TY - JOUR
T1 - Traveling waves on a falling weakly viscoelastic fluid film
AU - Amatousse, N.
AU - Ait Abderrahmane, H.
AU - Mehidi, N.
PY - 2012/5
Y1 - 2012/5
N2 - The weighted residual integral method is employed to investigate the flow of a thin layer of Walters-type B″ viscoelastic fluid flowing down an inclined plane. A simplified second-order two-equation model is derived; the model is analogous to the simplified model proposed by Ruyer-Quil and Manneville [Ruyer-Quil, C.; & Manneville, P. (2000). Improved modeling of flows down inclined planes. European Physical Journal B: Condensed Matter and Complex Systems, 15, 357-369] for Newtonian fluid. The normal mode analysis is used to investigate the linear stability of the Nusselt's flow and the correct critical condition for linear stability was found. The results of linear analysis indicate that the viscoelastic parameter, Γ, destabilizes the film flow as its magnitude increases. The two-equation model is used to investigate the particular case of traveling waves. The result is that the model exhibits bifurcation scenarios such heteroclinic, homoclinic, Hopf and period-doubling bifurcations. The influence of viscoelastic parameter on the nonlinear development of these traveling waves is discussed.
AB - The weighted residual integral method is employed to investigate the flow of a thin layer of Walters-type B″ viscoelastic fluid flowing down an inclined plane. A simplified second-order two-equation model is derived; the model is analogous to the simplified model proposed by Ruyer-Quil and Manneville [Ruyer-Quil, C.; & Manneville, P. (2000). Improved modeling of flows down inclined planes. European Physical Journal B: Condensed Matter and Complex Systems, 15, 357-369] for Newtonian fluid. The normal mode analysis is used to investigate the linear stability of the Nusselt's flow and the correct critical condition for linear stability was found. The results of linear analysis indicate that the viscoelastic parameter, Γ, destabilizes the film flow as its magnitude increases. The two-equation model is used to investigate the particular case of traveling waves. The result is that the model exhibits bifurcation scenarios such heteroclinic, homoclinic, Hopf and period-doubling bifurcations. The influence of viscoelastic parameter on the nonlinear development of these traveling waves is discussed.
KW - Falling film flow
KW - Weakly viscoelastic fluid
KW - Weighted residual approach
UR - https://www.scopus.com/pages/publications/84858032562
U2 - 10.1016/j.ijengsci.2012.01.008
DO - 10.1016/j.ijengsci.2012.01.008
M3 - Article
AN - SCOPUS:84858032562
SN - 0020-7225
VL - 54
SP - 27
EP - 41
JO - International Journal of Engineering Science
JF - International Journal of Engineering Science
ER -