The effect of film stability and wetting behavior under an imposed fluid distribution width on falling film transfer devices for thermal engineering systems are investigated with reference to a variational thermodynamic formulation. The principle of minimizing the energy of a given streamwise section of the film is applied to identify the stable condition as the most likely among the set of possible flow configurations. The evolution toward this stable condition is estimated while adopting a Lagrangian viewpoint. The Lagrange equation is written with reference to a single generalized wetting coordinate and its time derivative, under the effect of Rayleigh's dissipation function and a generalized force associated with a scalar potential defined as the energy excess with respect to the local energy minimum of the stable rivulet configuration. This methodology is extended to include the hysteresis behavior of the contact angle and wettability hysteresis when increasing or decreasing the mass flow rates. Finally, a qualitative and quantitative validation of the results is presented with reference to the visual data captured on a dedicated experimental test section.
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