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.
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Momoniat, E. An investigation of an Emden-Fowler equation from thin film flow. Acta Mech Sin 28, 300–307 (2012). https://doi.org/10.1007/s10409-012-0007-9
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DOI: https://doi.org/10.1007/s10409-012-0007-9