Platooning of connected and autonomous vehicles (CAVs) has a significant potential for throughput improvement. However, the interaction between CAVs and non-CAVs may limit the practically attainable improvement due to platooning. To better understand and address this limitation, we introduce a new fluid model of mixed-autonomy traffic flow and use this model to analyze and design platoon coordination strategies. We propose a tandem-link fluid model that considers randomly arriving platoons sharing highway capacity with non-CAVs. We derive verifiable conditions for stability of the fluid model by analyzing an underlying M/D/1 queuing process and establishing a Foster-Lyapunov drift condition for the fluid model. These stability conditions enable a quantitative analysis of highway throughput under various scenarios. The model is useful for designing platoon coordination strategies that maximize throughput and minimize delay. Such coordination strategies are provably optimal in the fluid model and are practically relevant. We also validate our results using standard macroscopic (cell transmission model) and microscopic (simulation for urban mobility) simulation models.