MATHEMATICAL MODEL AND NUMERICAL SIMULATION OF THIN FILM FLOW ON HORIZONTAL SUBSTRATE

A unique mathematical model is built to study the relative altitude for deposited thin liquid films on steel sheets in automobiles. The classical Navier-stokes equation is simplified based on the specialties in the dimension of thin liquid films and lubrication approximation theory. Then a model is derived after the boundary condition is taken into consideration. The pseudo-spectral method combined with Runge-Kutta scheme is implemented to solve the mathematical model. The numerical simulation on the uniformity of the deposited thin liquid films is conducted by a program written in MATLAB according to the model and algorithm illustrated in this paper. The comparison between the results from the experiment and numerical simulation proves the feasibility of the mathematical model and the algorithm. The results are concluded that the height of free surface of the thin liquid film tends to be homogeneous while the homogenization rate is limited.