### Abstract

The flow of liquid films on rotating discrete objects having complicated cross sections is encountered in coating processes for a broad variety of products. To advance fundamental understanding of this problem, we study viscous free-surface flows on rotating elliptical cylinders by solving the governing equations in a rotating reference frame using the Galerkin finite-element method. Results of our simulations agree well with Hunt's maximum-load condition [Hunt, Numer. Methods Partial Differ. Eqs. 24, 1094 (2008)0749-159X10.1002/num.20307], which was obtained in the absence of surface tension and inertia. The simulations are also used to track the transient behavior of the free surface. For O(1) cylinder aspect ratios, cylinder rotation results in a droplike liquid bulge hanging on the upward-moving side of the cylinder. This bulge shrinks in size due to surface tension provided that the liquid load is smaller than a critical value, leaving a relatively smooth coating on the cylinder. A decrease in cylinder aspect ratio leads to larger gradients in film thickness, but enhances the rate of bulge shrinkage and thus shortens the time required to obtain a smooth coating. Moreover, with a suitably chosen time-dependent rotation rate, more liquid can be supported by the cylinder relative to the constant-rotation-rate case. For cylinders with even smaller aspect ratios, film rupture and liquid shedding may occur over the cylinder tips, so simultaneous drying and rotation along with the introduction of Marangoni stresses will likely be especially important for obtaining a smooth coating.

Original language | English (US) |
---|---|

Article number | 094005 |

Journal | Physical Review Fluids |

Volume | 2 |

Issue number | 9 |

DOIs | |

State | Published - Sep 1 2017 |

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### Cite this

*Physical Review Fluids*,

*2*(9), [094005]. https://doi.org/10.1103/PhysRevFluids.2.094005

**Viscous free-surface flows on rotating elliptical cylinders.** / Li, Weihua; Carvalho, Marcio S.; Kumar, Satish.

Research output: Contribution to journal › Article

*Physical Review Fluids*, vol. 2, no. 9, 094005. https://doi.org/10.1103/PhysRevFluids.2.094005

}

TY - JOUR

T1 - Viscous free-surface flows on rotating elliptical cylinders

AU - Li, Weihua

AU - Carvalho, Marcio S.

AU - Kumar, Satish

PY - 2017/9/1

Y1 - 2017/9/1

N2 - The flow of liquid films on rotating discrete objects having complicated cross sections is encountered in coating processes for a broad variety of products. To advance fundamental understanding of this problem, we study viscous free-surface flows on rotating elliptical cylinders by solving the governing equations in a rotating reference frame using the Galerkin finite-element method. Results of our simulations agree well with Hunt's maximum-load condition [Hunt, Numer. Methods Partial Differ. Eqs. 24, 1094 (2008)0749-159X10.1002/num.20307], which was obtained in the absence of surface tension and inertia. The simulations are also used to track the transient behavior of the free surface. For O(1) cylinder aspect ratios, cylinder rotation results in a droplike liquid bulge hanging on the upward-moving side of the cylinder. This bulge shrinks in size due to surface tension provided that the liquid load is smaller than a critical value, leaving a relatively smooth coating on the cylinder. A decrease in cylinder aspect ratio leads to larger gradients in film thickness, but enhances the rate of bulge shrinkage and thus shortens the time required to obtain a smooth coating. Moreover, with a suitably chosen time-dependent rotation rate, more liquid can be supported by the cylinder relative to the constant-rotation-rate case. For cylinders with even smaller aspect ratios, film rupture and liquid shedding may occur over the cylinder tips, so simultaneous drying and rotation along with the introduction of Marangoni stresses will likely be especially important for obtaining a smooth coating.

AB - The flow of liquid films on rotating discrete objects having complicated cross sections is encountered in coating processes for a broad variety of products. To advance fundamental understanding of this problem, we study viscous free-surface flows on rotating elliptical cylinders by solving the governing equations in a rotating reference frame using the Galerkin finite-element method. Results of our simulations agree well with Hunt's maximum-load condition [Hunt, Numer. Methods Partial Differ. Eqs. 24, 1094 (2008)0749-159X10.1002/num.20307], which was obtained in the absence of surface tension and inertia. The simulations are also used to track the transient behavior of the free surface. For O(1) cylinder aspect ratios, cylinder rotation results in a droplike liquid bulge hanging on the upward-moving side of the cylinder. This bulge shrinks in size due to surface tension provided that the liquid load is smaller than a critical value, leaving a relatively smooth coating on the cylinder. A decrease in cylinder aspect ratio leads to larger gradients in film thickness, but enhances the rate of bulge shrinkage and thus shortens the time required to obtain a smooth coating. Moreover, with a suitably chosen time-dependent rotation rate, more liquid can be supported by the cylinder relative to the constant-rotation-rate case. For cylinders with even smaller aspect ratios, film rupture and liquid shedding may occur over the cylinder tips, so simultaneous drying and rotation along with the introduction of Marangoni stresses will likely be especially important for obtaining a smooth coating.

UR - http://www.scopus.com/inward/record.url?scp=85036561379&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevFluids.2.094005

DO - 10.1103/PhysRevFluids.2.094005

M3 - Article

VL - 2

JO - Physical Review Fluids

JF - Physical Review Fluids

SN - 2469-990X

IS - 9

M1 - 094005

ER -