Numerical studies of gravity destabilized percolation in 2D porous media

Two dimensional simulations of percolation are realized on square networks of pore throats with a random capillary pressure distribution. We analyse the influence of a destabilizing gravity field (g) and of the standard deviation of the distribution of the capillary pressure thresholds (W_t). The fragmentation process is not taken into account in this study. For an increase of g or/and when W_t decreases, two transitions are analyzed with three different regimes displacement patterns: Invasion percolation, invasion percolation in a gradient, and invasion in a pure gradient. The transitions are controlled both by the ratio g/W_t and by the sample size (L). A scaling law between the saturation at the percolation threshold and g/W_t allows delineating the three regimes in agreement with theoretical argument of the percolation in a gradient.     

Ageing of random porous media following fluid deterministic displacement, freezing, thawing

This paper introduces and investigates a simple model of random porous media degradation via several fluid displacing, freezing, and thawing cycles. The fluid transport is based on the deterministic method. The result shows that the topology and the geometry of porous media have a strong effect on displacement processes. The cluster size of the viscous fingering (VF) pattern in the percolation cluster increases with the increase of iteration parameter n. When iteration parameter , the VF pattern does not change with n. When and , the peak value of the distribution increases as n increases; is the normalized distribution of throat sizes after different displacement-damage but before the freezing. The distribution of throat size N(r) after displacement but before freezing damage, shows that the major change, after successive cycles, happens at r>0.9. The peak value of the distribution reaches a maximum when and r=1, where is the normalized distribution of the size of invaded throats for different iterations. This result is different from invasion percolation. The distribution of velocities normal to the interface of VF in the percolation cluster is also studied. When , the scaling function distribution is very sharp. The sweep efficiency E increases along with the increasing of iteration parameter n and decreases with the network size L. And E has a minimum as L increases to the maximum size of the lattice. The VF pattern in the percolation cluster has one frozen zone and one active zone. Received 30 March 1999 and Received in final form 8 August 1999     

Macroscopic thermodynamics of flowing polymeric liquids

The thermodynamics and mechanics of non-isothermal polymeric fluids are examined within the auspices of a new methodology wherein the laws of physics and principles of mechanics which are applicable to these thermodynamic systems are imbedded in a definite mathematical structure of a general, abstract equation. Such a concept allows new insight to be obtained concerning some aspects of non-isothermal flows of polymeric fluids, and permits a consistent expression and interpretation of other thermodynamic theories for these systems which have been developed over the past forty years. A major portion of this article is devoted to demonstrating the above statements, and in so doing some common misconceptions occurring in a significant fraction of the literature regarding this subject are exposed. The definite mathematical structure of the new methodology permits the thermodynamically consistent generalization of isothermal, incompressible models of polymeric fluids to non-isothermal, compressible conditions. Doing thus reproduces, corrects, and extends non-isothermal models which have been developed over the years, and also allows for simpler (but equivalent) representations of these models in terms of alternate variables with a clearer connection to the microstructure of the material than the stress tensor and heat flux vector fields. Furthermore, a generalization of the GENERIC structure is proposed that accommodates interactions between phenomena of differing parities, which impose antisymmetry upon the corresponding elements of the dissipative operator matrix. Received: 28 July 1998 Accepted: 6 November 1998     

Horizontal laminar flow of coarse nearly-neutrally buoyant particles in non-Newtonian conveying fluids: CFD and PEPT experiments compared

The horizontal flow of coarse particle suspensions in non-Newtonian carrier fluids was numerically simulated using an Eulerian–Eulerian CFD model. This study was concerned with nearly-neutrally buoyant particles of 5 and 10 mm diameter conveyed by fluids of Ellis rheology in laminar flow, in a 45 mm diameter pipe at concentrations up to 41% v/v. CFD predictions of solid phase velocity profiles and passage times were compared to experimental data obtained by a Positron Emission Particle Tracking (PEPT) technique and Hall effect sensors, and a very good agreement was obtained considering the complexity of the flows studied. CFD predictions of solid–liquid pressure drop were compared to a number of relevant correlations gleaned from the literature. Only one of them showed a good agreement over the whole range of conditions studied. Other correlations generally showed large deviations from CFD, and their limitations in predicting the influence of solids concentration and particle size have been demonstrated. Overall, it emerged that for the flows studied, CFD was capable of giving predictions of pressure drop which were probably better and more reliable than the correlations available in the literature.     

Criticality and transition for a steady reactive plane couette flow of a viscous fluid

Numerical integration is used to determine critical and transitional values of parameters for steady, reactive, viscous, one dimensional plane Couette flow of an incompressible, homogeneous fluid of third-grade with the lower plate at rest while the upper is in uniform motion. The solutions are found for the following cases: (i) Bimolecular (ii) Arrhenius and (iii) Sensitized temperature dependence. Specifically, it is shown that the parameter Λ controlling the non-Newtonian fluid does not affect the flow velocity in any sense while the influence on the viscous dissipation parameter Γ is examined. The results obtained are then compared with similar results in the literature.