scholarly journals Two-phase flow in Hele-Shaw cells: numberical studies of sweep efficiency in a five-spot pattern

1988 ◽  
Vol 29 (4) ◽  
pp. 375-400 ◽  
Author(s):  
Leonard W. Sahwartiz ◽  
Anthony J. Degregoria
Keyword(s):  
Dimensionless Parameter ◽  
Viscosity Ratio ◽  
Nonlinear Behavior ◽  
Boundary Integral ◽  
Porous Media Flow ◽  
Sweep Efficiency ◽  
Two Phase ◽  
Production Wells ◽  
Range Of Values

AbstractThe unsteady Hele-Shaw problem is a model nonlinear system that, for a certain parameter ranger, exhibits the phenomenon known as viscous fingering. While not directly applicable to multiphase porous-media flow, it does prove to be an adequate mathematical model for unstable dieplacement in laboratory parallel-plate devices. We seek here to determine, by use of an accurate boundary-integral frount-tracking scheme, the extent to which the simplified system captures the canonical nonlinear behavior of displacement flows and, in particular, to ascertain the role of noise in such systems. We choose to study a particular pattern of injection and production “wells.” The pattern chosen is the isolated “five-spot,” that is a single source surrounded by four symmetrically-placed sinks in an infinite two-dimensional “reservoir.” In cases where the “pusher” fluid has negligible viscosity, sweep efficiency is calculated for a range of values of the single dimensionless parameter τ, an inverse capillary number. As this parameter is reduced, corresponding to increased flow rate or reduced interfacial tension, this efficiency decreases continuously. For small values of τ, these stable displacements change abruptly to a regime characterized by unstable competing fingers and a significant reduction in sweep efficiency. A simple stability argument appears to correctly predict the noise level required to transit from the stable to the competing-finger regimes. Published compilations of experimental results for sweep efficiency as a function of viscosity ratio showed an unexplained divergence when the pusher fluid is less viscous. Our simulations produce a similar divergence when, for a given viscosity ratio, the parameter τ is varied.

scholarly journals The Role of Elasticity in the Vortex Formation in Polymeric Flow around a Sharp Bend

2021 ◽  
Vol 11 (14) ◽  
pp. 6588
Author(s):  
Brian Wojcik ◽  
Jason LaRuez ◽  
Michael Cromer ◽  
Larry A. Villasmil Urdaneta
Keyword(s):  
Newtonian Fluid ◽  
Viscosity Ratio ◽  
Fluid Dynamic ◽  
Flow Behavior ◽  
Weissenberg Number ◽  
Base Case ◽  
Dimensionless Numbers ◽  
Two Phase ◽  
Elasticity Number

Fluid dynamic simulations using the FENE-P model of polymer physics are compared to those of an incompressible Newtonian fluid base case in order to understand the role of elasticity in the formation of vortices in a 90° bend narrow channel. The analysis bridges the flow behavior of a purely elastic fluid and that of a Newtonian fluid. We evaluated how four dimensionless numbers—Reynolds number (Re), Weissenberg number (Wi), viscosity ratio (β), and elasticity number (El)—affect the formation of vortices. It is shown that increasing Re and Wi, or lowering β will cause vortices to grow in size. Two phase space diagrams, β vs. El and β vs. Re, were created to show the range of values where inertial and elastic vortices form. Both diagrams have three zones. Depending on the polymer viscosity ratio and the elasticity number, the vortices form either upstream of the bend (elasticity driven) or form downstream of the bend (inertia driven), are suppressed. Our predictions are in good agreement with previous experimental and numerical works.

scholarly journals The role of interfaces on dynamic damage in two phase metals

2012 ◽  
Author(s):  
Ellen Cerreta ◽  
Saryu Fensin ◽  
Juan P. Escobedo ◽  
George Thompson Gray III ◽  
Adam Farrow ◽  
...  
Keyword(s):  
Two Phase ◽  
Dynamic Damage

Role of the Interphase in the Interfacial Flow Stability in Coextrusion of Compatible Multilayered Polymers

2013 ◽  
Vol 554-557 ◽  
pp. 1738-1750 ◽  
Author(s):  
Hua Gui Zhang ◽  
Khalid Lamnawar ◽  
Abderrahim Maazouz
Keyword(s):  
Shear Stress ◽  
Viscosity Ratio ◽  
Flow Instability ◽  
Interfacial Shear Stress ◽  
Flow Stability ◽  
Interfacial Shear ◽  
Interfacial Instability ◽  
Interfacial Flow ◽  
Rheological Modeling

This work aims to highlight the importance of interphase triggered from interdiffusion at neighboring layers on controlling the interfacial flow instability of multilayer coextrusion based on a compatible bilayer system consist of poly(methyl methacrylate) (PMMA) and poly(vinylidene fluoride) (PVDF) melt streams. A fundamental rheological measurement on the bilayer structures provides a good strategy to probe the mutual diffusion process occurred at neighboring layers and to quantify the rheology and thickness of the interphase generated thereof. By implementing steady shear measurements on the multilayer’s, subtle interfacial slippage can be observed at a condition of short welding time and rather high shear rate due to the disentanglement of chains at the interphase. Pre-shear at an early stage on the multilayer was found to greatly promote the homogenizing process by inducing branched structures and hence increasing interfacial area. In coextrusion, some key classical decisive parameters concerning the interfacial instability phenomena such as viscosity ratio, thickness ratio and elasticity ratio, etc. were highlighted. These key factors that are significant in controlling the interfacial stability of coextrusion in an incompatible system seem not that important in a compatible system. In comparison to the severe flow instability observed in the coextrusion of PMMA/PE incompatible bilayer, the coextrusion of PMMA/PVDF compatible bilayer appears to be smooth without apparent interfacial flow instability due to the presence of the interphase. Interdiffusion can reduce (even eliminate) the interfacial flow instability of coextrusion despite of the very high viscosity ratio of PVDF versus PMMA at low temperatures. Indeed, in the coextrusion process, on one hand, the interdiffusion should be studied by taking into account of the effect of polymer chain orientation which was demonstrated to decelerate the diffusion coefficient. On the other hand, the interfacial shear stress was able to promote mixing and homogenizing process at the interface, which favours the development of the interphase and guarantees the stable interfacial flow. The degree of the interphase is related to a lot of parameters like contact time, processing temperature, interfacial shear stress and compatibility of the polymers, etc. Therefore, apart from the classical mechanical parameters, the interphase created from the interdiffusion should be taken into consideration as an important factor on determining the interfacial instability phenomena. References [1] H. Zhang, K. Lamnawar, A. Maazouz, Rheological modeling of the diffusion process and the interphase of symmetrical bilayers based on PVDF and PMMA with varying molecular weights. Rheol. Acta 51 (2012) 691-711 [2] H. Zhang, K. Lamnawar, A. Maazouz, Rheological modeling of the mutual diffusion and the interphase development for an asymmetrical bilayer based on PMMA and PVDF model compatible polymers, Macromolecules (2012), Doi: http://dx.doi.org/10.1021/ma301620a [3] H. Zhang, K. Lamnawar, A. Maazouz, Role of the interphase in the interfacial flow stability of multilayer coextrusion based on PMMA and PVDF compatible polymers, to be submitted. [4] K. Lamnawar, A. Maazouz, Role of the interphase in the flow stability of reactive coextruded multilayer polymers, Polymer Engineering & Science, 49, (2009), 727 - 739 [5] K. Lamnawar, H. Zhang, A. Maazouz, one chapter” State of the art in co-extrusion of multilayer polymers: experimental and fundamental approaches” in Encyclopedia of Polymer Science and Technology (wiley library) (feature article)

Microstructure of Polycrystalline MgO Penetrated by a Silicate Liquid

1996 ◽  
Vol 2 (3) ◽  
pp. 113-128 ◽  
Author(s):  
Sundar Ramamurthy ◽  
Michael P. Mallamaci ◽  
Catherine M. Zimmerman ◽  
C. Barry Carter ◽  
Peter R. Duncombe ◽  
...  
Keyword(s):  
Grain Boundaries ◽  
Grain Growth ◽  
Glassy Phase ◽  
Silicate Liquid ◽  
Two Phase ◽  
The Matrix ◽  
Devitrification Process ◽  
Phase Mixture

Dense, polycrystalline MgO was infiltrated with monticellite (CaMgSiO4) liquid to study the penetration of liquid along the grain boundaries of MgO. Grain growth was found to be restricted with increasing amounts of liquid. The inter-granular regions were generally found to be comprised of a two-phase mixture: crystalline monticellite and a glassy phase rich in the impurities present in the starting MgO material. MgO grains act as seeding agents for the crystallization of monticellite. The location and composition of the glassy phase with respect to the MgO grains emphasizes the role of intergranular liquid during the devitrification process in “snowplowing” impurities present in the matrix.

Intence Atmospheric Vortices. Edited by L. BENGTSSON and J. LIGHTHILL. Springer, 1982. 326 pp. DM56.- (soft cover). Stability of Thermodynamic Systems. Edited by J. CASAS-VÁZQUEZ and G. LEBON. Springer, 1982. 321 pp. DM 38.- (soft cover). Stability of Mechanics of Continua. Edited by F. H. SCHROEDER. Springer, 1982. 412 pp. DM89.- (hardback). Mécanique Expérimentale des Fluides. Vol. II: Dynamique des Fluids Réels, Turbomachines, 3rd edn. By R. COMOLET. Masson, 1982. 453 pp. FF305.- (soft cover). Engineering Meteorology. Edited by E. PLATE, Elsevier, 1982. 740 pp. $162.75. The Boundary Integral Equation Method for Porous Media Flow. By J. A. LIGGETT and P. L-F. LIU. Allen & Unwin, 1983. 255 pp. £20 (hardback). Methods of Experimental Physics: vol. 18, Fluid Dynamics, Part A. Edited by R. J. EMRICH. Academic, 1981. 404 pp. $50.00 (hardback). Flow, its Measurement and Control in Science and Industry: vol. 2, 1981. Edited by WILLIAM W. DURGIN. Wiley, 1981. 867 pp. £45.75. Flow Visualization II. Edited by W. MERZKIRCH. Hemisphere, 1982. 803 pp. $90.00. Evaporation into the Atmosphere. By W. H. BRUTSAERT. Reidel, 1981. 340 pp. $34.95 Industrial Heat Exchangers: a basic guide. By G. WALKER. Hemisphere, 1982. 408 pp. $41.50. Engineering Fluid Mechanics (with separate Solution manual). By A. MIRONER. McGraw Hill, 1979. 592 pp. £28.50 (cloth), £7.50 (paperback). Unsteady Turbulent Shear Flows. Edited by R. MICHEL, J. COUSTEIX and R. HOUDEVILLE. Springer, 1981, 424 pp. $39.00.

1984 ◽  
Vol 138 ◽  
pp. 436-439
Keyword(s):  
Fluid Dynamics ◽  
Heat Exchangers ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Porous Media Flow ◽  
Turbulent Shear ◽  
Experimental Physics ◽  
And Control ◽  
Atmospheric Vortices ◽  
Measurement And Control

Role of activation energies of individual phases in two-phase range on constitutive equation of Zr–2.5Nb–0.5Cu alloy

2017 ◽  
Vol 27 (1) ◽  
pp. 172-183 ◽  
Author(s):  
K.K. SAXENA ◽  
S.K. JHA ◽  
V. PANCHOLI ◽  
G.P. CHAUDHARI ◽  
D. SRIVASTAVA ◽  
...  
Keyword(s):  
Constitutive Equation ◽  
Activation Energies ◽  
Two Phase ◽  
Phase Range

On the Role of Nonlinearity in the Dynamic Behavior of Rubber Components

1986 ◽  
Vol 59 (5) ◽  
pp. 740-764 ◽  
Author(s):  
J. Harris ◽  
A. Stevenson
Keyword(s):  
Dynamic Behavior ◽  
Nonlinear Behavior ◽  
Material Composition ◽  
Geometrical Design ◽  
Linear Spring ◽  
Case Design

Abstract This paper has discussed the transmissibility behavior of rubber mounts with reference to nonlinearity originating from the material composition and from the geometrical design. It has been shown that in many cases, linear assumptions can be made, provided the limitations of these assumptions are understood. In this case, design can proceed as for a linear spring. Finally, there is some indication of how the nonlinear behavior can be exploited to advantage in the design of novel suspension components.

Viscous Flows Involving a Liquid-Vapor Compound Droplet

2001 ◽  
Author(s):  
D. Palaniappan
Keyword(s):  
Exact Solutions ◽  
Viscosity Ratio ◽  
Numerical Algorithms ◽  
Flow Fields ◽  
Continuous Phase ◽  
Boundary Integral ◽  
Liquid Volume ◽  
Drag Forces ◽  
Compound Droplet ◽  
Fluid Interactions

Abstract Exact analytical solutions for steady-state axisymmetric creeping flows in and around a compound multiphase droplet are presented. The solutions given here explain the droplet fluid interactions in uniform and nonuniform flow fields. The compound droplet has a two-sphere geometry with the two spherical surfaces (of unequal radii) intersecting orthogonally. The surface tension forces are assumed to be sufficiently large so that the interfaces have uniform curvature. The singularity solutions for the uniform and paraboloidal flows in the presence of a compound droplet are derived using the method of reflections. The exact solutions for the velocity and pressure fields in the continuous and dispersed phases are given in terms of the fundamental singularities (Green’s functions) and their derivatives. It is found that flow fields and the drag forces depend on two parameters namely, the viscosity ratio and the radii ratio. In the case of paraboloidal flows, a single or a pair of eddies is noticed in the continuous phase for various values of these parameters. The eddies changes their size and shape if the size of the droplet is altered. These observations may be useful in the study of hydrodynamic interactions of compound droplets in complex situations. It is found that the Stokes resistance is greater when the liquid volume is large compared to the vapor volume in uniform flow. It is also noticed that the maximum value of the drag in paraboloidal flow depends on the viscosity ratio and significantly on the liquid volume in the dispersed phase. The exact solutions presented here may be useful for boundary integral formulations that are based on special kernels and also in validating numerical algorithms and codes on multiphase flow and droplet-fluid interactions.

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