The Influence of Boundaries on Gravity Currents and Thin Films: Drainage, Confinement, Convergence, and Deformation Effects

Thin film flows, whether driven by gravity, surface tension, or the relaxation of elastic boundaries, occur in many natural and industrial processes. Applications span problems of oil and gas transport in channels to hydraulic fracture, subsurface propagation of pollutants, storage of supercritical CO2 in porous formations, and flow in elastic Hele–Shaw configurations and their relatives. We review the influence of boundaries on the dynamics of thin film flows, with a focus on gravity currents, including the effects of drainage into the substrate, and the role of the boundaries to confine the flow, force its convergence to a focus, or deform, and thus feedback to alter the flow. In particular, we highlight reduced-order models. In many cases, self-similar solutions can be determined and describe the behaviors in canonical problems at different timescales and length scales, including self-similar solutions of both the first and second kind. Additionally, the time transitions between different solutions are summarized. Where possible, remarks about various applications are provided.

Content characterization of Latin American film productions on Netflix: a Bolivian perspective

We study international film flows between Bolivia and Latin America to explore the lack of Bolivian content on Netflix and its limited presence in other SVOD platforms. We characterize Netflix originals, third-party content, and recent Bolivian films, and develop a thematic analysis of their synopsis and genre description, completed with the results of a survey on the Bolivian consumption of streaming content. We identify common patterns in Netflix content and show how it differs from the more nationally minded Bolivian cinematic tradition. Our results point to a homogenizing effect SVOD platforms like Netflix might have on film productions.

Secondary instability in thin film flows under an inclined plane: growth of lenses on spatially developing rivulets

The response of a thin film flowing under an inclined plane, modelled using the lubrication equation, is studied. The flow at the inlet is perturbed by the superimposition of a spanwise-periodic steady modulation and a decoupled temporally periodic but spatially homogeneous perturbation. As the consequence of the spanwise inlet forcing, the so-called rivulets grow downstream and eventually reach a streamwise-invariant state, modulated along the direction perpendicular to the flow. The linearized dynamics in the presence of a time-harmonic inlet forcing shows the emergence of a time-periodic flow characterized by drop-like structures (so-called lenses) that travel on the rivulet. The spatial evolution is rationalized by a weakly non-parallel stability analysis. The occurrence of the lenses, their spacing and thickness profile, is controlled by the inclination angle, flow rate, and the frequency and amplitude of the time-harmonic inlet forcing. The faithfulness of the linear analyses is verified by nonlinear simulations. The results of the linear simulations with inlet forcing are combined with the computations of nonlinear travelling lenses solutions in a double-periodic domain to obtain an estimate of the dripping length, for a large range of conditions.

Instability of Liquid-Film Flows With Temperature-Dependent properties Down A Heated Incline

In this thesis we investigate the stability of free-surface flow on a heated incline. We develop a complete mathematical model for the flow which captures the Marangoni effect and also accounts for changes in the properties of the fluid with temperature. We apply a linear stability analysis to determine the stability of the steady and uniform flow. The associated eigenvalue problem is solved numerically by means of a spectral colocation method.

Instability of Liquid-Film Flows With Temperature-Dependent properties Down A Heated Incline

In this thesis we investigate the stability of free-surface flow on a heated incline. We develop a complete mathematical model for the flow which captures the Marangoni effect and also accounts for changes in the properties of the fluid with temperature. We apply a linear stability analysis to determine the stability of the steady and uniform flow. The associated eigenvalue problem is solved numerically by means of a spectral colocation method.

Asymptotic turbulent friction in 2D rough-walled flows

The friction f is the property of wall-bounded flows that sets the pumping cost of a pipeline, the draining capacity of a river, and other variables of practical relevance. For highly turbulent rough-walled pipe flows, f depends solely on the roughness length scale r, and the f − r relation may be expressed by the Strickler empirical scaling f ∝ r1/3. Here, we show experimentally that for soap film flows that are the two-dimensional (2D) equivalent of highly turbulent rough-walled pipe flows, f ∝ r and the f − r relation is not the same in 2D as in 3D. Our findings are beyond the purview of the standard theory of friction but consistent with a competing theory in which f is linked to the turbulent spectrum via the spectral exponent α: In 3D, α = 5/3 and the theory yields f ∝ r1/3; in 2D, α = 3 and the theory yields f ∝ r.