## 2 Experimental Setup
According to the calculation [23], the protrusion height of the riblet \(h_{\rm p}\) = 0.17 s, which means the zero point's coordinate is 0.204 mm below the tip of the riblet. For the \(x\)-\(z\) plane, the origin's streamwise coordinate is also located 150 mm from the front edge of the recess, and the spanwise coordinate is located at the midpoint in the spanwise direction of the model. The experiment is divided into two steps: First, under clear water conditions, the flow field information on the surfaces of the smooth and riblet walls is recorded, respectively, to determine the parameters of the clear water flow field and verify the drag reduction effect of the riblet walls. Then, keeping other conditions unchanged, solid particles are dispersed to measure the two-phase flow field over the smooth and riblet walls, studying the role of the riblets in two-phase flow. The experiment uses polystyrene particles with a diameter \(D_{p}\) = 15 \(\upmu\)m as tracer particles in the liquid phase, and solid phase particles with a diameter \(D_{p}\) = 155 \(\upmu\)m are selected to explore the impact of particles smaller than the Kolmogorov scale on the riblet wall turbulent boundary layer. The density of the polystyrene particles is \(\rho_{p}\) = 1050 kg/m\({}^{3}\). Solid particles are pre-prepared into a mixture with a liquid-solid mass ratio of 1000:1 (water: solid particles), and are dispersed into the water channel from 1200 mm upstream of the flat plate, 300 mm below the water surface. The experiment is conducted after the flow stabilizes. According to calculations, the Strouhal number of all  
Figure 2: Schematic diagram of riblet plate: (**a**) the size of riblets; (**b**) top view of 30\({}^{\circ}\) divergent riblets. solid particles in this experiment is less than 0.4, allowing them to perfectly suspend in the flow field [37], and inter-particle interactions can be neglected [38]. The experimental data was collected using the PIV system from LaVision company in Gottingen, Germany. It mainly consists of a laser illumination system, an image acquisition system, and an image processing system. The image acquisition method is dual-frame dual-exposure, where the laser and camera are connected through a synchronizer to ensure the synchronicity of sampling. The image acquisition frequency is 90 Hz, and the time interval between two frames is set to meet the required displacement of 5-8 pixels for measurement. The observation area for a single camera is 100 mm \(\times\) 100 mm, with an interrogation window of 32 \(\times\) 32 pixels, and an overlap rate of 50%. For each condition, 8000 samples are collected to provide a sufficient number of samples for related calculations to ensure convergence. The captured images are processed using Gaussian filtering and median filtering to obtain images that contain only solid particles. Then, by subtracting the solid particle images from the original images, the required liquid phase flow field images are obtained. Finally, after processing with a cross-correlation algorithm, the uncertainty of the velocity vectors is ultimately detected to be less than 0.1 pixel, corresponding to an uncertainty of less than 1%.