  This paper derives and analyzes continuous time random walk (CTRW) models in
radial flow geometries for the quantification of non-local solute transport
induced by heterogeneous flow distributions and by mobile-immobile mass
transfer processes. To this end we derive a general CTRW framework in radial
coordinates starting from the random walk equations for radial particle
positions and times. The particle density, or solute concentration is governed
by a non-local radial advection-dispersion equation (ADE). Unlike in CTRWs for
uniform flow scenarios, particle transition times here depend on the radial
particle position, which renders the CTRW non-stationary. As a consequence, the
memory kernel characterizing the non-local ADE, is radially dependent. Based on
this general formulation, we derive radial CTRW implementations that (i)
emulate non-local radial transport due to heterogeneous advection, (ii) model
multirate mass transfer (MRMT) between mobile and immobile continua, and (iii)
quantify both heterogeneous advection in a mobile region and mass transfer
between mobile and immobile regions. The expected solute breakthrough behavior
is studied using numerical random walk particle tracking simulations. This
behavior is analyzed by explicit analytical expressions for the asymptotic
solute breakthrough curves. We observe clear power-law tails of the solute
breakthrough for broad (power-law) distributions of particle transit times
(heterogeneous advection) and particle trapping times (MRMT model). The
combined model displays two distinct time regimes. An intermediate regime, in
which the solute breakthrough is dominated by the particle transit times in the
mobile zones, and a late time regime that is governed by the distribution of
particle trapping times in immobile zones.
