The leaching of a mineral from the ground is considered using injection and recovery holes drilled into the rock. In this simplified analysis, the holes are arranged vertically and an appropriate caustic leaching flui...
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The leaching of a mineral from the ground is considered using injection and recovery holes drilled into the rock. In this simplified analysis, the holes are arranged vertically and an appropriate caustic leaching fluid is introduced into the uppermost hole. The leaching liquor percolates down through the rock, dissolving the mineral of interest, and is pumped out when it arrives at the second hole. Water is introduced at the bottom hole in an attempt to increase the feasible recovery fraction of mineral-bearing liquor. Tire model problem is solved numerically using a boundary-integral formulation. Maximum feasible recovery fractions for the leaching fluid are obtained and their dependence upon the separation distance between the injection and recovery points and upon the pumping rate for water at the bottom hole are studied The volume of rock inundated by the leaching liquor is assessed, and a possible practical strategy for in situ leaching of low-grade ores is proposed.
Steady, two-dimensional, two-layer flow over an arbitrary topography is considered. The fluid in each layer is assumed to be inviscid and incompressible and flows irrotationally. The interfacial surface is found using...
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Steady, two-dimensional, two-layer flow over an arbitrary topography is considered. The fluid in each layer is assumed to be inviscid and incompressible and flows irrotationally. The interfacial surface is found using a boundary integral formulation, and the resulting integrodifferential equations are solved iteratively using Newton's method. A linear theory is presented for a given topography and the non-linear theory is compared against this to show how the non-linearity affects the problem.
Forced motion of a spherical bubble in an incompressible viscous fluid is considered. The system is assumed to be governed by the Rayleigh-Plesset equation, and the forcing occurs by means of a harmonically varying pr...
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Forced motion of a spherical bubble in an incompressible viscous fluid is considered. The system is assumed to be governed by the Rayleigh-Plesset equation, and the forcing occurs by means of a harmonically varying pressure field at infinity. A perturbation solution is presented, which extends previously published results in that it gives a complete qualitative description of the behaviour near the primary resonance, as well as for all the superharmonic and subharmonic resonances. These low order results are confirmed and extended to large amplitude motion by means of a numerical shooting algorithm. The method is capable of computing stable and unstable periodic solutions with equal ease, and it determines the stability automatically by using a numerical implementation of Floquet theory. The application of this numerical method to a non-analytical model of bubble behaviour is briefly discussed.
Atmospheric waves at the interface between two flowing layers of air are studied in this paper. The lower layer is assumed to be incompressible and to flow irrotationally, and its motion might be the result of a dista...
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Atmospheric waves at the interface between two flowing layers of air are studied in this paper. The lower layer is assumed to be incompressible and to flow irrotationally, and its motion might be the result of a distant thunderstorm, for example. The upper layer is modeled as a compressible isothermal atmosphere, so that if it were stationary, its density and pressure would both decrease exponentially with height. The equations of motion in the upper layer are linearized under the assumption that the lower layer of incompressible fluid is ''thin'' (its weight is a small fraction of the total), but the possibility of large-amplitude disturbances at the interface is nevertheless allowed. A linearized theory of wave propagation in this system is discussed, and a numerical scheme is outlined for the solution of the nonlinear equations. The results confirm the predictions of a model of Forbes and Belward [Phys. Fluids A 4, 2222 (1992)], in which the upper atmosphere was assumed stationary, and demonstrate that this simpler model gives results that are likely to be useful over most of the range of values of the speed in the upper layer encountered in practice. Nonlinear waves near the limiting height are discussed, and a very significant qualitative difference between the predictions of the linearized theory and the nonlinear results concerning progressive waves is analyzed, and may be of importance in meteorology.
Waves at the interface of a two-layer fluid are considered. The fluid in the lower layer is incompressible with constant density and is flowing irrotationally. In the upper layer, the fluid is stationary but compressi...
Waves at the interface of a two-layer fluid are considered. The fluid in the lower layer is incompressible with constant density and is flowing irrotationally. In the upper layer, the fluid is stationary but compressible, and corresponds to an isothermal atmosphere with a density profile that decreases exponentially with height. The interface between the two fluids is assumed sharp. The formation of waves at the interface would come about typically as a result of the interaction of the moving lower layer of fluid with local topographical features, as with the classical problem of the generation of waves on the lee side of a mountain range. It is shown that the present model is capable of supporting the formation of interfacial waves that are similar in many respects to the classical gravity wave of Stokes, and that are ultimately limited in every case by the formation of a 120-degrees angle at the wave crest. The highly nonlinear wave profiles are computed numerically and compared with the predictions of linearized theory. An extended perturbation analysis is given near the point at which the inter-facial waves break down as a result of the Kelvin-Helmholtz instability.
The calculation of flows in pipe networks and in networks of mine shafts and the calculations of the currents in electrical circuits can be represented as variational problems. There are two approaches: the nodal meth...
The calculation of flows in pipe networks and in networks of mine shafts and the calculations of the currents in electrical circuits can be represented as variational problems. There are two approaches: the nodal method and the loop method. There is a variational representation for each of these. This paper describes the relationship between the two representations and in particular shows that the loop formulation is the Wolfe dual of the nodal formulation after the application of Legendre transformations to the variables and to the objective function.
A simple model for underground mineral leaching is considered, in which liquor is injected into the rock at one point and retrieved from the rock by being pumped out at another point. In its passage through the rock, ...
A simple model for underground mineral leaching is considered, in which liquor is injected into the rock at one point and retrieved from the rock by being pumped out at another point. In its passage through the rock, the liquor dissolves some of the ore of interest, and this is therefore recovered in solution. When the injection and recovery points lie on a vertical line, the region of wetted rock forms an axi-symmetric plume, the surface of which is a free boundary. We present an accurate numerical method for the solution of the problem, and obtain estimates for the maximum possible recovery rate of the liquor, as a fraction of the injected flow rate. Limiting cases are discussed, and other geometries for fluid recovery are considered.
We present here a package, ADVISE, which acts as a communication interface between the client, typically a graphics device, and the server, a computing resource such as a vector supercomputer, a parallel computer or s...
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The paper explores the gravity-driven flow of the thin film of a viscoelastic-fluid-based nanofluids(VFBN)along an inclined plane under non-isothermal conditions and subjected to convective cooling at the *** Newton’...
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The paper explores the gravity-driven flow of the thin film of a viscoelastic-fluid-based nanofluids(VFBN)along an inclined plane under non-isothermal conditions and subjected to convective cooling at the *** Newton’s law of cooling is used to model the convective heat-exchange with the ambient at the *** Giesekus viscoelastic constitutive model,with appropriate modifications to account for non-isothermal effects,is employed to describe the polymeric *** unsteady and coupled non-linear partial differential equations(PDEs)describing the model problem are obtained and solved via efficient semi-implicit numerical schemes based on finite difference methods(FDM)implemented in *** response of the VFBN velocity,temperature,thermal-conductivity and polymeric-stresses to variations in the volume-fraction of embedded nanoparticles is *** is shown that these quantities all increase as the nanoparticle volume-fraction becomes higher.
Portable and effcient ways for calling numerical high performance software libraries from HPF programs are investigated. The methods suggested utilize HPF’s EXTRINSIC mechanism and are independent of implementation d...
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