Emergent Flows, Irreversibility and Unsteady Effects in Asymmetric and Looped Geometries

Abstract

Fluid transport networks are important in many natural settings and engineering applications, from animal cardiovascular and respiratory systems to plant vasculature to plumbing networks and chemical plants. Understanding how network topology, connectivity, internal boundaries and other geometrical aspects affect the global flow state is a challenging problem that depends on complex fluid properties characterized by different length and time scales. The study of flow in micro-scale networks focuses on low Reynolds numbers where small volumes of fluids move at slow speeds. The flow physics at these scales is governed by the Stokes equation, which is linear. This linearity property allows for relatively simple theoretical and computational solutions that greatly aid in the understanding, modeling and designing of micro-scale networks. At larger scales and faster flow rates, macrofluidic networks are also important but the flow physics is quite different. The underlying Navier-Stokes equation is nonlinear, theoretical results are few, simulations are challenging, and the mapping between geometry and desired flow objectives are all much more complex. The phenomenology for such high-Reynolds-number or inertially-dominated flows is well documented and well-studied: Flows are retarded in thin boundary layers near solid surfaces; such flows are sensitive to geometry and tend to separate from surfaces; and vortices, wakes, jets and unsteadiness abound. The counter-intuitive nature of inertial flows is exemplified by the breakdown of reversibility. This dissertation explores two general ways of how rectified flows emerge in macrofluidic networks as a consequence of irreversibility and unsteady effects: When branches or channels of a network have asymmetric internal geometry and the second when a network contains loops.