In this paper, we have studied the droplet movements and continuous flows confined between two rough and hydrophobic surfaces. A recently proposed mean-field free-energy lattice Boltzmann model was employed. The movement of contact point over a well-patterned rough surface displays a periodic sticking-jumping-slipping behavior; while the dynamic contact angle changes accordingly from maximum to minimum values. These complex varying behaviors are totally different from those on flat surfaces and implies more carefulness is necessary in interpreting measured contact angles on rough surfaces. Two regimes were found of the droplet velocity changing with the surface roughness: first decreasing and then increasing; and qualitative analysis was given. We have also studied the continuous flow rates and two cases, with and without vapor trapped, were compared. Simulation results show the vapor trapped can indeed reduce the resistance to fluid motion from the channel surfaces, and such information could be useful for microfluidic applications.

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