# American Institute of Mathematical Sciences

October  2016, 21(8): 2905-2926. doi: 10.3934/dcdsb.2016079

## A numerical study of three-dimensional droplets spreading on chemically patterned surfaces

 1 School of Mathematics and Statistics, Guangdong University of Finance and Economics, China 2 Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong, China 3 Computational Transport Phenomena Laboratory, King Abdullah University of Science and Technology, Saudi Arabia

Received  August 2015 Revised  March 2016 Published  September 2016

We study numerically the three-dimensional droplets spreading on physically flat chemically patterned surfaces with periodic squares separated by channels. Our model consists of the Navier-Stokes-Cahn-Hilliard equations with the generalized Navier boundary conditions. Stick-slip behavior and contact angle hysteresis are observed. Moreover, we also study the relationship between the effective advancing/receding angle and the two intrinsic angles of the surface patterns. By increasing the volume of droplet gradually, we find that the advancing contact line tends gradually to an equiangular octagon with the length ratio of the two adjacent sides equal to a fixed value that depends on the geometry of the pattern.
Citation: Hua Zhong, Xiao-Ping Wang, Shuyu Sun. A numerical study of three-dimensional droplets spreading on chemically patterned surfaces. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2905-2926. doi: 10.3934/dcdsb.2016079
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