Schlumberger was interested in investigating a process for manufacturing small, hollow gel-sleeves (see fig. 1). Through this process, gel "sleeves" are made by injecting a solution containing one of the reactancts (say reactant A) into the center of a flowing solution containing another reactant (say reactant B). The resulting flow environment is a coaxial flow, where an annular flow encloses an axisymmetric flow (see fig. 2). The diffusion of reactants across the interface allows a gelation reaction to take place, resulting in an evolving gel-layer between the co-flowing fluids.
We modelled this system to better understand how the apparatus set-up controls the final properties of the gel-sleeves. By considering a number of interesting limits we were able to obtain good, leading-order predictions for some useful properties of the gel (e.g. the gel-sleeve diameter, and the rate of gel-mass increase along the axis of flow).