Analysis and Simulations of Two-Phase Fluid on Patterned Surfaces

In this thesis, we investigate two-phase fluid on patterned surfaces. For two-dimensional case, we consider the fluid in a patterned channel or a patterned Y-shaped tube. From calculating the minimizer of the free energy, we observe stick-slip behavior of contact line and contact angle hysteresis. For the Y-shapedtube, relative wetting is determined through quasistatic analysis. For three-dimensional case, we study droplets spreading on the patterned surfaces with periodic squares separated by channels with different intrinsic contact angles. Stick-slip behavior and contact angle hysteresis are also obtained from numerical simulations based on the phase field model with the generalized Navier boundary condition. We find that the effective advancing and receding contact angles are linearly or piecewise linearly dependent on one of the two intrinsic angles withthe other fixed. By increasing the volume of droplet gradually, the contact linetends to be an equiangular octagon. Moreover the cubic root of volume of droplet at jump forms an arithmetic sequence and the contact angle jump tends to zero.