Compare numerical modeling and improved understanding of dynamic sessile drop contact angle analysis in Liquid-Solid-Gas system

Abstract

Dynamic contact angle measurement; as a standard method for surface wettability analysis, is usually conducted through the analysis of sessile drops formed following the low rate injection of fluid from beneath through a drilled hole via an injection needle. However, understanding/characterizing the changes of drop contact angle from the point where the flat solid surface begins is not well discussed yet. Moreover, during the evaluation of size-dependent behavior of contact angle of millimeter-scale drops, the effect of the drilled hole is ignored. In this regard, in the current study, the experimental and thermodynamic characterizations of the sessile drop advancing contact angle measurements for a liquid-solid-air system are presented. To do this, a set of dynamic contact angle experiments for a water-calcite-air system with different devised hole diameters and roughness is conducted, and Gibbs free energy analysis is then utilized to propose a modeling scheme. Experimental results revealed a transient region from zero infinite contact angle at the hole to infinite contact angle of the solid surface, which was equal to 74.61° and 69.05° for nanoscale, and microscale surface roughness. In addition, it was shown that with a decrease in the hole diameter, the transient region met a lower value of contact angle at different dimensionless volumes. The result of higher advancing contact angle measured for the system with smaller drilled hole diameter was attributed to higher contact-line velocity. However, the assumption of low rate advancing contact angle was not violated for the hole diameter larger than 1.4 mm. Numerical studies demonstrated that in the case of zero line tension, two straight lines with positive slop could be fitted to the data; attributed to drilled hole effect. Besides, it was concluded that this behavior should not be interpreted as a negative line tension effect. The obtained values of line tension and equilibrium advancing contact angle, as matching parameters, were in agreement with those reported in the previous studies. Results of this work could help for better analyzing the size-dependent behavior of millimeter-scale drop through a suggested size-dependent model.