Thermodynamic Phase Transitions and Creeping Flows in Cavities

We discuss the analogy between the stream line function of creeping flows in rectangular cavities and the thermodynamic potential at critical points and at phase transitions. Assuming no-slip boundary conditions, the corners of the rectangular cavity are stationary (fixed) points. We analyze two such points: 1. Corner where one wall is moving and the other is stationary; 2. Corner where both walls are stationary. The first one is analogous to a to a first-order transition (discontinuity) point while the second one is analogous to a thermodynamic critical point (second-order transition). Moffatt eddies, which impede mixing [P. S. Fodor, M. Kaufman, Proceedings of PPS-30, AIP Conf. Proc. 1664 (2015)], are present in the neighborhood of the second stationary point. The results discussed here are based on numerical solutions of the Navier-Stokes equations combined with analytical work valid in the vicinity of the stationary points.