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Mobulid rays (manta and devil rays) use a highly specialized filtering apparatus to separate plankton food particles from seawater. Recent studies have indicated that captive vortices form within the microscale pores of the filter, which enhance filtration efficiency through a novel mechanism referred to as ricochet separation. The high throughput and clog resistance of this filtration process have led to the development of several bioinspired engineered filtration systems. However, it is still unclear how changes to the filter morphology influence the surrounding flow patterns and filtration efficiency. We address this question by examining the flow fields around and filtering properties of mobulid filters with systematically varied morphologies, using a combination of computational fluid dynamics and experiments on physical models. While the pore size is the principal determinant of filtration efficiency in a sieve filter, we found that the captive vortices in a mobulid filter grow or shrink to fill the pore, and changes in the pore size have modest effects. By contrast, the filtration efficiency appears to be highly sensitive to the orientation of the filter lobes (microscale plate-like structures). These results provide a foundation for interpreting the morphological differences between species and also for generating optimized bioinspired designs.