Dependency of Contact Angles on Three-Phase Contact Line: A Review

The wetted area of a sessile droplet on a practical substrate is limited by the three-phase contact line and characterized by contact angle, contact radius and drop height. Although, contact angles of droplets have been studied for more than two hundred years, there are still some unanswered questions. In the last two decades, it was experimentally proven that the advancing and receding contact angles, and the contact angle hysteresis of rough and chemically heterogeneous surfaces, are determined by interactions of the liquid and the solid at the three-phase contact line alone, and the interfacial area within the contact perimeter is irrelevant. However, confusion and misunderstanding still exist in this field regarding the relationship between contact angle and surface roughness and chemical heterogeneity. An extensive review was published on the debate for the dependence of apparent contact angles on drop contact area or the three-phase contact line in 2014. Following this old review, several new articles were published on the same subject. This article presents a review of the novel articles (mostly published after 2014 to present) on the dependency of contact angles on the three-phase contact line, after a short summary is given for this long-lasting debate. Recently, some improvements have been made; for example, a relationship of the apparent contact angle with the properties of the three-phase line was obtained by replacing the solid–vapor interfacial tension term, γSV, with a string tension term containing the edge energy, γSLV, and curvature of the triple contact line, km, terms. In addition, a novel Gibbsian thermodynamics composite system was developed for a liquid drop resting on a heterogeneous multiphase and also on a homogeneous rough solid substrate at equilibrium conditions, and this approach led to the same conclusions given above. Moreover, some publications on the line energy concept along the three-phase contact line, and on the “modified” Cassie equations were also examined in this review.