Among these, riblet surfaces have received sustained attention in fluid mechanics due to their ease of fabrication, cost-effectiveness, and notable drag-reduction performance. Early research primarily focused on streamwise riblet arrangements, with subsequent studies optimizing riblet shape and size to maximize drag reduction [23]. Serrated riblets, in particular, have demonstrated favorable overall performances, achieving drag reduction rates of up to 10% by tuning geometric parameters [23; 24; 25; 26]. With advances in biomimetic design, researchers have drawn inspiration from biological surfaces--such as shark skin sensory organs and the feathers of flying birds [27; 28]--to explore novel riblet arrangements. This has led to investigations of convergent and divergent riblet configurations and their impact on turbulent boundary layers. In contrast to streamwise riblets, which primarily affect the near-wall region, convergent-divergent riblets influence the entire boundary layer [29; 30]. [PERSON] et al. [31; 32; 33] showed that the convergent and divergent regions exhibit distinct flow responses due to differences in local secondary flows. In the divergent region, a downward motion replenishes the high mass flux along the riblets. Simultaneously, transverse flow near the riblet tips induces spiral motion within the riblet grooves, which interacts with the crossflow boundary layer and plays a key role in suppressing transverse secondary flows. However, [PERSON] et al. [34] reported that although such riblet structures can effectively reduce skin friction, they may increase the form drag in the divergent region--a result of spanwise modulation caused by large-scale secondary motions. Overall, most studies agree that the dominant control mechanism of convergent--divergent riblets lies in their ability to generate secondary flows that modulate turbulence in the spanwise direction, leading to differentiated turbulent states across the boundary layer. In recent years, the control of boundary layers using convergent and divergent riblet surfaces has attracted significant attention due to the secondary flows induced by these geometries, which play a critical role in the evolution of turbulent structures. [PERSON] et al. [35] investigated the control effects of convergent and divergent riblet walls on liquid-solid two-phase turbulent boundary layers using particle image velocimetry. They found that these riblets suppress the development of near-wall coherent structures such as hairpin vortices and reduce Reynolds shear stress, with particle addition further enhancing this suppression. However, their study did not address the dynamics of ejection and sweep events--critical components in the self-sustaining turbulence mechanism. To better approximate realistic flow conditions and expand upon previous findings, the present study introduces convergent and divergent riblet surfaces into liquid-solid two-phase turbulent boundary layers. In such environments, suspended particles introduce additional complexity. Prior research has demonstrated that particle-induced modulation of turbulence is closely related to a critical particle size--often associated with the Kolmogorov scale--below which particles can effectively attenuate turbulence intensity [36]. This interaction is particularly relevant in two-phase flow regimes and must be accounted for when analyzing near-wall turbulence structures. To this end, proper orthogonal decomposition (POD) and two-point correlation functions are employed to examine modifications to near-wall streaks under different wall configurations. Furthermore, an improved quadrant splitting method is utilized to investigate the topology of burst events and the distribution of Reynolds shear stress. By jointly examining these coherent structures, this study aims to elucidate the influence of convergent and divergent riblet surfaces on the self-sustaining turbulence cycle and to provide physical insights into drag modification mechanisms in turbulent liquid-solid two-phase boundary layers.