On the analysis of the contact angle for impacting droplets using a polynomial fitting approach

Miguel A Quetzeri-Santiago,Alfonso A Castrejón-Pita,J Rafael Castrejón-Pita

doi:10.1007/s00348-020-02971-1

Miguel A Quetzeri-Santiago, Alfonso A Castrejón-Pita + Show 1 more

Open Access

https://doi.org/10.1007/s00348-020-02971-1

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Abstract

Practical considerations on the measurement of the dynamic contact angle and the spreading diameter of impacting droplets are discussed in this paper.The contact angle of a liquid is commonly obtained either by a polynomial or a linear fitting to the droplet profile around the triple-phase point. Previous works have focused on quasi-static or sessile droplets, or in cases where inertia does not play a major role on the contact angle dynamics.Here, we study the effect of droplet shape, the order of the fitting polynomial and the fitting domain, on the measurement of the contact angle on various stages following droplet impact where the contact line is moving. Our results, presented in terms of the optical resolution and the droplet size, show that a quadratic fitting provides the most consistent results for a range of various droplet shapes. As expected, our results show that contact angle values are less sensitive to the fitting conditions for the cases where the droplet can be approximated to a spherical cap.Our experimental conditions include impact events with liquid droplets of different sizes and viscosities on various substrates. In addition, validating past works, our results show that the maximum spreading diameter can be parameterised by the Weber number and the rapidly advancing contact angle.Graphic abstract

Highlights

Quantifying the wettability of a liquid on a solid substrate is critically important for situations where either liquid adhesion or repellence is required
How much a liquid wets a solid is known to depend on the properties of both, the liquid and the solid substrate, and is commonly studied through the measurement of the contact angle. This contact angle is defined as the geometric angle between the tangent of the droplet surface and the tangent to the solid surface at the triple point, i.e. the angle formed by the intersection of the liquid–solid and the liquid–vapour interfaces (Joanny and De Gennes 1984; Eral and Oh 2013)
A solid, a liquid droplet and the surrounding gas are all in contact, creating three relevant surface effects, i.e. the solid–liquid sl, solid–gas sv and liquid–gas lv forces

Summary

Introduction

Quantifying the wettability of a liquid on a solid substrate is critically important for situations where either liquid adhesion or repellence is required. Industrial processes such as coating (Yarin 2006) and the spraying of pesticides (Bergeron et al 2000) are examples where maximising the liquid adherence to a solid is desired. Repellence is sought in the design of materials with anti-icing properties (Liu et al 2017) or impermeable clothing Repellence is sought in the design of materials with anti-icing properties (Liu et al 2017) or impermeable clothing (Zhang et al. Vol.:(0123456789) 143 Page 2 of 13

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