ANALYSIS OF WAVE MODES IN LIQUID-FILM FALLING DOWN A VERTICAL OSCILLATING PLATE

The stability of periodic two-dimensional waves on a liquid film falli ng down a vertical oscillating plate was studied experimentally using the aqueous solutions of carboxymethylcellulose. A set of capacitance probes was used to measure the instantaneous film thickness. Artificia l flow fluctuations induced by the plate oscillations caused distinct intensification of the wavy flow. We use the methods of phase space re construction and deterministic chaos analysis to show that the dynamic s can be understood within the framework of deterministic chaos. We fi nd that regions of relatively ordered and more complex chaotic dynamic s alternate as the frequency of oscillations is varied. There are part icular oscillating frequencies at which the system is close to a three -frequency quasiperiodic motion with the spectrum of Lyapunov exponent s of type (0, 0, 0, -, ...), elsewhere the system is either in a simpl e chaotic mode with the spectrum of type (+, 0, 0, -, ...) or in a hyp erchaotic mode with spectrum of type (+, +, 0, -, ...). (C) 1997 Elsev ier Science Ltd.