(155c) An Analytical Model Describing Diffusion-Controlled Deposition and Ablation for Polymers Crosslinking in Situ in Microscale Flows

When polymers crosslink in flow through small channels, the resulting polymer gel can deposit on the channel walls, thus occluding the flow. At constant flow rate, this occlusion leads to an increase in the local velocity and viscous shear stress in the region of the deposited gel. If the deposit grows sufficiently large, the increase in shear stress can remove the gel. In this talk, we explore an experimentally measured phenomenon by applying an analytical transport model describing convection and diffusion. The experimental system involves alginate, a biopolymer, becoming crosslinked by calcium ions as two fluid streams meet at a Y-junction in a microfluidic channel. Flow is driven at constant flow rate, and the resulting pressure drop is measured. The analytical model assumes the crosslinking reaction time-scale is much faster than either timescale governing the convection or diffusion of the crosslinked gel. Further, the model assumes that deposition occurs in a diffusive boundary layer near the channel wall. With these assumptions for flow in a cylindrical channel, the model predicts pressure drop as a function of time as the deposited gel occludes the channel. Interestingly, when the analytical model is applied to the measurements, the assumption that the gelation reaction time is very fast seems to be a reasonable assumption. Further, in comparing the results of the model to the experiments, we find that we can estimate both the deposition efficiency of the gel and obtain order-of-magnitude estimates of its adhesion strength. Alginate is a very common biopolymer, used often in 3D printing systems and other common biomedical applications. As such, by improving the understanding of alginate flows in small channels, our results may have wide ranging implications for optimizing bioprinting inks and processes.