2021/11/21 by Rodrigo P. P. Almeida, Rodrigo Almeida, Almeida, Rodrigo +2 · 1 citation
Chemical Engineering · Computer Science · Engineering · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Biological Physics (physics.bio-ph) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Lattice Boltzmann Simulation Studies #Rheology and Fluid Dynamics Studies #physics.bio-ph #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.2111.15350
6 pages, 5 figures
arxiv created 2021/11/21 · openalex publication_date 2021/11/21 · arxiv updated 2021/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive a class of equations describing low Reynolds number steady flows of incompressible and viscous fluids in networks made of straight channels, with several sources and sinks, and adaptive conductivities. The flow is controlled by the fluxes at sources and sinks. The network is represented by a graph and the adaptive conductivities describe the transverse channel elasticities, mirroring several network structures found in physics and biology. Minimising the dissipated energy per unit time, we have found an explicit form for the adaptation equations and, asymptotically in time, a steady state tree geometry for the graph connecting sources and sinks is reached. A phase transition tuned by an order parameter for the adapted steady sate graph has been found.