Abstract
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 language | English |
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Pages (from-to) | 300-307 |
Number of pages | 8 |
Journal | Acta Mechanica Sinica/Lixue Xuebao |
Volume | 28 |
Issue number | 2 |
DOIs | |
Publication status | Published - Apr 2012 |
Externally published | Yes |
Keywords
- Contact angle
- Emden-Fowler equation
- Finite differences
- Thin film
- Third-order ODE
ASJC Scopus subject areas
- Computational Mechanics
- Mechanical Engineering