Model of Advancing and Receding Contact Angles on Rough Surfaces

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.