Conclusion

We find that the behavior of the distortion growth when the matrix fluid is confined between parallel plates is much different from that in the unconfined regime. An initially axisymmetric cylindrical thread transforms into a nonaxisymmetric thread in the confined regime while that at the unconfined regime maintains an axisymmetric shape. The rate of the distortion growth and the observed dimensionless wavenumber (2R₀/) in the confined regime is much smaller than that for the unconfined regime. Below a certain ratio of gap width/thread diameter, the thread does not exhibit a distortion growth at all but is quite stable for a long period, if not indefinitley. The lattice-Boltzmann simulations confirm the physical assumptions made in the surface area analysis; in particular, they indicate that the necks are circular while the bulges are nonaxisymmetric as quantified by the Fourier decomposition relations. A simple calculation of the surface area of the nonaxisymmetric sinusoidal thread indicates that the increase in wavelength of the distortion in the confined regime is caused by the increase in the minimum wavelength required in order to have a net decrease in surface area. Finally, we note that the construction of a linear stability analysis for this nonaxisymmetric case would greatly enhance our understanding of this intriguing phenomenon.

Acknowledgment

We acknowledge Jack Douglas for important discussions.