high interfacial curvature, are counterbalanced and then eventually dominated either by electrohydrodynamic or thermocapillary forces which rapidly undergo self-reinforcement, leading to fluid elongations with long range order.…”

Section: Introductionmentioning

confidence: 99%

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

Fiedler

McLeod

Troian

2019

Journal of Applied Physics

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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 ...

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Section: Introductionmentioning

confidence: 99%

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

Fiedler

McLeod

Troian

2019

Journal of Applied Physics

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“…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.…”

Section: Long Wavelength Model For Growth Of Protrusions By Runaway Tmentioning

confidence: 52%

“…All else equal, a larger difference in temperature ∆ leads to growing undulations of smaller wavelength. Recent [35,36,37] and ongoing experiments to confirm the mechanism leading to instability so far indicate good agreement with analytic predictions for the fastest growing wavelength and its growth rate.…”

Section: Virtual Singularitymentioning

confidence: 52%

“…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.…”

Section: Resultsmentioning

confidence: 99%

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

Zhou

Troian

2019

New J. Phys.

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Many physical systems give rise to dynamical behavior leading to cuspidal shapes which represent a singularity of the governing equation. The cusp tip often exhibits self-similarity as well, indicative of scaling symmetry invariant in time up to a change of scale. Cuspidal shapes even occur in liquid systems when the driving force for fluid elongation is sufficiently strong to overcome leveling by capillarity. In almost all cases reported in the literature, however, the moving interface is assumed to be shear-free and the operable forces orient exclusively in the direction normal to the advancing boundary. Here we focus on a system in which a slender liquid film is exposed to large thermocapillary stresses, a system previously shown to undergo a linear instability resembling microlens arrays. We demonstrate by analytic and numerical means how in the nonlinear regime runaway thermocapillary forces induce cuspidal formations terminated by a conical tip whose slope is given by an analytic relation. On a fundamental level, this finding broadens our understanding of known categories of flows that can generate cuspidal forms. More practically, the system examined here introduces a potentially novel lithographic method for one-step non-contact fabrication of cuspidal microarrays.

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“…So far, studies on thermocapillary patterning have been focused on the dynamic process of film flow and height evolution (Mukherjee & Sharma 2015; Fiedler & Troian 2016). In these studies, the fluid flow is usually approximated as one-dimensional flow and a tangential stress (i.e.…”

Section: Introductionmentioning

confidence: 99%

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

Yang

et al. 2021

J. Fluid Mech.

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Early time instability in nanofilms exposed to a large transverse thermal gradient: Improved image and thermal analysis

Abstract: A new quantitative image analysis method for improving breast cancer diagnosis using DCE-MRI examinations Med. Phys. 42, 103 (2015); 10.1118/1.4903280Investigating the solid-liquid phase transition of water nanofilms using the generalized replica exchange method

Cited by 8 publications

References 19 publications

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

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

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

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

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