3 research outputs found
Long-wave Dynamics of Single- and Two-layer Flows
Thin-film flows are central to a number of industrial, biomedical and daily-life applications, which
include coating flow technology, enhanced oil recovery, microfluidics, and surfactant replacement
therapy. Though these systems have received a lot of attention in a variety of settings, the understanding
of the dominant physics governing the flows is not completely thorough; this is especially
true in cases where the free surface of the film or, in two-layer flows, the fluid-fluid interface is susceptible
to instabilities leading to the break-up of the film and the formation of fingering patterns.
The elucidation of the underlying mechanisms behind the onset of these instabilities is of utmost
importance to several industrial processes.
The work in this thesis focusses on modelling the dynamics of thin-film flows in the presence of
complexities; the latter arise from the presence of surface-active chemicals and spatial confinement.
The lubrication approximation, which is valid in the limit of small film aspect ratios, is used to
simplify the governing equations; this facilitates the derivation of an evolution equation for the
interfacial position. This methodology is employed extensively in the present thesis to examine co- and
counter-current two-layer flows in a closed, rectangular channel and the dynamics of a thin film
laden with surfactant, driven to climb up an inclined substrate.
In the two-fluid case, the dynamics of the flow are described by a single, two-dimensional, fourth-order
nonlinear partial differential equation. Analysis of the one-dimensional flow demonstrate the
existence of travelling-wave solutions which take the form of Lax shocks, undercompressive shocks,
and rarefaction waves. In unstably-stratified cases, a Rayleigh-Taylor mechanism spawns the formation
of large-amplitude capillary waves. A wide range of parameters is studied, which include
the density and viscosity ratios of the two fluids, the flow configuration (whether co- or counter-current),
the heights of the films at the channel ends and the channel inclination. The stability
of these structures to perturbations in the spanwise direction, is also examined through a linear
stability analysis and transient, two-dimensional numerical simulations. These analyses demonstrate
successfully that some of the structures observed in the one-dimensional flow are unstable to fingering
phenomena. In the case of the climbing film, two configurations are examined, namely,
constant flux and constant volume whereby the evolution equation for the interface is coupled to
convective-diffusive equations for the concentration of surfactant, present in the form of monomers
and micelles. The former are allowed to exist at the gas-liquid and liquid-solid interfaces, and in the
bulk; the latter can only be present in the bulk. For the constant flux case, the flow is simulated
by a continuously-fed uncontaminated fluid and surfactant at the flow origin allowed to spread on
a solid substrate which has been prewetted by a thin, surfactant-free precursor layer. The constant
volume configuration simulates the deposition of a finite drop, laden with surfactant, spreading on a
thin, uncontaminated film. In the absence of spanwise disturbances, the one-dimensional solutions
demonstrate how the climbing rate and the structural deformation of the film are influenced by
gravity, and physico-chemical parameters such as surfactant concentration (whether above or below
the critical micelle concentration), and rates of adsorption of monomers at the two interfaces. The
stability of the flow is examined through linear theory and transient solutions of the full, nonlinear,
two-dimensional system of equations revealing the growth of spanwise perturbations into full-length
fingers.
A brief introduction to the experimental design of an apparatus, aimed at validating channel flow
results, is also described. The objective of the experiment was to investigate the physical features
associated with the counter-current, pressure-driven flow of a gas-liquid system. Preliminary experimental
results revealed that upon perturbing the flow, an initially uniform liquid film becomes
unstable, resulting in the formation of fingers which elongated downstream as time progressed. Finally,
we conclude with recommendations for future work, representing natural extensions to the
theoretical work described in the present thesis
Experimental investigation of bidensity slurries on an incline
We investigate the dynamics of bidensity slurries on an incline. The particle-fluid mixture consists of two species of negatively buoyant particles that have roughly the same size but significantly variant densities. This mismatch in particle densities induces or prevents settling depending on the relative amount of heavy to light particles, leading to complex regimes also found in the monodisperse case. In addition, when settling effects dominate within the thin film, we observe the phase separation down the incline between the particles and the liquid, as well as between two particle types. © 2014 Springer-Verlag Berlin Heidelberg