Similarity solutions for unsteady shear-stress-driven flow of Newtonian and power-law fluids : slender rivulets and dry patches

Unsteady flow of a thin film of a Newtonian fluid or a non-Newtonian power-law fluid with power-law index N driven by a constant shear stress applied at the free surface, on a plane inclined at an angle α to the horizontal, is considered. Unsteady similarity solutions representing flow of slender rivulets and flow around slender dry patches are obtained. Specifically, solutions are obtained for converging sessile rivulets (0 < α < π/2) and converging dry patches in a pendent film (π/2 < α < π), as well as for diverging pendent rivulets and diverging dry patches in a sessile film. These solutions predict that at any time t, the rivulet and dry patch widen or narrow according to |x|3/2, and the film thickens or thins according to |x|, where x denotes distance down the plane, and that at any station x, the rivulet and dry patch widen or narrow like |t|−1, and the film thickens or thins like |t|−1, independent of N

A computational fluid dynamics model for drug delivery in a nasal cavity with inferior turbinate hypertrophy

10.1089/jamp.2009.0776Journal of Aerosol Medicine and Pulmonary Drug Delivery235329-33