Recent experiments have shown that polymer crystallisation can be used to “move” and organize nanoparticles. As a first effort at modelling this situation we consider the classical Stefan problem modified for a polymer melt but driven by a heat sink.
Microswimmers interacting with passive particles in confinement is common in many systems, e.g., spermatozoa cells encountering other cells or debris in female reproductive tract or active particles interacting with polymers...
It has been proposed that the nonisothermal directional crystallization of a polymer driven by a moving sink has an exact analogy to an equivalent isothermal crystallization protocol. We show that this is substantially true because polymers are poor thermal conductors; thus, polymer crystallization occurs over a relatively narrow spatial regime, while the thermal gradients created by this freezing occur over a much broader scale. This separation of scales allows us to replace the crystallization process, which is spatially distributed, with an equivalent step. The temperature at this step, which corresponds to the desired equivalent isothermal crystallization temperature, scales linearly with sink velocity. However, a few metrics, such as the Avrami exponent characterizing the kinetics of crystallization are very different in the two cases. These findings provide new insights into the physics of these spatially varying crystallization protocols and should inspire new experiments to probe the underlying equivalences more deeply.
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