Secondary flow induced by inertia in a thin-fluid layer between two parallel plates

We study the indentation of a rigid object into a layer of a cohesive or non-cohesive plastic material. Existing approaches to this problem using slip-line theory assume that the penetration depth is relatively small, employing perturbation theory about a flat surface. Here, we use two alternative approaches to account for large penetration depths, and for the consequent spreading and uplift of the surrounding material. For a viscoplastic fluid, which reduces to an ideal plastic under the limit of vanishing viscosity, we adopt a viscoplastic version of lubrication theory. For a Mohr–Coulomb material, we adopt an extension of slip-line theory between two parallel plates to account for arbitrary indenter shapes. We compare the theoretical predictions of penetration and spreading with experiments in which a flat plate, circular cylinder or sphere are indented into layers of Carbopol or glass spheres with successively higher loads. We find reasonable agreement between theory and experiment, though with some discrepancies that are discussed. There is a clear layer-depth dependence of the indentation and uplift for the viscoplastic material. For a cylinder indented into a Mohr–Coulomb material, there is a much weaker dependence on layer depth.

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Self Organized Structure of Microbubble Plume in a Thin Fluid Layer

ASME-JSME-KSME 2011 Joint Fluids Engineering Conference: Volume 1, Symposia – Parts A, B, C, and D ◽

10.1115/ajk2011-11006 ◽

2011 ◽

Cited By ~ 1

Author(s):

Yoshihito Miyagishima ◽

Tomoaki Watamura ◽

Yuji Tasaka ◽

Yuichi Murai

Keyword(s):

Liquid Phase ◽

Large Scale ◽

Fluid Layer ◽

Bubbly Flow ◽

The Self ◽

Bubbly Flows ◽

Bubble Plume ◽

Accumulation Pattern ◽

Thin Fluid ◽

Self Organized

This study aims to clarify the self-organized structure of microbubble plume as a result of two-way interaction between microbubbles and a flow of the surrounding liquid medium. We observed a sequence on a development of microbubble plumes in a thin fluid layer. Here the microbubbles show accumulation pattern with a different wavenumber depending on the height in the vessel. Variation of spatial wavenumber in the developing process was determined from visualization images, and three areas were distinguished in this process; (1) the area of rising microbubbles with a large wavenumber in a horizontal direction without time dependence; (2) the area of forming a large-scale flow structure, called ‘microbubble plume’ here, which keeps the primary information, horizontal wavenumber of the bubble accumulation with a large wavenumber; (3) the area where the microbubble distribution takes a smaller wavenumber and makes vertical accumulation pattern inside the bubbly flow that is due to the mutual interaction between rising microbubbles and a flow induced by bubbles. To clarify these mutual interactions between liquid and gas phases, we visualized fluid motion of the liquid phase around the microbubble plumes by laser induced fluorescence, LIF. In this way, swaying motions on the tip of rising up bubble plume and liquid phase entrainment into the bubble plumes were visualized. We found the mechanisms for the creation of the self-organized distribution of microbubbles in bubbly flows and its temporal change as the result of the interaction between gas and liquid phase motions in bubbly flows.

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Seismic reflectivity of hydraulic fractures approximated by thin fluid layers

Geophysics ◽

10.1190/geo2012-0269.1 ◽

2013 ◽

Vol 78 (4) ◽

pp. T79-T87 ◽

Cited By ~ 7

Author(s):

A. Oelke ◽

D. Alexandrov ◽

I. Abakumov ◽

S. Glubokovskikh ◽

R. Shigapov ◽

...

Keyword(s):

Analytical Solutions ◽

Fluid Layer ◽

Synthetic Data ◽

P Wave ◽

Hydraulic Fractures ◽

Reflection Coefficients ◽

S Wave ◽

Reservoir Properties ◽

Thin Fluid ◽

Theoretical Results

We have analyzed the angle-dependent reflectivity of microseismic wavefields at a hydraulic fracture, which we modeled as an ideal thin fluid layer embedded in an elastic, isotropic solid rock. We derived full analytical solutions for the reflections of an incident P-wave, the P-P and P-S reflection coefficients, as well as for an incident S-wave, and the S-S and S-P reflection coefficients. The rather complex analytical solutions were then approximated and we found that these zero-thickness limit approximations are in good agreement with the linear slip model, representing a fracture at slip contact. We compared the analytical solutions for the P-P reflections with synthetic data that were derived using finite-difference modeling and found that the modeling confirmed our theoretical results. For typical parameters of microseismic monitoring by hydraulic fracturing, e.g., a layer thickness of [Formula: see text] and frequencies of [Formula: see text], the reflection coefficients depend on the Poisson’s ratio. Furthermore, the reflection coefficients of an incident S-wave are remarkably high. Theoretical results suggested that it is feasible to image hydraulic fractures using microseismic events as a source and to solve the inverse problem, that is, to interpret reflection coefficients extracted from microseismic data in terms of reservoir properties.

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