Drag reduction by superhydrophobic surfaces has become a research focus in recent years. However, in some cases, the use of superhydrophobic surfaces has led to increased drag. Whether superhydrophobic surfaces on macroscopic objects reduce drag needs further research. The surface adhesion force is a metric to judge the drag reduction effect of superhydrophobic surfaces. The lattice Boltzmann method (LBM) is an efficient numerical method with the advantages of simple algorithm formulation, natural parallelism, and simple boundary treatment. Based on the LBM, we propose a new boundary condition with switchable adhesive force to specify the adhesion-regulated superhydrophobic surfaces. The proposed method is validated by the numerical simulation of the Couette flow with superhydrophobic coatings. Numerical results show good agreements with the theoretical analysis and the experimental results. Then the method is adopted for the simulation of the flow around a square cylinder with superhydrophobic coatings. The influence of the Reynolds number and the surface adhesive force on drag reduction is deeply studied.


Drag reduction is an important topic in marine engineering. Inspired by nature, more and more attentions are paid to the drag reduction effect of superhydrophobic surfaces (Samaha et al., 2012). Researchers (Voronov et al., 2008) found that the drag reduction effect is owing to the presence of velocity slip on the superhydrophobic surfaces. The phenomenon of velocity slip has been confirmed by both experiments and simulations (Rothstein, 2010). However, some researches show that the use of superhydrophobic surfaces is not always beneficial to the drag reduction and even leads to increased drag. Min et al. (2004) used a slip boundary condition to represent the hydrophobic surfaces and found that the drag is increased when the slip boundary condition is applied in the spanwise direction. Steinberger et al. (2007) found that the superhydrophobic surfaces will turn from slippery to sticky and promote high friction if the liquid-gas menisci is not controlled reasonably and effectively. Su et al. (2009) declared that a superhydrophobic ball may fall more slowly under water than the normal one because the micro-bubbles may enhance the friction drag. Cheng et al. (2015) fabricated three types of superhydrophobic surfaces and one of them caused a drag-increasing effect of 13.6% because of the transition from the Cassie state to the Wenzel state. Debates continue on whether superhydrophobic surfaces on macroscopic objects can reduce drag.

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