عنوان مقاله [English]
Controlling surface properties, such as wetting, plays an important role in the
research and development of various industries. Even though wettability has
many applications in diverse technologies, such as painting, filtration, printing, porous media saturation, medicine, climate, soil, plant biology, and oil recovery enhancement, the effect of roughness pattern on contact angle and wetting needs more attention. In this study, application of the Cassie---Baxter equation for calculating the apparent contact angle of drops with different sizes on the rough surfaces is investigated. To do this, the free energy equation is analyzed on a rough and chemically homogeneous surface to study the Cassie-Baxter equation along with line tension and roughness. The contact angle calculated by using the surface fraction approximation of Cassie-Baxter for rough pattern surfaces has been compared with the values obtained from the developed numerical method. Moreover, the concept of length fraction proposed by Jaroslaw and Miller is discussed, and a numerical method is established to compute its value. To do this, spherical drops of different sizes are simulated on an artificial rough surface consisting of an array of cubic roughness. The line and surface fraction occupied by the drop are calculated and compared with the Cassie-Baxter approximation of surface fraction. Furthermore, the difference in advancing contact angle obtained by the numerical method and Cassie-Baxter model are compared. By using a developed numerical method, the length fraction and surface fraction can be computed for a wide range of drop sizes and roughness dimensions. The length fraction and surface fraction obtained in this work show oscillation behavior around the Cassie-Baxter approximation. When the drop radius tends to infinity, both values of surface and length fraction are equal to the Cassie-Baxter approximation. The results of this work help analyze predict the apparent contact angle value for a wide range of drop sizes on rough surfaces for wettability determination.