Chemistry and Biochemistry
Mathematics and Natural Sciences
We demonstrate that Snell’s law of refraction can be applied to thermal fronts propagating through a boundary between regions that support distinct frontal velocities. We use the free-radical frontal polymerization of a triacrylate with clay filler that allows for two domains containing two different concentrations of a peroxide initiator to be molded together. Because the polymerization reaction rates depend on the initiator concentration, the propagation speed is different in each domain. We study fronts propagating in two parallel strips in which the incident angle is 90°. Our data fit Snell’s law vr/vi = sin θr/sin θi, where vr is the refracted velocity, vi is the incident velocity, θr is the angle of refraction, and θi is the incident angle. Further, we study circular fronts propagating radially from an initiation point in a high-velocity region into a low-velocity region (and vice versa). We demonstrate the close resemblance between the numerically simulated and experimentally observed thermal reaction fronts. By measuring the normal velocity and the angle of refraction of both simulated and experimental fronts, we establish that Snell’s law holds for thermal frontal polymerization in our experimental system. Finally we discuss the regimes in which Snell’s law may not be valid.
(2007). Snell's Law of Refraction Observed in Thermal Frontal Polymerization. Chaos, 17(3).
Available at: https://aquila.usm.edu/fac_pubs/9009