Integrating flowing cells, such as immune cells or circulating tumour cells, within a microphysiological system is crucial for body-on-a-chip applications. However, ensuring unimpeded recirculation of cells is a significant challenge. Closed microfluidic devices have a no-slip boundary condition along channel walls and a defined chip geometry (laminar flow) that hinders the ability to freely control cell flow. Open microfluidic devices, where the bottom device boundary is an air-liquid interface (ALI), e.g., hanging drop networks (HDNs), offer the advantage of an easily-actuatable fluid-phase geometry, where cells can either flow or stagnate. In this paper, we optimized a hanging-drop-integrated pneumatic-pump system for closed-loop recirculation of particles (i.e., beads or cells). Experiments with both beads and cells in cell culture medium initially resulted in particle stagnation, which was suggestive of a pseudo-no-slip boundary condition at the ALI. Transmission electron microscopy and dynamic light scattering measurements of the ALI suggested that aggregation of submicron-scale cell-culture-medium components is the cause of the pseudo-no-slip boundary condition. We used the finite element method to study the forces on particles at the ALI and to optimize HDN design (drop aperture) and operation (drop height) parameters. Based on this analysis, we report a phase diagram delineating the conditions for free flow or stagnation of particles at the ALI of hanging drops. Using our experimental setup with 3.5 mm drop apertures, we conducted particle flow experiments while actuating drop heights. We confirmed the ability to control the flow or stagnation of particles by actuating the height of hanging drops: a drop height over 300 μm led to particle stagnation and a drop height under 300 μm allowed for particle flow. This particle-flow control, combined with the ease of integrating scaffold-free organ models (microtissues or organoids) in HDNs, constitutes the basis for an experimental setup enabling the control of the residence time of single cells around 3D organ models.