Nonlinear stability analysis of thin viscoelastic film flow traveling down along a vertical cylinder

Po Jen Cheng, Cha’o Kuang Chen, Steven Hsin-Yi Lai

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

This paper investigates the weakly nonlinear stability theory of a thin viscoelastic liquid film flowing down along the outside surface of a vertical cylinder. The long-wave perturbation method is employed to solve for generalized nonlinear kinematic equations with free film interface. The normal mode approach is first used to compute the linear stability solution for the film flow. The method of multiple scales is then used to obtain the weak nonlinear dynamics of the film flow for stability analysis. The modeling results indicate that both the subcritical instability and supercritical stability conditions are possible to occur in a viscoelastic film flow system. The degree of instability in the film flow is further intensified by the lateral curvature of cylinder. This is somewhat different from that of the planar flow. The modeling results also indicate that by increasing the viscoelastic effect and decreasing the radius of the cylinder the film flow can become less stable as traveling down along the vertical cylinder.

Original languageEnglish
Article number275252
Pages (from-to)305-332
Number of pages28
JournalNonlinear Dynamics
Volume24
Issue number3
DOIs
Publication statusPublished - 2001 Jan 1

Fingerprint

Nonlinear Stability
Nonlinear Analysis
Stability Analysis
Vertical
Thin films
Liquid films
Method of multiple Scales
Normal Modes
Stability Theory
Linear Stability
Perturbation Method
Modeling
Stability Condition
Kinematics
Nonlinear Dynamics
Lateral
Curvature
Radius
Liquid

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering

Cite this

@article{0632b586d1644f0095c66004a234d25d,
title = "Nonlinear stability analysis of thin viscoelastic film flow traveling down along a vertical cylinder",
abstract = "This paper investigates the weakly nonlinear stability theory of a thin viscoelastic liquid film flowing down along the outside surface of a vertical cylinder. The long-wave perturbation method is employed to solve for generalized nonlinear kinematic equations with free film interface. The normal mode approach is first used to compute the linear stability solution for the film flow. The method of multiple scales is then used to obtain the weak nonlinear dynamics of the film flow for stability analysis. The modeling results indicate that both the subcritical instability and supercritical stability conditions are possible to occur in a viscoelastic film flow system. The degree of instability in the film flow is further intensified by the lateral curvature of cylinder. This is somewhat different from that of the planar flow. The modeling results also indicate that by increasing the viscoelastic effect and decreasing the radius of the cylinder the film flow can become less stable as traveling down along the vertical cylinder.",
author = "Cheng, {Po Jen} and Chen, {Cha’o Kuang} and Lai, {Steven Hsin-Yi}",
year = "2001",
month = "1",
day = "1",
doi = "10.1023/A:1008304906043",
language = "English",
volume = "24",
pages = "305--332",
journal = "Nonlinear Dynamics",
issn = "0924-090X",
publisher = "Springer Netherlands",
number = "3",

}

Nonlinear stability analysis of thin viscoelastic film flow traveling down along a vertical cylinder. / Cheng, Po Jen; Chen, Cha’o Kuang; Lai, Steven Hsin-Yi.

In: Nonlinear Dynamics, Vol. 24, No. 3, 275252, 01.01.2001, p. 305-332.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Nonlinear stability analysis of thin viscoelastic film flow traveling down along a vertical cylinder

AU - Cheng, Po Jen

AU - Chen, Cha’o Kuang

AU - Lai, Steven Hsin-Yi

PY - 2001/1/1

Y1 - 2001/1/1

N2 - This paper investigates the weakly nonlinear stability theory of a thin viscoelastic liquid film flowing down along the outside surface of a vertical cylinder. The long-wave perturbation method is employed to solve for generalized nonlinear kinematic equations with free film interface. The normal mode approach is first used to compute the linear stability solution for the film flow. The method of multiple scales is then used to obtain the weak nonlinear dynamics of the film flow for stability analysis. The modeling results indicate that both the subcritical instability and supercritical stability conditions are possible to occur in a viscoelastic film flow system. The degree of instability in the film flow is further intensified by the lateral curvature of cylinder. This is somewhat different from that of the planar flow. The modeling results also indicate that by increasing the viscoelastic effect and decreasing the radius of the cylinder the film flow can become less stable as traveling down along the vertical cylinder.

AB - This paper investigates the weakly nonlinear stability theory of a thin viscoelastic liquid film flowing down along the outside surface of a vertical cylinder. The long-wave perturbation method is employed to solve for generalized nonlinear kinematic equations with free film interface. The normal mode approach is first used to compute the linear stability solution for the film flow. The method of multiple scales is then used to obtain the weak nonlinear dynamics of the film flow for stability analysis. The modeling results indicate that both the subcritical instability and supercritical stability conditions are possible to occur in a viscoelastic film flow system. The degree of instability in the film flow is further intensified by the lateral curvature of cylinder. This is somewhat different from that of the planar flow. The modeling results also indicate that by increasing the viscoelastic effect and decreasing the radius of the cylinder the film flow can become less stable as traveling down along the vertical cylinder.

UR - http://www.scopus.com/inward/record.url?scp=0035278806&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035278806&partnerID=8YFLogxK

U2 - 10.1023/A:1008304906043

DO - 10.1023/A:1008304906043

M3 - Article

VL - 24

SP - 305

EP - 332

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

IS - 3

M1 - 275252

ER -