  The modelling of electrokinetic flows is a critical aspect spanning many
industrial applications and research fields. This has introduced great demand
in flexible numerical solvers to describe these flows. The underlying phenomena
are microscopic, non-linear, and often involve multiple domains. Therefore
often model assumptions and several numerical approximations are introduced to
simplify the solution. In this work, we present a multi-domain multi-species
electrokinetic flow model including complex interface and bulk reactions. After
a dimensional analysis and an overview of some limiting regimes, we present a
set of general purpose finite-volume solvers, based on \of, capable of
describing an arbitrary number of electrochemical species over multiple
interacting (solid or fluid) domains \cite{spnpfoam}. We provide verification
of the computational approach for several cases involving electrokinetic flows,
reactions between species, and complex geometries. We first present three
one-dimensional verification test cases, and then show the capability of the
solver to tackle two- and three-dimensional electrically driven flows and ionic
transport in random porous structures. The purpose of this work is to lay the
foundation for a general-purpose open-source flexible modelling tool for
problems in electrochemistry and electrokinetics at different scales.
