The Galactic bar plays a critical role in the evolution of the Milky Ways Central Molecular Zone (CMZ), as its potential drives mass inward toward the Galactic Center via gas flows known as dust lanes. To explore the interaction between the CMZ and the dust lanes, we run hydrodynamic simulations in Arepo, modeling the potential of the Milky Ways bar in the absence of gas self-gravity and star formation physics, and we study the flows of mass using Monte Carlo tracer particles. We estimate the efficiency of the inflow via the dust lanes, finding that only about a third (30 +/- 12%) of the dust lanes mass initially accretes onto the CMZ, while the rest overshoots and accretes later. Given observational estimates of the amount of gas within the Milky Ways dust lanes, this suggests that the true total inflow rate onto the CMZ is 0.8 +/- 0.6 Msun yr$^{-1}$. Clouds in this simulated CMZ have sudden peaks in their average density near apocenter, where they undergo violent collisions with inflowing material. While these clouds tend to counter-rotate due to shear, co-rotating clouds occasionally occur (~52% are strongly counter-rotating, and ~7% are strongly co-rotating of the 44 cloud sample), likely due to the injection of momentum from collisions with inflowing material. We investigate the formation and evolution of these clouds, finding that they are fed by many discrete inflow events, providing a consistent source of gas to CMZ clouds even as they collapse and form stars.
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