  Recently, an effective {\it membrane theory} was proposed that describes the
``hydrodynamic'' regime of the entanglement dynamics for general chaotic
systems. Motivated by the new {\it bit threads} formulation of holographic
entanglement entropy, given in terms of a convex optimization problem based on
flow maximization, or equivalently tight packing of bit threads, we reformulate
the membrane theory as a max flow problem by proving a max flow-min cut
theorem. In the context of holography, we explain the relation between the max
flow program dual to the membrane theory and the max flow program dual to the
holographic surface extremization prescription by providing an explicit map
from the membrane to the bulk, and derive the former from the latter in the
``hydrodynamic'' regime without reference to minimal surfaces or membranes.
