Model of Advancing and Receding Contact Angles on Rough Surfaces

Abstract

Contact angle hysteresis is a basic phenomenon in many industrial applications, such as material surface engineering and enhanced oil recovery. The mechanism of continuous change of the contact angle during hysteresis is not well understood and described, and it is also important to predict advancing and receding angles by the Young contact angle and surface roughness. In this work, a contact angle hysteresis model is developed based on several metastable contact angle models. The fraction difference between gas and liquid prefilling the solid grooves is assumed to be variable, so is the fraction difference of gas and liquid displaced by the other phase. Besides these two newly introduced variables, the solid area fraction, the ratio of the real surface area to the projected surface area, and the Young contact angle together influence the advancing and receding angles. Energy input or work is the external cause of hysteresis. The new variables are the intrinsic cause of hysteresis, enabling the continuous change of the contact angle and ensuring a minimal surface energy during hysteresis. The advancing and receding angles are explicitly expressed in a function of the factors mentioned above. The results from this model are in good coincidence with experiments from the literature. Through comparison, it is found that the model in this paper can be reduced as the Wenzel model, Cassie−Baxter model, etc., under special conditions.

Fabrication of superhydrophobic transparent cyclic olefin copolymer (COC)‐SiO2 nanocomposite surfaces

“…11,[18][19][20][21][22][23] The contact angles on superhydrophobic surfaces and the effect of roughness are generally presented in two models by explaining different physical mechanisms. 3,[24][25][26][27][28][29][30][31][32] In Wenzel model, the water droplet penetrates roughness and fully wets the solid surface under it. 24 In Cassie-Baxter model, droplet sits on the air pockets that exist between the roughness and only wets the top area of the surface bulges.…”

“…Two main factors control the hydrophobicity of a surface: one is to reduce the surface free energy value of the surface and the other is to produce micro/nanoscale roughness on the top of the surface 11,18–23 . The contact angles on superhydrophobic surfaces and the effect of roughness are generally presented in two models by explaining different physical mechanisms 3,24–32 . In Wenzel model, the water droplet penetrates roughness and fully wets the solid surface under it 24 .…”

Numerical Calculation of Apparent Contact Angles on the Hierarchical Surface with Array Microstructures by Wire Electrical Discharge Machining

“…Pakkanen and Hirvi 28 studied the hydrophobicity of PE and PVC polymer surfaces by molecular dynamics simulation, where the contact angles on columnar structures with different spacing and heights are predicted. Lin et al 29 proposed a contact angle hysteresis model to obtain the relationship between receding and advancing angles. Nosonovsky et al 30 researched the wettability of rough surfaces with multiscale structures considering disjoining pressure and liquid thin film at the interface, in which effective roughness factor R eff was introduced.…”

How Surfactants Affect Droplet Wetting on Hydrophobic Microstructures

“…49,50 We also do not predict W contact angles using the current theory because previous studies have shown the need to incorporate extensive pinning for W drops, whose pinning effects are often estimated with various phenomenological models empirically fitting the data. 48,51 In essence, eq 1 quantitatively predicts the variation of the cosine of the CB contact angle from that of pure water wetting on the microstructures due to the surfactant adsorption on the sl and lv interfaces. One intriguing future direction is to investigate the change of CB contact angle with an active control using electrowetting, 52,53 by varying the sl interfacial tension while keeping γ lv constant.…”

“…Here, we quantify the influence of surfactant adsorption on the sl and lv interfaces using a rigorous thermodynamic theory. In this theoretical model, we do not include any contributions from pinning, because a predictive theory for pinning in the CB state on a microtextured surface is to our knowledge unavailable, unlike for nanorough surfaces with low defect density. , We also do not predict W contact angles using the current theory because previous studies have shown the need to incorporate extensive pinning for W drops, whose pinning effects are often estimated with various phenomenological models empirically fitting the data. , …”