Unstable spreading of a fluid filament on a vertical plane: Experiment and simulations

J. DIEZ, A. G. GONZÁLEZ, J. M. GOMBA, R. GRATTON

PHYSICA D - NONLINEAR PHENOMENA

Elsevier

Año: 2005 vol. 209 p. 49 - 61

0167-2789

We present results of experiments and numerical simulations on thespreading of a constant volume of fluid flowing down a vertical plate inthe form of a micrometric thin film. In the experiments, the initialcondition is generated from a horizontal fluid filament (PDMS) oftypical diameter $approx 0.4~mm$, and the flow is probed with twooptical  techniques: one based on an anamorphic system, and the other onthe schlieren method. The first one yields the thickness profile and thesecond one captures the bidimensional pattern of the transversal filminstability. The numerical simulations are performed under thelubrication approximation and using a precursor film to overcome thecontact line divergence.  The comparison between numerical andexperimental profiles shows a  very good agreement, and therefore allows to estimate the thickness of the precursor film needed to model theflow.  We find that this thin precursor (of thickness $43~nm$) is  verydemanding for the numerical description of the  instability, since itrequires the use of a very fine grid.  We show that the use of thickerprecursor allows to  obtain numerical results which describequalitatively well the experimental data. In order to study the earlytimes of the instability, we develop a linear model to account  for theevolution of  the modal amplitudes of the spatial Fourier spectrum ofthe contact line. The model is in good agreement with  both experiments and simulations for the appropriate precursor film thickness in eachcase.  We find that the precursor film  thickness mainly influences thegrowth rates of the unstable modes, but it does not modify the mainfeatures of instability development.