Howell, P. D. and Scheid, B. and Stone, H. A. (2010) Newtonian pizza: spinning a viscous sheet. Journal of Fluid Mechanics, 659 . pp. 123. ISSN 00221120

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Abstract
We study the axisymmetric stretching of a thin sheet of viscous fluid driven by a centrifugal body force. Timedependent simulations show that the sheet radius R(t) tends to infinity in finite time. As time t approaches the critical time t∗, 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 h in the central region is described by a similarity solution of the second kind, with h ∝ (t∗ − t)α where the exponent α satisfies a nonlinear eigenvalue problem. Finally, for nonzero surface tension, we find that the exponent increases rapidly to infinity at a critical value of the rotational Bond number B = 1/4. For B > 1/4, surface tension defeats the centrifugal force, causing the sheet to retract rather than to stretch, with the limiting behaviour described by a similarity solution of the first kind.
Item Type:  Article 

Subjects:  D  G > Fluid mechanics 
Research Groups:  Oxford Centre for Industrial and Applied Mathematics 
ID Code:  1557 
Deposited By:  Peter Howell 
Deposited On:  11 Jul 2012 06:22 
Last Modified:  29 May 2015 19:15 
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