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Recent experimental observations have demonstrated interesting instabilityphenomenon during thermal drawing of microstructured glass/polymer fibers, andthese observations motivate us to examine surface-tension-driven instabilitiesin concentric cylindrical shells of viscous fluids. In this paper, we focus ona single instability mechanism: classical capillary instabilities in the formof radial fluctuations, solving the full Navier--Stokes equations numerically.In equal-viscosity cases where an analytical linear theory is available, wecompare to the full numerical solution and delineate the regime in which thelinear theory is valid. We also consider unequal-viscosity situations (similarto experiments) in which there is no published linear theory, and explain thenumerical results with a simple asymptotic analysis. These results are thenapplied to experimental thermal drawing systems. We show that the observedinstabilities are consistent with radial-fluctuation analysis, but cannot bepredicted by radial fluctuations alone---an additional mechanism is required.We show how radial fluctuations alone, however, can be used to analyze variouscandidate material systems for thermal drawing, clearly ruling out somepossibilities while suggesting others that have not yet been considered inexperiments.

Capillary instability in concentric-cylindrical shell: numerical simulation and applications in composite microstructured fibers