We demonstrate through numerical simulations and a mean-field calculation that immiscible twophase flow in a porous medium behaves effectively as a Bingham viscoplastic fluid. This leads to a generalized Darcy equation where the volumetric flow rate depends quadratically on an excess pressure difference in the range of flow rates where the capillary forces compete with the viscous forces. At higher rates, the flow is Newtonian.
We present an experimental and numerical study of immiscible two-phase flow of Newtonian fluids in three-dimensional (3D) porous media to find the relationship between the volumetric flow rate (Q) and the total pressure difference () in the steady state. We show that in the regime where capillary forces compete with the viscous forces, the distribution of capillary barriers at the interfaces effectively creates a yield threshold (), making the fluids reminiscent of a Bingham viscoplastic fluid in the porous medium. In this regime, Q depends quadratically on an excess pressure drop (). While increasing the flow rate, there is a transition, beyond which the overall flow is Newtonian and the relationship is linear. In our experiments, we build a model porous medium using a column of glass beads transporting two fluids, deionized water and air. For the numerical study, reconstructed 3D pore networks from real core samples are considered and the transport of wetting and non-wetting fluids through the network is modeled by tracking the fluid interfaces with time. We find agreement between our numerical and experimental results. Our results match with the mean-field results reported earlier.Electronic supplementary materialThe online version of this article (doi:10.1007/s11242-017-0874-4) contains supplementary material, which is available to authorized users.
The ALICE Collaboration has measured inclusive J/ψ production in pp collisions at a center of mass energy √ s = 2.76 TeV at the LHC. The results presented in this Letter refer to the rapidity ranges |y| < 0.9 and 2.5 < y < 4 and have been obtained by measuring the electron and muon pair decay channels, respectively. The integrated luminosities for the two channels are L e int = 1.1 nb −1 and L µ int = 19.9 nb −1 , and the corresponding signal statistics are N e + e − J/ψ = 59 ± 14 and N= 1364 ± 53. We present dσ J/ψ /dy for the two rapidity regions under study and, for the forward-y range, d 2 σ J/ψ /dydp t in the transverse momentum domain 0 < p t < 8 GeV/c. The results are compared with previously published results at √ s = 7 TeV and with theoretical calculations.Inclusive J/ψ production in pp collisions at √ s = 2.76 TeV 3 IntroductionAlmost forty years after the discovery of charmonium, its production in hadronic collisions still remains not completely understood, and charmonium production data represent a complex and severe test for QCD-inspired models [1].Recently, first results from the Large Hadron Collider (LHC) on J/ψ production in pp collisions at √ s = 7 TeV became available [2][3][4][5][6], significantly extending the energy reach beyond that of the Tevatron and RHIC hadron colliders [7][8][9]. A reasonable description of the transverse momentum spectra has been obtained by theoretical models [10][11][12][13], and first results on J/ψ polarization, a crucial testing ground for theory [14][15][16], are also available [17] at LHC energy.At the beginning of 2011, the LHC delivered pp collisions at √ s = 2.76 TeV. The main goal of this short run was to provide a reference for the Pb-Pb data which were taken at the same √ s per nucleon-nucleon collision. On the other hand, these data offer the possibility of studying J/ψ production at an intermediate energy between Tevatron and the present LHC top energy, and represent therefore an interesting test for models.In this Letter, we present results on inclusive J/ψ production at √ s = 2.76 TeV as obtained by the ALICE experiment [18]. J/ψ particles were measured, down to zero transverse momentum, via their decay into e + e − at mid-rapidity (|y| < 0.9) and into µ + µ − at forward rapidity (2.5 < y < 4). Results from ALICE on J/ψ production at √ s = 7 TeV were recently published [5,17]. Since the experimental apparatus and the data analysis procedure are basically the same for the two data samples, they will be concisely described, referring where necessary to our previous publications. Results will then be shown for dσ J/ψ /dy at central and at forward rapidity. For the region 2.5 < y < 4 the differential cross section d 2 σ J/ψ /dydp t will also be given, for the transverse momentum range 0 < p t < 8 GeV/c. A comparison with the previous results at √ s = 7 TeV will be carried out and next-to-leading order Non-Relativistic QCD (NLO NRQCD) theoretical calculations will be compared to the experimental data. Experimental apparatus and data analysisThe ma...
Based on thermodynamic considerations we derive a set of equations relating the seepage velocities of the fluid components in immiscible and incompressible two-phase flow in porous media. They necessitate the introduction of a new velocity function, the co-moving velocity. This velocity function is a characteristic of the porous medium. Together with a constitutive relation between the velocities and the driving forces, such as the pressure gradient, these equations form a closed set. We solve four versions of the capillary tube model analytically using this theory. We test the theory numerically on a network model.
It is well known that the transient behavior during drainage or imbibition in multiphase flow in porous media strongly depends on the history and initial condition of the system. However, when the steady-state regime is reached and both drainage and imbibition take place at the pore level, the influence of the evolution history and initial preparation is an open question. Here, we present an extensive experimental and numerical work investigating the history dependence of simultaneous steady-state two-phase flow through porous media. Our experimental system consists of a Hele-Shaw cell filled with glass beads which we model numerically by a network of disordered pores transporting two immiscible fluids. From measurements of global pressure evolution, histograms of saturation, and cluster-size distributions, we find that when both phases are flowing through the porous medium, the steady state does not depend on the initial preparation of the system or on the way it has been reached.
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