  The flow network model is an established approach to approximate
pressure-flow relationships in a bifurcating network, and has been widely used
in many contexts. Existing models typically assume unidirectional flow and
exploit Poiseuille's law, and thus neglect the impact of bifurcation geometry
and finite-sized objects on the flow. We determine the impact of bifurcation
geometry and objects by computing Stokes flows in a two-dimensional (2D)
bifurcation using the LARS (Lightning-AAA Rational Stokes) algorithm, a novel
mesh-free algorithm for solving 2D Stokes flow problems utilising an applied
complex analysis approach based on rational approximation of the Goursat
functions. We compute the flow conductances of bifurcations with different
channel widths, bifurcation angles, curved boundary geometries, and fixed
circular objects. We quantify the difference between the computed conductances
and their Poiseuille's law approximations to demonstrate the importance of
incorporating detailed bifurcation geometry into existing flow network models.
We parameterise the flow conductances of 2D bifurcation as functions of the
dimensionless parameters of bifurcation geometry and a fixed object using a
machine learning approach, which is simple to use and provides more accurate
approximations than Poiseuille's law. Finally, the details of the 2D Stokes
flows in bifurcations are presented.
