The discovery of paleo-meanders on Mars and debates about the occurrence of meandering on prevegetation early Earth have stimulated field studies of channel morphology and deposit stratigraphy in arid environments. They show that mud can provide the cohesive strength to retard outer bank erosion, enabling inner bank lateral accretion (including mud deposition) to keep pace and thus sustain meandering. The process by which mud is deposited in the lateral accretion deposits, however, is poorly known. Building on previous fieldwork in the muddy meandering Quinn River, we use Delft3D and the Partheniades-Krone model for cohesive sediment transport to predict erosion and deposition patterns in a 2,300 m long reach. While flocculation of mud increases the settling velocity and hence the likelihood of deposition, the standard metric for distinguishing washload from suspended load, (i.e. settling velocity to shear velocity ratio), does not indicate relative deposition rate. Mud deposition is driven by the product of settling velocity times basal concentration: w(s)c(b). Relatively low w(s) but high c(b) can induce deposition. We show that with sufficiently high basal concentrations, significant net lateral accretion deposition occurs in areas where elevated flocculation settling velocities are > 100 times lower than the local shear velocity. Observed grain size distributions of lateral accretion deposits are predicted. Just by introducing a period of elevated mud load with no change in discharge creates a distinct muddy interbed. Our model points to multiple ways lateral accretion deposits can vary sedimentologically, including creating mud-sand couplets, and lead to single thread, active meandering channels in muddy rivers.