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See Below

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Paddy Mortimer – Capillary driven flows in a non-uniform Hele-Shaw cell

We consider flow driven by capillary forces in a channel with a non-uniform gap width. We first present similarity solutions for a finite release of fluid in a channel where the cross-sectional profile is described by some power law. We find that this power law significantly influences the shape of the current and the rate of migration through the channel. We then we look to relate the well-known confined solution from Romero and Yost (1996) to the unconfined solution from Wieslogel and Lichter (1998) by showing the transition time from the former to the latter is a function of the aspect ratio of the confined current. Then by including gravity effects in the cross-channel direction we show a transition from early time gravity current to later time capillary current behaviour. We also show experimentally, that an along channel component of gravity can lead to shock solutions with a capillary dominated boundary layer, migrating through the thinnest section of the channel. In the final section we present some calculations in the context of CO2 sequestration, which show that post-injection, late time capillary behaviour may lead to an increase the final extent of the current and a decrease in the trapping efficiency.

Eric Newland – On Particle Fountains in a Stratified Environment

There are a number of situations in which particle laden fluid is released into the environment, leading to the formation of a particle laden flow. Important examples include volcanic eruption columns in both sub-aqueous and sub-aerial settings; turbidity currents which run down the continental shelf and particle plumes formed during deep sea mining. The dynamics of these flows are complex, involving both the buoyancy of the particle laden suspension and also the separation of the particles and the fluid, especially when the convective flow speeds become comparable to the particle fall speed. Although the dynamics of particle laden buoyant plumes and gravity currents have received considerable attention , there has been less attention placed on particle laden fountains, although these are of considerable relevance for the dynamics of volcanic eruption columns in both sub-aerial and sub-aqueous environments.

I present a series of experiments exploring the dynamics of particle-laden fountains rising through a stratified environment with zero buoyancy flux at the source. We find that the ratio U between the particle sedimentation speed Vs and the characteristic fountain velocity has a profound effect on the structure of the fountain and the dispersal of the particles. We compare the observations with some simple integral models of the fountain flow, to predict the height of rise of the fountain and of the intrusions which develop as the particles separate from the flow and the fountain fluid spreads radially from the fountain. We also describe the radial extent of the particles as they settle from the flow.

This talk is part of the Institute for Energy and Environmental Flows (IEEF) series.

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