Aperture total internal reflection (A-TIR) for contact angle measurement

Abstract

Recently, aperture total internal reflection (A-TIR) was proposed to characterize the microdroplet patterns, such as the coverage fraction of the droplet, by placing the aperture just in front of the detector in classical total internal reflection (TIR). However, the reflection from the curved liquid-air interface was simulated using simple two-dimensional modeling, causing inaccuracy in A-TIR measurement. In addition, the reflectance dependency on the aperture size and the working distance of the aperture was not investigated, hindering its applications. In this study, the simulation based on three-dimensional (3-D) ray tracing with Fresnel equation modeling was successfully developed and verified to explain the internal reflection from the curved droplet liquid-air interface. With this developed 3-D modeling, A-TIR characteristics were explored using the parameters of the aperture size and the working distance of the aperture as well as the droplet surface coverage fraction, which shows a good agreement between the experiment and the simulation. Furthermore, it was for the first time demonstrated that the droplet contact angle can be effectively determined by obtaining the droplet thickness from the analytic quadratic solution by subtracting the measured reflectance at the two different sized apertures and using the spherical profile relation. Low contact angles in the range of 1∼ 15° were determined experimentally for the micro- and macro-sized droplets with a droplet diameter of 70 ∼ 7000 µm by the measured thickness of 1 ∼ 450 µm using A-TIR and compared with Fizeau interferometry and side-view imaging to show a good agreement. The simulation shows that A-TIR can be a new optical diagnostic tool to measure the contact angles 0 ∼ 90° regardless of the droplet diameter by adjusting the aperture size and the working distance. In addition, A-TIR can effectively determine the small contact angles less than 5°, even ultrasmall contact angles less than 1° for the submicron thickness, not requiring the complicated microscope setup. Thus, we can observe a sessile droplet's drastic contact angle change during wetting phenomena from 90° to 0° on the same A-TIR setup. Additionally, A-TIR can be used for a single or an array of micro or nanodroplets with a microscope objective by reducing the laser beam size and scanning methodology.