  The behavior of crosslinking polymer solutions as they transition from
liquid-like to solid-like material in flow determines success or failure in
several applications, from 3D printing to oil recovery in the earth's
subsurface to a wide variety of biological flows. Dilute polymer solutions flow
easily, while concentrated polymers or crosslinked polymer gels can clog pores,
nozzles, or channels. We have recently uncovered and described a third regime
of flow dynamics in polymers that occurs when crosslinking happens during flow:
intermittent flows. In a model system of alginate and calcium meeting at a
Y-shaped junction in a microfluidic channel, a persistent and regular pattern
of intermittent flow occurs when driven at a constant volume flow rate. At the
junction, calcium crosslinks alginate to form an alginate gel, which
subsequently deposits on the channel wall. As gel continues to deposit, it
obstructs the channel, causing the driving pressure to increase to maintain a
constant flow rate. At a critical pressure, corresponding to a critical shear
stress, the fluid pulls the gel from the wall, removing the gel from the device
and resulting in a clear channel. The gel deposit begins again, and the process
then repeats as long as flow continues. Chemical concentrations and flow rate
control both the frequency of ablation and the critical shear stress. In this
work, we provide an analytical framework to quantitatively describe the
intermittent behavior as a result of diffusively driven deposition in a high
Peclet number flow where convection dominates. Fitting the experimental data to
the model allows estimation of the deposition efficiency, or the fraction of
flowing material that sticks to the channel walls. By correlating the results
of the model with bulk rheology measurements, we find that deposition
efficiency increases with the stiffness of the gel formed in flow.
