Spherically propagating frontal polymerization (FP) waves were observed for the first time in condensed media. After a brief period of ignition in a spherical domain by an external UV source, the front began to expand radially. Once the front attained a critical size, it became unstable, resulting in so-called 'spin modes'. These spin modes are manifested as slightly raised regions that travel on the surface of the expanding spherical front. The onset of these instabilities from a stable, uniformly propagating spherical front can be described by a linear stability analysis. The bifurcation parameter is the Zeldovich number which is related to the activation energy of the reaction. A basic solution was constructed which describes a spherically symmetric outward propagating front of radius R. An asymptotic analysis was then employed under the assumption that R is large. This corresponds to the case where the conditions of ignition do not affect front propagation. It was found to leading order that the front propagates at a constant velocity and corrections to velocity due to curvature have been determined. The linear stability analysis shows that for the Zeldovich number in a certain range, there exists a situation in which the sphere will be unstable but will recover its stability in time as it expands.

Frontal Polymerization (FP) is a process that converts monomers into polymers by means of a propagating spatially localized reaction front. In the simplest case, a mixture of monomers and initiator is placed into a test tube and upon initiation of the reaction at one end of the tube, a self-sustained wave develops and propagates through the tube. Monomer/initiator systems can suffer from a limited pot life, meaning that over a period of time the systems will spontaneously polymerize before they can be used. One way to avoid the undesirable spontaneous polymerization is by microencapsulating the initiator. A mathematical model of nonadiabatic FP waves with encapsulated initiator is presented.

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