The Significance of the Contact Angle in Relation to the Solid Surface

A modified Cassie–Baxter relationship to explain contact angle hysteresis and anisotropy on non-wetting textured surfaces

“…Note that / d remains an areal ratio, which can be simplified to the previously proposed [10,28] linear fractions only under certain limiting cases (see Supplementary material). The concept of the differential area parameter is especially useful when the TCL is located on the boundary between heterogeneous regions, a boundary for which neither linear fraction nor local areal fraction can be uniquely defined.…”

“…Furthermore, many of the studies in category (ii) did not actually compute the apparent contact angles because the linear fractions of the solid and air are extremely hard to predict due to the contorted nature of the TCL on heterogeneous surfaces. To overcome this limitation, certain studies have assumed the existence of an undistorted TCL [10,28,29], which strongly contradicts the fundamental assumption made by groups in category (i) above.…”

“…The different modifications can be broadly classified into two categories, based on the inherent assumptions used to correlate the details of the surface texture with the resulting apparent contact angles; (i) The observed apparent contact angles deviate from the predictions of the CB model due to distortion of the TCL [8,9,25,26]. (ii) The contact angles are determined by the linear fractions of solid and air calculated along the TCL, not by the overall areal fractions [5,7,10,[27][28][29]. However, most of these studies, with the noteworthy exception of the work of Extrand [10], did not quantitatively compare their predictions with experimental values, or reported only contact angles on prototypical textured geometries.…”

Superhydrophobicity and Contact-Line Issues

“…The works of Pease, 27 Bartell and Shepard, 28 and Extrand 29 also provide explanations of superhydrophobicity, in addition to the common Wenzel and Cassie theories. 7 Two of us recently contended 7 that interfacial area (the r in Equation 2 and f 1 and f 2 in Equation 3) does not affect the degree of hydrophobicity and that modeling contact angles onedimensionally, from the perspective of the contact line, better explains surface behavior.…”

Structure-induced spreading of liquid in micropillar arrays

“…For this reason there have been many efforts to link the local properties of a solid at the contact line with the macroscopic wetting behavior. It is generally accepted that the local structure near the contact line, rather than total structure, of the solid surface and its inherent wettability are related to measured contact angles (Marmur and Bittoun 2009;Pease 1945;Swain and Lipowsky 1998). To reflect this, / is often replaced by the so-called line fraction, l, which represents the solid properties along (in the immediate vicinity) the contact line and h 1 and h 2 are measured values, rather than the true Young contact angle.…”