Simultaneous reflectometry and interferometry for measuring thin-film thickness and curvature

Real-Time Reflectance Measurement Using an Astigmatic Optical Profilometer

An astigmatic optical profilometer with a commercial optical pickup head provides benefits, such as high resolution, compact size, and low cost. To eliminate artifacts caused by complex materials with different reflectances, a z-axis modulation mode is proposed to obtain quantitative surface morphology by measuring S curves on all image pixels. Moreover, the slope of the linear region in the S curve shows a positive relationship with the surface reflectance. However, the slope was calculated using an offline curve fitting method, which did not allow real-time reflectance imaging. Furthermore, quantitative reflectance data were unavailable because of the lack of calibration. In this study, we propose a novel method for real-time reflectance imaging by measuring the amplitude of a focus error signal (FES). The calibration results displayed a linear relationship between the FES amplitude and reflectance. The reflectance image of a grating sample with chrome patterns on a glass substrate demonstrates accurate reflectance measurements with a micrometer spatial resolution.

Interferometric Probing of Physical and Chemical Properties of Solutions: Noncontact Investigation of Liquids

Interferometry is a highly versatile tool for probing physical and chemical phenomena. In addition to the benefit of noncontact investigations, even spatially resolved information can be obtained by choosing a suitable setup. This review presents the evolution of the various setups that have evolved since the first interferometers were developed in the mid-nineteenth century and highlights the benefits, limitations, and typical areas of application. This review focuses on interferometry based on electromagnetic waves in the near-infrared and visible range applied to liquid samples, categorizes the chemical/physical properties (e.g., pressure, temperature, composition) and phenomena (e.g., evaporation, crystal growth, diffusion, thermophoresis) that can be assessed, and presents a comprehensive literature review of specific existing applications. Finally, it discusses some fundamental open questions with respect to geometric considerations and overlapping effects. Expected final online publication date for the Annual Review of Chemical and Biomolecular Engineering, Volume 13 is October 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Local Meniscus Curvature During Steady-State Evaporation from Micropillar Arrays

Micropillar arrays are an ideal model system for capillary-aided thin film evaporation that can be fabricated with precise geometric control using microfabrication methods. The capillary limit leading to dryout is a critical performance metric for capillary-aided thin film evaporation and is proportional to the product of the permeability and capillary pressure. Capillary flow models for steady-state thin-film evaporation typically employ capillary pressure and permeability as separate parameters; however, it is difficult to separate the two from experimental hemiwicking characterizations or dryout observations. Furthermore, for micropillar arrays, local permeability depends on meniscus curvature varying spatially and with the evaporation rate. In this work, we use thin-film interference microscopy to profile local meniscus curvature during steady-state evaporation of water in a pure vapor environment. Local capillary pressure is calculated from curvature without requiring knowledge of contact angle or permeability. Results are compared against a Darcian semianalytical model for flow through micropillar wicks incorporating local permeability due to meniscus curvature. Although traditionally a slip boundary condition has been assumed at the liquid-vapor interface, we find much better agreement using a no-slip condition. The consequence of no-slip behavior is larger pressure gradients for a given evaporation flux and a lower dryout heat flux relative to a full slip condition. Heat transfer coefficient data are also presented and discussed in terms of curvature and sample geometry.

A simple analytic model for predicting the wicking velocity in micropillar arrays

Hemiwicking is the phenomena where a liquid wets a textured surface beyond its intrinsic wetting length due to capillary action and imbibition. In this work, we derive a simple analytical model for hemiwicking in micropillar arrays. The model is based on the combined effects of capillary action dictated by interfacial and intermolecular pressures gradients within the curved liquid meniscus and fluid drag from the pillars at ultra-low Reynolds numbers \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{(}}{{\bf{10}}}^{{\boldsymbol{-}}{\bf{7}}}{\boldsymbol{\lesssim }}{\bf{Re}}{\boldsymbol{\lesssim }}{{\bf{10}}}^{{\boldsymbol{-}}{\bf{3}}}{\boldsymbol{)}}$$\end{document}(10−7≲Re≲10−3). Fluid drag is conceptualized via a critical Reynolds number: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bf{Re}}{\boldsymbol{=}}\frac{{{\bf{v}}}_{{\bf{0}}}{{\bf{x}}}_{{\bf{0}}}}{{\boldsymbol{\nu }}}$$\end{document}Re=v0x0ν, where v₀ corresponds to the maximum wetting speed on a flat, dry surface and x₀ is the extension length of the liquid meniscus that drives the bulk fluid toward the adsorbed thin-film region. The model is validated with wicking experiments on different hemiwicking surfaces in conjunction with v₀ and x₀ measurements using Water \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{(}}{{\bf{v}}}_{{\bf{0}}}{\boldsymbol{\approx }}{\bf{2}}\,{\bf{m}}{\boldsymbol{/}}{\bf{s}}{\boldsymbol{,}}\,{\bf{25}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{\lesssim }}{{\bf{x}}}_{{\bf{0}}}{\boldsymbol{\lesssim }}{\bf{28}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{)}}$$\end{document}(v0≈2m/s,25µm≲x0≲28µm), viscous FC-70 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{(}}{{\boldsymbol{v}}}_{{\bf{0}}}{\boldsymbol{\approx }}{\bf{0.3}}\,{\bf{m}}{\boldsymbol{/}}{\bf{s}}{\boldsymbol{,}}\,{\bf{18.6}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{\lesssim }}{{\boldsymbol{x}}}_{{\bf{0}}}{\boldsymbol{\lesssim }}{\bf{38.6}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{)}}$$\end{document}(v0≈0.3m/s,18.6µm≲x0≲38.6µm) and lower viscosity Ethanol \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{(}}{{\boldsymbol{v}}}_{{\bf{0}}}{\boldsymbol{\approx }}{\bf{1.2}}\,{\bf{m}}{\boldsymbol{/}}{\bf{s}}{\boldsymbol{,}}\,{\bf{11.8}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{\lesssim }}{{\bf{x}}}_{{\bf{0}}}{\boldsymbol{\lesssim }}{\bf{33.3}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{)}}$$\end{document}(v0≈1.2m/s,11.8µm≲x0≲33.3µm).