Thin liquid films are nanoscopic elements of foams, emulsions and
suspensions, and form a paradigm for nanochannel transport that eventually test
the limits of hydrodynamic descriptions. Here we use classical dynamical
systems characteristics to study the complex interplay of thermal convection,
interface and gravitational forces which yields turbulent mixing and transport:
Lyapunov exponents and entropies. We induce a stable two eddy convection in an
extremely thin liquid film by applying a temperature gradient. Experimentally,
we determine the small-scale dynamics using the motion and deformation of spots
of equal size/equal color, we dubbed that technique "color imaging
velocimetry". The large-scale dynamics is captured by encoding the left/right
motion of the liquid directed to the left or right of the separatrix between
the two rolls. This way, we characterize chaos of course mixing in this
peculiar fluid geometry of a thin, free-standing liquid film
