Diffusion-driven deposition model suggests stiffer gels deposit more efficiently in microchannel flows

The behavior of cross-linking polymer solutions as they transition from liquid-like to solid-like material in flow determines success or failure in several applications. Dilute polymer solutions flow easily, while concentrated polymers or crosslinked polymer gels can clog pores, nozzles, or channels. We have recently described a third regime of flow dynamics in polymers that occurs when cross-linking happens during flow: persistent intermittency. When a dilute alginate solution meets calcium at a Y-shaped microfluidic junction, a persistent and regular pattern of gel deposition and ablation emerges when driven at a constant volumetric flow rate. Chemical concentrations and flow rate control both the gel deposition and critical shear stress required to ablate the adhered gel. In this work, we provide an analytical framework to quantitatively describe the intermittent behavior as resulting from diffusively driven deposition in a high Peclet number flow. Fitting the experimental data shows that higher component concentrations lead to more efficient deposition and more swollen gels. Increasing the flow rate increases the deposition rate, but the resulting gels are much less swollen. Ablation occurs when applied shear stresses overcome either the adhesive energy of the gel or its yield stress. The shear stress required at ablation decreases with increased component concentrations. By correlating the results of the analytical analysis with bulk rheology measurements, we find that deposition efficiency increases with the stiffness of the gel formed in flow. Softer gels withstand higher shear stresses before ablation. Both deposition efficiency and gel stiffness increase in flow conditions nearing complete clogging.