| The role of inertia, gravity and exit conditions in thin-film flow of Newtonian and viscoelastic fluids is investigated in this thesis. In particular, two types of flow are considered: shear-dominated and elongation-dominated flows. In shear flow, only a Newtonian fluid is considered. The film is assumed to emerge from a channel and flows freely (jet flow) or over a rigid substrate (coating flow). The thin-film equations governing the flow are of the boundary-layer type. In contrast with the commonly used depth averaging method, the equations are solved by expanding spectrally the flow field in terms of orthonormal modes depthwise, thus preserving nonlinearity. The Galerkin projection is then used, combined with integration along the flow direction. The method predicts the shape of the free surface and the flow field. It is found that inertia plays an important role in the transient behavior of the thin-jet flow. The jet mayor may not develop a shock, depending on the flow parameters and initial conditions. It is found, for instance, that if the initial film thickness is streamwise decreasing, the film tends to form a wave that propagates downstream in time with continuous steepening, leading to shock formation. The rapid transient nonlinear behavior suggests the existence of a wide range of geometrical and flow parameters under which steady state cannot be achieved. The type of exit conditions is found to have a significant effect on the development of the free surface and flow field near the exit. The film thickness can exhibit a local depression or monotonic increase, depending on the velocity profile at the channel exit. A hydraulic-jump-like structure in the flow is predicted when gravity effect is considered. It is found that the distance between the jump and the channel exit increases with inertia while the height of the jump is inertia independent.;Keywords: Newtonian fluid, Viscoelasticity, Inertia, Thin-film flow, Free surface, Spectral method, Film casting, Stability.;Elongation flows in this thesis are represented by the thin-filament and thin-film flows, as it is the case in fiber spinning and film casting, respectively. Linear and nonlinear stability analyses are carried out for the Newtonian thin-filament flow. Both inertia and gravity are found to enhance the stability of steady flow, inertia being more dominant regarding the critical parameter. Above criticality, finite-amplitude disturbances are amplified, and sustained oscillation is achieved. Transient post-critical calculations show that the nonlinearity can be effectively halted by inertia and gravity. The interplay between inertia and elasticity is examined for the film casting of viscoelastic fluids of the Phan-Thien Tanner type. Similarly to filament flow, inertia is found to stabilize the process. Two branches of the neutral stability curve are observed at higher inertia Furthermore, inertia is most effective in stabilizing the flow with extensional-thickening elongational viscosity. It is also shown that the onset of draw resonance for higher-elasticity fluids is sensitive to the choice of stress boundary conditions. |
