### Abstract

A nonlinear evolution equation for the thickness of a thin viscoelastic film flowing down an inclined plane is derived for an Oldroyd-B fluid, using a long wave approximation. The evolution equation is valid to the second order in a small parameter which measures the relative thickness of the film to a typical wavelength. For a very thin film, viscoelasticity dominates the stability of the film and it can cause a purely elastic instability. The weakly nonlinear development of a monochromatic wave resulting from this elastic instability is studied using the second-order evolution equation which allows us to investigate the effects of inclination angle on the bifurcation. It is found that although extremely long waves bifurcate subcritically, the linearly most amplified wave does bifurcate supercritically when the surface tension parameter J > 13.8035. It is demonstrated that for a fixed bifurcation parameter δ = Wi - Wi_{c}, increasing the inclination angle can reduce the equilibrium amplitude for a supercritical bifurcating wave.

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

Pages (from-to) | 243-252 |

Number of pages | 10 |

Journal | Journal of Non-Newtonian Fluid Mechanics |

Volume | 57 |

Issue number | 2-3 |

DOIs | |

State | Published - 1995 |

### Fingerprint

### Keywords

- Bifurcation
- Elastic instability
- Thin viscoelastic films

### ASJC Scopus subject areas

- Chemical Engineering(all)
- Mechanical Engineering
- Materials Science(all)
- Applied Mathematics
- Condensed Matter Physics
- Fluid Flow and Transfer Processes

### Cite this

**Nonlinear elastic instability of gravity-driven flow of a thin viscoelastic film down an inclined plane.** / Kang, Feng; Chen, Kangping.

Research output: Contribution to journal › Article

*Journal of Non-Newtonian Fluid Mechanics*, vol. 57, no. 2-3, pp. 243-252. https://doi.org/10.1016/0377-0257(94)01333-D

}

TY - JOUR

T1 - Nonlinear elastic instability of gravity-driven flow of a thin viscoelastic film down an inclined plane

AU - Kang, Feng

AU - Chen, Kangping

PY - 1995

Y1 - 1995

N2 - A nonlinear evolution equation for the thickness of a thin viscoelastic film flowing down an inclined plane is derived for an Oldroyd-B fluid, using a long wave approximation. The evolution equation is valid to the second order in a small parameter which measures the relative thickness of the film to a typical wavelength. For a very thin film, viscoelasticity dominates the stability of the film and it can cause a purely elastic instability. The weakly nonlinear development of a monochromatic wave resulting from this elastic instability is studied using the second-order evolution equation which allows us to investigate the effects of inclination angle on the bifurcation. It is found that although extremely long waves bifurcate subcritically, the linearly most amplified wave does bifurcate supercritically when the surface tension parameter J > 13.8035. It is demonstrated that for a fixed bifurcation parameter δ = Wi - Wic, increasing the inclination angle can reduce the equilibrium amplitude for a supercritical bifurcating wave.

AB - A nonlinear evolution equation for the thickness of a thin viscoelastic film flowing down an inclined plane is derived for an Oldroyd-B fluid, using a long wave approximation. The evolution equation is valid to the second order in a small parameter which measures the relative thickness of the film to a typical wavelength. For a very thin film, viscoelasticity dominates the stability of the film and it can cause a purely elastic instability. The weakly nonlinear development of a monochromatic wave resulting from this elastic instability is studied using the second-order evolution equation which allows us to investigate the effects of inclination angle on the bifurcation. It is found that although extremely long waves bifurcate subcritically, the linearly most amplified wave does bifurcate supercritically when the surface tension parameter J > 13.8035. It is demonstrated that for a fixed bifurcation parameter δ = Wi - Wic, increasing the inclination angle can reduce the equilibrium amplitude for a supercritical bifurcating wave.

KW - Bifurcation

KW - Elastic instability

KW - Thin viscoelastic films

UR - http://www.scopus.com/inward/record.url?scp=0029307975&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029307975&partnerID=8YFLogxK

U2 - 10.1016/0377-0257(94)01333-D

DO - 10.1016/0377-0257(94)01333-D

M3 - Article

AN - SCOPUS:0029307975

VL - 57

SP - 243

EP - 252

JO - Journal of Non-Newtonian Fluid Mechanics

JF - Journal of Non-Newtonian Fluid Mechanics

SN - 0377-0257

IS - 2-3

ER -