Thin-film evolution and fingering instability of self-rewetting films flowing down an inclined plane

Abstract

This paper examines the evolution patterns and essential mechanisms of flow instability of a self-rewetting fluid (SRF) coating on an inclined plane. Considering that the self-rewetting liquid has an anomalous surface tension with temperature change, some interesting phenomena will be found and should be explained. Using the thin-film model, the evolution equation of the air–liquid interface is derived, and the thickness of the liquid film is determined by a fourth-order partial differential equation. Taking T0 (temperature corresponding to the minimum of surface tension) as a cutoff point, two representative cases of the nonlinear flow are comprehensively discussed. One is the case of Ti > T0, and the other is Ti < T0 (interfacial temperature Ti). Based on traveling wave solutions, linear stability analysis (LSA) of the small perturbation applied to the initial condition is given, and the results of LSA are confirmed and explained by the numerical simulations. Results show that the inclined angle and the Weber number always stabilize the free surface, while the Marangoni effect and the Biot number play different roles for the two cases. As Ti − T0 varies from a negative value to a positive value, the Marangoni effect switches to the reverse Marangoni effect. With Ti − T0 < 0, the Marangoni effect enhances the fingering instability, while the Marangoni effect makes the flow more stable if Ti − T0 > 0. The Biot number Bi = 1 corresponds to the most unstable state for Ti < T0 and to the most stable state for Ti > T0.