Modeling gel fiber formation in an emerging coaxial flow from a nozzle

It is important to understand the operational aspects which affect the continuous fabrication of alginate gel fibers, here the cross-linking reaction with an alginate precursor that is injected into a coaxial annular pipe flow of a calcium chloride solution. It is also an interesting example of an emerging solid interface that interacts with the flow in its neighbourhood. We advance on earlier works [Example, Bonhomme, Leng & Colin (2012), Soft Matter, 8, 10641], by relaxing assumptions of a fixed spatial domain to explore and observe mechanisms controlling gel radius. We use two different models. The first one represents the gel layer as a capillary interface between two immiscible liquids and captures the effect of surface tension. A second model is introduced to treat the cross-linking chemical reaction and its effect on the viscosity as the alginate gel forms. Through numerical simulations and analytical approximations of the downstream behavior, we determine the shape of the fiber in the pipe flow and its impact on the flow velocity as well as on the total production of gel.