Fractal dewetting of a viscous adhesive film between separating parallel plates

A dewetting cylindrical film between two separating plates is observed to produce fractal finger patterns that penetrate radially inward. In lieu of the classical tip splitting, this fractal is generated by successive shielding of alternating fingers. By analyzing this key shielding dynamics via a forced two-dimensional Hele–Shaw model with global force balance, a self-similar scaling for the shielding distance and shielding time were obtained for every generation of shielding events. The theory predicts that the plate detach time is reduced by a factor of 12 due to the fractal fingers. This is confirmed experimentally for large Bond numbers when there are sufficient fingers to justify a continuum approximation in the theory. A cumulative node number density, which is not a power law, is also predicted but not confirmed experimentally.

[1]  S. Tanveer Evolution of Hele-Shaw interface for small surface tension , 1991, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[2]  Y. Couder,et al.  The Saffman–Taylor instability: From the linear to the circular geometry , 1989 .

[3]  I. Goodwin Science Loses an Urbane Champion in Congress with Death of George Brown after 18 Terms , 1999 .

[4]  D. Acheson Elementary Fluid Dynamics , 1990 .

[5]  P. Pelcé Dynamics of curved fronts , 1988 .

[6]  G. Homsy,et al.  Two-phase displacement in Hele Shaw cells: theory , 1984, Journal of Fluid Mechanics.

[7]  G. Taylor,et al.  The peeling of a flexible strip attached by a viscous adhesive , 1966, Journal of Fluid Mechanics.

[8]  A. Zosel,et al.  Adhesion and tack of polymers: Influence of mechanical properties and surface tensions , 1985 .

[9]  G. Taylor,et al.  The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid , 1958, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[10]  Sander,et al.  Diffusion-limited aggregation as a deterministic growth process. , 1985, Physical review. A, General physics.

[11]  P. van Meurs,et al.  The Instability of Slow, Immiscible, Viscous Liquid-Liquid Displacements in Permeable Media , 1959 .

[12]  T. Ondarçuhu Tack of a polymer melt : Adhesion measurements and fracture profile observations , 1997 .

[13]  Qing Nie,et al.  Singularities in Hele-Shaw Flows , 1998, SIAM J. Appl. Math..