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

Sahwartiz, Leonard W.; DeGregoria, A. J.

doi:10.1017/s0334270000005890

Cited by 5 publications

(2 citation statements)

References 21 publications

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“…In fact, for the largest At values the fingering patterns resemble those more typically observed in immiscible flows. 35,36 This behavior perhaps points towards the presence of additional stresses due to the large local concentration, viscosity, and density gradients, which may introduce an effective surface tension between the miscible fluids. [24][25][26][27][28]30 Regarding this issue, cf.…”

Section: B Resultsmentioning

confidence: 99%

Miscible quarter five-spot displacements in a Hele-Shaw cell and the role of flow-induced dispersion

et al. 1999

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Miscible quarter five-spot displacements in a Hele-Shaw cell are investigated by means of experimental measurements and numerical simulations. The experiments record both the volumetric as well as the surface efficiency at breakthrough as a function of the dimensionless flow rate in the form of a Peclet number and the viscosity contrast. For small flow rates, both of these efficiency measures decrease uniformly with increasing Peclet numbers. At large flow rates, an asymptotic state is reached where the efficiencies no longer depend on the Peclet number. Up to Atwood numbers of approximately 0.5, the less viscous fluid occupies close to 23 of the gap width, which indicates a near-parabolic velocity profile across the gap. Consequently, in this parameter range a Taylor dispersion approach should be well suited to account for flow-induced dispersion effects. For larger viscosity contrasts, accompanying two-dimensional numerical simulations based on Taylor dispersion predict an increased stabilization for high flow rates, which is not confirmed by the experiments. This suggests that, in order to extend the range of applicability to larger viscosity contrasts, the components of the dispersion tensor will have to be amended in order to account for the presence of quasi-steady fingers.

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Section: B Resultsmentioning

confidence: 99%

Miscible quarter five-spot displacements in a Hele-Shaw cell and the role of flow-induced dispersion

et al. 1999

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“…Hele-Shaw [47]) describes the pressure of two immiscible viscous fluids trapped between two parallel glass plates and has attracted considerable attention in the literature, both on the analytical side [23,27,28,29,33,38,51,54,63] and on the numerical side [2,6,7,8,12,25,26,49,50,65]. This list of references also encompasses work related to the one-sided Hele-Shaw model, which arises as a limit when the viscosity of one of the fluids approaches zero.…”

Section: Introductionmentioning

confidence: 99%

A numerical scheme for moving boundary problems that are gradient flows for the area functional

Mayer

2000

Eur. J. Appl. Math

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Many moving boundary problems that are driven in some way by the curvature of the free boundary are gradient flows for the area of the moving interface. Examples are the Mullins-Sekerka flow, the Hele-Shaw flow, flow by mean curvature, and flow by averaged mean curvature. The gradient flow structure suggests an implicit finite differences approach to compute numerical solutions. The proposed numerical scheme will allow to treat such free boundary problems in both IR 2 and IR 3 . The advantage of such an approach is the re-usability of much of the setup for all of the different problems.As an example of the method we will compute solutions to the averaged mean curvature flow that exhibit the formation of a singularity. IntroductionIn this paper we will study geometric evolution problems for surfaces driven by curvature. These moving boundary problems arise from models in physics and the material sciences, and they describe phase changes, or more generally, phenomena in fluid flow.The Hele-Shaw model (named after H.S. ) describes the pressure of two immiscible viscous fluids trapped between two parallel glass plates and has attracted considerable attention in the literature, both on the analytical side [23,27,28,29,33,38,51,54,63] and on the numerical side [2,6,7,8,12,25,26,49,50,65]. This list of references also encompasses work related to the one-sided Hele-Shaw model, which arises as a limit when the viscosity of one of the fluids approaches zero. Furthermore, the Hele-Shaw model has classically been considered on a bounded domain, but many of the references above also address the problem on an unbounded domain. We shall only consider the problem on all of IR n ; for the precise formulation see (4.4).The Mullins-Sekerka model was first proposed by (and much later named after) Mullins and Sekerka to study solidification of materials of negligible specific heat [58]. For a while this model was also called the Hele-Shaw model, leading to a somewhat confused literature. Pego [61], and then Alikakos, Bates, and Chen [3], and also Stoth [68], established this model as a singular limit of the Cahn-Hilliard equation [17], a fourth order partial differential equation modelling nucleation and coarsening phenomena in a melted binary alloy. The Mullins-Sekerka model is considered to be a good model to describe the stage of Ostwald ripening in phase transitions, which is the stage after the initial nucleation has 2 U. F. Mayer essentially been completed and where some particles grow at the cost of others in an effort to decrease interfacial energy (surface area). The literature focuses mainly on the modelling and analytical aspects of the problem [11,16,18,19,21,32,34,46,56,66,71,72] though there are numerical simulations for the two-dimensional case [10,73]. We shall consider the two-phase problem on all of IR n , see (4.3).The mean curvature flow is probably the most studied geometric moving boundary problem, it is in some way also the simplest: the normal velocity is equal to the mean curvature of the interface. This sha...

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An experimental investigation of initial oscillations in a radial Hele-Shaw cell

Burns

Advani

1996

Experiments in Fluids

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Hele-Shaw cell is a laboratory device consisting of two parallel plates of glass separated by a thin gap. In this cell, in the flow of two immiscible fluids, when a fluid of higher viscosity is displaced by a fluid of lower viscosity, the less viscous fluid is observed to form "fingers" into the more viscous one due to the unstable interface. The Saffman-Taylor or viscous finger instability has been examined and modeled for over forty years for the rectilinear Hele-Shaw cell and about half as long for the radial Hele-Shaw cell. In this paper, we study, in detail, the early development of viscous instabilities in a radial Hele-Shaw cell. This source flow configuration has been chosen so that the instability can be monitored precisely. The objective of this study is to examine the onset of fingering, i.e. initial number of fingers that form, and the evolution of interface instability. Our experiments suggest that there may be some order in this formation process and one can model this aspect by considering the unsteady velocity components and predicting temporal changes in wavenumber responsible for the initial number of fingers and may be later accounting for the fingertip oscillations and splitting.We injected a water-based fluid into an oil in a radial Hele-Shaw cell at constant flow rate and recorded the movement of the less viscous droplet as it evolved. The relative curvature changes on the expanding droplet boundary was plotted with the angular positions about the interface and subtracting out the average radius, resulting in a plot of the change in amplitude with respect to time for the interface configuration. Three unstable configured tests at kinematic viscosity contrast (v ~ of 0.34, 0.68, and 0.94 were run at approximately the same flow rate (2~z cm2/s). The droplet exhibited oscillatory movement for these unstable configuration. The amplitude and the rate of oscillations were measured from digitized data. The smaller the viscosity difference, the

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

Cited by 5 publications

References 21 publications

Miscible quarter five-spot displacements in a Hele-Shaw cell and the role of flow-induced dispersion

Miscible quarter five-spot displacements in a Hele-Shaw cell and the role of flow-induced dispersion

A numerical scheme for moving boundary problems that are gradient flows for the area functional

An experimental investigation of initial oscillations in a radial Hele-Shaw cell

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