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  • 1
    Electronic Resource
    Electronic Resource
    Modeling electrodeposition for LIGA microdevice fabrication (1998)
    Springer
    Microsystem technologies 4 (1998), S. 98-101 
    Details
    ISSN: 1432-1858
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s005420050105
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  • 2
    Electronic Resource
    Electronic Resource
    Estimates of Barometric Pumping of Moisture Through Unsaturated Fractured Rock (1999)
    Springer
    Transport in porous media 36 (1999), S. 85-119 
    Details
    ISSN: 1573-1634
    Keywords: barometric pumping ; two-phase flow ; fractured rock.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract We present a theory for the motion of water vapor at depth in a discretely fractured permeable medium induced by atmospheric barometric pressure fluctuations, or ‘barometric pumping’. The theory involves multiphase mass and energy transport in a fracture/matrix system, with discrete representation of the fracture system. The barometric pressure fluctuations are approximated as periodic in time, with amplitude corresponding to measured values. To simplify the analysis, a ‘single-horizon’ approximation is applied in which the time-mean gradient is used to evaluate the vertical advective flux in the fractures. Time-periodic solutions are obtained numerically, enabling the calculation of the net efflux of moisture per cycle. The model is applied to material representative of the Yucca Mountain region of southwestern Nevada. The results indicate that the efflux of moisture carried upward from significant depths by barometric pumping is much less than the near surface efflux that is commonly estimated by assuming that air enters the medium dry and is returned to the atmosphere fully saturated with water vapor. This near surface efflux consists primarily of moisture discharged from the upper layer which is frequently replenished by precipitation. Of greater interest to nuclear waste repository design and estimations of net infiltration in arid regions is the fraction of the total moisture efflux that comes from significant depths. This deep transport is quantified by the fracture/matrix transport model described here. Although the transport by barometric pumping from depth is small compared to the total moisture expelled from the surface layer, it is an order of magnitude greater than the vertical moisture flux carried from depth by diffusion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006593628835
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  • 3
    Electronic Resource
    Electronic Resource
    Transient two-dimensional diffusion along a high-diffusivity lamina which bisects a half-space (1980)
    Springer
    Journal of engineering mathematics 14 (1980), S. 263-282 
    Details
    ISSN: 1573-2703
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Summary The right half-space Ω is bisected by a high-diffusivity planar sheet Γ which lies along the x-axis. A sudden increase in the potential on ∂Ω (y-axis) causes longitudinal diffusion along Γ coupled with transverse diffusion from Γ into Ω. Restricting to the case of large diffusivity ratio, Γ to Ω, it is demonstrated that the problem possesses a sequence of three distinct time domains in which self-similar solutions become asymptotically valid. The early, intermediate, and late solutions are each functions of only two independent variables; they are universally valid for all parameter values; and they are easily computed and readily applied. Transitions between asymptotics are described by expansions in time, the perturbations being regular in the early-intermediate period but singular in the intermediate-late period. The considered problem is a linear example which affords the opportunity for comparison with Fourier-Laplace analysis, and has application to thermal or electric conduction, diffusion mass transfer, and Darcy-flow of fluid in a fractured or layered porous medium. Methodology and qualitative observations are applicable to more complex nonlinear problems of the same class.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00052911
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  • 4
    Electronic Resource
    Electronic Resource
    Inverted Cauchy problem for the Laplace equation in engineering design (1974)
    Springer
    Journal of engineering mathematics 8 (1974), S. 329-337 
    Details
    ISSN: 1573-2703
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Summary A Cauchy problem for the Laplace equation is solved by analytic continuation of the space variables on the plane of the complex potential, thereby obtaining an explicit expression for the geometry of physical boundaries of interest. In an illustrative application to the inverse free boundary problem of electrochemical machining, the general solution comprises a closed-form description of a tool family which can be used to machine a prescribed workpiece. The method is extended to include the effects of variable electrolyte conductivity, and a general tool design procedure is suggested in which an analytic series with correct asymptotic behavior is used to represent the given workpiece geometry. Applications in other fields such as heat conduction and hydrodynamics are discussed. The inverted formulation described herein affords considerable advantage and generality in solving Cauchy problems which are encountered in engineering design.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02353499
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  • 5
    Electronic Resource
    Electronic Resource
    An integral method for predicting hydraulic fracture propagation driven by gases or liquids (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 10 (1986), S. 191-211 
    Details
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: Hydraulic fracture propagation is predicted by a general numerical procedure which satisfies the transport equations in a global or integral sense over the entire fracture and over a small control volume near the leading edge. At each discrete time step the pressure distribution is selected from a four-parameter family of profiles such that the stress intensity is equal to the critical value at the tip of the fracture and the integral equations are satisfied. Comparisons with previous analytical and, numerical solutions indicate accuracy within 10 per cent for a variety of test problems include wedge-shaped and envelope-shaped fractures, laminar and turbulent flows, incompressible liquids and ideal gases, permeable and impermeable media, prescribed inlet pressure and prescribed flow rates. CPU time is typically a few seconds for a tenfold increase in fracture length. The method has been applied to explosively driven and propellant-driven gas fracturing problems as well as the traditional pump-driven hydraulic fracturing problem.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nag.1610100207
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  • 6
    Electronic Resource
    Electronic Resource
    Double-porosity modelling of oscillatory gas motion and contaminant transport in a fractured porous medium (1990)
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 14 (1990), S. 565-585 
    Details
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A double-porosity model is used to describe the oscillatory gas motion and associated contaminant transport induced by cyclical variations in the barometric pressure at the surface of a fractured porous medium. Flow along the fractures and within the permeable matrix blocks is locally one-dimensional. The interaction between fractures and blocks includes seepage of fluid as well as diffusion of contaminant. To guard against artificial numerical diffusion, the FRAM filtering remedy and methodology of Chapman is used in calculating the advective fluxes along fractures and within blocks. The entire system of equations, including the fracture-matrix interaction terms, is solved by a largely implicit non-iterative algorithm which remains stable and conservative even when the computational time step is large compared to the cross-block transit time of pressure waves. The numerical accuracy is tested by comparison with exact solutions for oscillatory and unidirectional flows, some of which include diffusion interaction between the fracture and the matrix. The method is used to estimate the rate of vertical transport of radioactive gases through the rubblized chimney produced by an underground nuclear explosion.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nag.1610140804
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  • 7
    Electronic Resource
    Electronic Resource
    Similarity solutions for wedge-shaped hydraulic fractures driven into a permeable medium by a constant inlet pressure (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 12 (1988), S. 477-495 
    Details
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: Similarity solutions are derived for wedge-shaped hydraulic fractures driven by a constant inlet pressure P0 into a permeable medium under a uniform confining stress σ. These results describe the seepage-dominated regime in which most of the injected fluid is lost into the permeable walls of the fracture; they complement previous results for the capacitance-dominated regime in which seepage is negligible. Fracture propagation velocity is obtained as an analytical function of fracture length, driving pressure, confining stress, material properties and a single separation constant or eigenvalue which is determined numerically. Self-similar profiles of pressure, opening displacement and fluid velocity along the fracture are presented, together with the self-similar isobars of the two-dimensional pressure field within the permeable medium. Comprehensive results are reported for laminar or turbulent flow of a constant-compressibility liquid or an ideal gas driven by overpressures (P0-σ)/σ ranging from 10-2 to 102.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nag.1610120503
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  • 8
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    Countercurrent convection in a double-diffusive boundary layer (1985)
    Cambridge University Press
    Details
    Publication Date: 1985-11-01
    Description: Countercurrent flowmay be induced by opposing buoyancy forces associated with compositional gradients and thermal gradients within a fluid. The occurrence and structure of such flows is investigated by solving the double-diffusive boundary-layer equations for steady laminar convection along a vertical wall of finite height. Non-similar solutions are derived using themethod ofmatched asymptotic expansions, under the restriction that the Lewis and Prandtl numbers are both large. Two sets of asymptotic solutions are constructed, assuming dominance of one or the other of the buoyancy forces. The two sets overlap in the central region of the parameter space; each setmatches up with neighbouring unidirectional similarity solutions at the respective borderlines of incipient counterflow. Interaction between the buoyancymechanisms is controlled by their relative strength R and their relative diffusivity Le. Flow in the outer thermal boundary layer deviates from single-diffusive thermal convection, depending upon themagnitude of the parameter RLe. Flow in the inner compositional boundary layer deviates from single-diffusive compositional convection, depending upon themagnitude of RLe1/3. © 1985, Cambridge University Press. All rights reserved.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Cambridge University Press
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  • 9
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    Shock–like structure of phase-change flow in porous media (1981)
    Cambridge University Press
    Details
    Publication Date: 1981-03-01
    Description: Shock-like features of phase-change flows in porous media are explained, based on the generalized Darcy model. The flow field consists of two-phase zones of parabolic/hyperbolic type as well as adjacent or imbedded single-phase zones of either parabolic (superheated, compressible vapour) or elliptic (subcooled, incompressible liquid) type. Within the two-phase zones or at the two-phase/single-phase interfaces, there may be steep gradients in saturation and temperature approaching shock-like behaviour when the dissipative effects of capillarity and heat-conduction are negligible. Illustrative of these shocked, multizone flow-structures are the transient condensing flows in porous media, for which a self-similar, shock-preserving (Rankine–Hugoniot) analysis is presented.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Cambridge University Press
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  • 10
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    Atmospheric pumping: A mechanism causing vertical transport of contaminated gases through fractured permeable media (1991)
    American Geophysical Union
    Details
    Publication Date: 1991-12-10
    Print ISSN: 0148-0227
    Electronic ISSN: 2156-2202
    Topics: Geosciences
    Published by American Geophysical Union
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