Spinning viscous sheets, or pizza, pancakes and doughnuts

11 February 2010
Peter Howell (OCIAM)
We study the axisymmetric stretching of a thin sheet of viscous fluid driven by a centrifugal body force. Time-dependent simulations show that the sheet radius tends to infinity in finite time. As the critical time is approached, the sheet becomes partitioned into a very thin central region and a relatively thick rim. A net momentum and mass balance in the rim leads to a prediction for the sheet radius near the singularity that agrees with the numerical simulations. By asymptotically matching the dynamics of the sheet with the rim, we find that the thickness in the central region is described by a similarity solution of the second kind. For non-zero surface tension, we find that the similarity exponent depends on the rotational Bond number B, and increases to infinity at a critical value B=1/4. For B>1/4, surface tension defeats the centrifugal force, causing the sheet to retract rather than stretch, with the limiting behaviour described by a similarity solution of the first kind.
  • Differential Equations and Applications Seminar