Experimental investigation of thermal structures in regular three-dimensional falling films

Interfacial waves on the surface of a falling liquid film are known to modify heat and mass transfer. Under non-isothermal conditions, the wave topology is strongly influenced by the presence of thermocapillary (Marangoni) forces at the interface which leads to a destabilization of the film flow and potentially to critical film thinning. In this context, the present study investigates the evolution of the surface topology and the evolution of the surface temperature for the case of regularly excited solitary-type waves on a falling liquid film under the influence of a wall-side heat flux. Combining film thickness (chromatic confocal imaging) and surface temperature information (infrared thermography), interactions between hydrodynamics and thermocapillary forces are revealed. These include the formation of rivulets, film thinning and wave number doubling in spanwise direction. Distinct thermal structures on the films’ surface can be associated to characteristics of the surface topology.

Localization in systems of non-identical oscillators

A singular perturbation method is applied to a non-conservative system of two weakly coupled strongly nonlinear non-identical oscillators. For certain parameters, localized solutions exist for which the amplitude of one oscillator is an order of magnitude smaller than the other. It is shown that these solutions are described by coupled equations for the phase difference and scaled amplitudes. Three types of localized solutions are obtained as solutions to these equations which correspond to phase locking, phase drift, and phase entrainment. Quantitative results for the phases and amplitudes of the oscillators and the stability of these phenomena are expressed in terms of the parameters of the model.