Mathematical Model And Numerical Simulation Of Thin Film Flow On Horizontal Substrate

The visual appearance of automobile body depends on the deposition quality of thin film coating.Uniform coating is the objective for carmakers because relatively consistent thin film coating means better quality of visual appearance.It is obvious that there exists crucial theoretical and practical significance of the mathematical model and numerical simulation on thin liquid film flow.The physical model for thin liquid film is built based on the coating process used in automobile industry as well as the special dimension of thin liquid film,aimed at studying how thin liquid film flow altitude on the free surface changes with respect to time.Lubrication approximation is firstly introduced to simplify the governing equations,verifying that the pressure of thin liquid film flow is independent of the z coordinate.According to no-slip boundary condition and mechanical equilibrium along the normal direction of free surface,both two-dimension and three-dimension mathematical models can be derived respectively based on mass conservation equation.In addition,it can be concluded from the dimensionless form of mathematical model that the altitude of thin liquid film depends on the dimensionless parameter capillary number.The mathematical model derived above consists of nonlinear high order PDEs,the manipulation of high order partial derivatives is difficult.Considering that the calculation of high order partial derivatives in physical space can be converted to multiplication in Fourier space,so Fourier pseudo-spectral method is applied to conduct numerical calculation.Then zero padding is applied to avoid aliasing caused by discrete Fourier transform.In the end,mathematical equations describing how altitude of thin liquid film flow on free surface varies are simplified to systems of ODEs.If suitable Runge-Kutta scheme is chosen,the numerical solution can be obtained.Taking MATLAB as a tool,code is programmed based on the mathematical model together with numerical implementation to simulate the free surface topography of thin liquid film flow.The comparison between experimental result and simulation result verifies the rationality of mathematical model.Related evolvement rule for thin liquid film flow can be obtained from the simulation result.In addition,the role of evaporation is also studied.