Asymptotic analysis of a thin fluid layer flow between two moving surfaces

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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Convection in directionally solidifying alloys under inclined rotation

Journal of Fluid Mechanics ◽

10.1017/s0022112000008247 ◽

2000 ◽

Vol 412 ◽

pp. 93-123 ◽

Cited By ~ 9

Author(s):

C. A. CHUNG ◽

FALIN CHEN

Keyword(s):

Boundary Layer ◽

Inclination Angle ◽

Boundary Layer Flow ◽

Fluid Layer ◽

Longitudinal Mode ◽

Point Of View ◽

Induced Flow ◽

Layer Flow ◽

Parallel Shear Flow ◽

Induced Velocity

In an experiment on binary alloys directionally solidifying from below, Sample & Hellawell (1984) showed that the plume convection can be successfully prohibited by rotating the cooling tank around an inclined axis. In the present paper we interpret their experimental observation by an analytical approach. Results show that there is a flow induced by the inclination. The induced flow in the fluid layer is a parallel shear flow consisting of three parts: the thermal boundary-layer flow, the solute boundary- layer flow, and the Ekman-layer flow. In the mush, the induced flow is also a parallel flow but of much smaller velocity, consisting of two flows of opposite directions. The induced velocity in the fluid layer increases with inclination angle and decreases with the effective Taylor number Te. The induced velocity in the mush also increases with inclination angle but remains virtually the same on varying the speed of rotation. The linear stability analysis of the mushy layer shows that, due mostly to the reduction of buoyancy, the mush becomes more stable as the inclination angle increases. In the precession-only case, the most-unstable mode of instability is the longitudinal mode, which propagates in a direction perpendicular to the induced flow. In the spin (with or without precession) case, the instability modes propagating in different directions are of equal stability. Because the induced flow changes direction with a frequency equal to the spin angular velocity, the flow scans over all the directions of the system and stabilizes equally the modes in different directions. We conclude on the basis of the present results and from the practical point of view that spin-only rotation is more effective than the precession-only rotation in stabilizing the convection during solidification.

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