An investigation of an Emden-Fowler equation from thin film flow

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2 Citations (Scopus)


A third-order ordinary differential equation (ODE) for thin film flow with both Neumann and Dirichlet boundary conditions is transformed into a second-order nonlinear ODE with Dirichlet boundary conditions. Numerical solutions of the nonlinear second-order ODE are investigated using finite difference schemes. A finite difference formulation to an Emden-Fowler representation of the second-order nonlinear ODE is shown to converge faster than a finite difference formulation of the standard form of the second-order nonlinear ODE. Both finite difference schemes satisfy the von Neumann stability criteria. When mapping the numerical solution of the second-order ODE back to the variables of the original third-order ODE we recover the position of the contact line. A nonlinear relationship between the position of the contact line and physical parameters is obtained.

Original languageEnglish
Pages (from-to)300-307
Number of pages8
JournalActa Mechanica Sinica/Lixue Xuebao
Issue number2
Publication statusPublished - Apr 2012
Externally publishedYes


  • Contact angle
  • Emden-Fowler equation
  • Finite differences
  • Thin film
  • Third-order ODE

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanical Engineering


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