Radial Hele-Shaw Cell Research Articles

S0501-2-4 高分子流体を用いた、化学反応により引き起こされるViscous fingeringの実験研究([S0501-2 ]複雑流体の流動現象(2))

The term "Viscous fingering" is usually used to refer to the instabilities that occur at the interface when a more viscous fluid is displaced by a less viscous fluid.However, we succeed an experimental study of viscous fingering fully triggered by a chemical reaction involving a viscosity increase and decrease when a less viscous fluid is displaced by a more viscous fluid in a radial Hele-Shaw cell. This is done by making use of a polymer (polyacrylic acid , sodium polyacrylate) solution's dependence of viscosity on pH. We show that a difference in fingering patterns is observed, depending on whether the viscosity is increased or decreased by the reactions.

Experimental investigation of the onset of instability in a radial Hele-Shaw cell

The initial stage of interface instability upon radial displacement of a fluid in a Hele-Shaw cell is investigated. An air-silicone oil system is analyzed. The critical radii of stability relative to long-wave perturbations are determined. It is found that, in the investigated range of parameters, instability most often begins by a translational mechanism. It is ascertained that in the overwhelming majority of cases the critical radii of instability are smaller than the values predicted by the linear stability theory and external effects make this difference even greater. The obtained results are discussed and compared with the existing theories.

An experimental study of non-isothermal miscible displacements in a Hele-Shaw cell

Non-isothermal miscible displacements in a radial Hele-Shaw cell were experimentally investigated using a scheme in which room temperature liquids of relatively high viscosity were displaced by high-temperature (80 °C), less-viscous liquids. Fundamental characteristics have been presented regarding how the effect of a non-isothermal field on miscible displacement patterns varies in terms of factors such as the viscosity ratio of the more- and less-viscous liquids at 20 °C, M 20, the rate of an increase in the pattern’s area, R, and the gap width of the cell, b. The concept of area density was used to quantitatively evaluate the effect of the non-isothermal fields on the patterns. We have found that the effect of the non-isothermal field on the patterns does not monotonically vary with M 20 and b. In contrast, it increases with R in the present experimental condition. The experimental results can be explained by introducing an assumption in which heat is transferred mainly to the plates of the cell, in other words, the temperature of the more-viscous liquid remains constant, whereas that of the less-viscous liquid spatiotemporally decreases and the viscosity of it increases along with the temperature decrease. Visualization of non-isothermal field in the cell has been done by means of a thermo sheet and the results support the assumption mentioned above.

Spiral pattern in a radial displacement involving a reaction-producing gel

We have shown experimentally that the pattern created by the displacement of a more viscous fluid by a less viscous one in a radial Hele-Shaw cell develops not radially but spirally when a more viscous sodium polyacrylate solution is displaced by a less viscous trivalent iron ion (Fe3+) solution with a sufficiently high concentration of Fe3+ . Another experiment revealed that an instantaneous chemical reaction takes place between the two fluids, and at high Fe3+ concentrations it produces a film of the gel at the contact plane. The gel film is proposed to be responsible for the spiral pattern.

Radial viscous fingering in miscible Hele-Shaw flows: A numerical study

A modified version of the usual viscous fingering problem in a radial Hele-Shaw cell with immiscible fluids is studied by intensive numerical simulations. We consider the situation in which the fluids involved are miscible, so that the diffusing interface separating them can be driven unstable through the injection or suction of the inner fluid. The system is allowed to rotate in such a way that centrifugal and Coriolis forces come into play, imposing important changes on the morphology of the arising patterns. In order to bridge from miscible to immiscible pattern forming structures, we add the surface tensionlike effects due to Korteweg stresses. Our numerical experiments reveal a variety of interesting fingering behaviors, which depend on the interplay between injection (or suction), diffusive, rotational, and Korteweg stress effects. Whenever possible the features of the simulated miscible fronts are contrasted to existing experiments and other theoretical or numerical studies, usually resulting in close agreements. A number of additional complex morphologies, whose experimental realization is still not available, are predicted and discussed.

Experimental study on miscible viscous fingering involving viscosity changes induced by variations in chemical species concentrations due to chemical reactions

When a reactive and miscible less-viscous liquid displaces a more-viscous liquid in a Hele-Shaw cell, reactive miscible viscous fingering takes place. We succeed in showing experimentally how a reactive miscible viscous fingering pattern in a radial Hele-Shaw cell changes when the viscosity of the more-viscous liquid is varied owing to variation in chemical species concentration induced by an instantaneous chemical reaction. This is done by making use of a polymer solution's dependence of viscosity on pH. When the viscosity is increased by the chemical reaction, the shielding effect is suppressed and the fingers are widened. As a result, the ratio of the area occupied by the fingering pattern in a circle whose radius is the length of the longest finger is larger in the reactive case than in the non-reactive case. When the viscosity is decreased by the chemical reaction, in contrast, the shielding effect is enhanced and the fingers are narrowed. These lead to the area ratio being smaller in the reactive case than in the non-reactive case. A physical model to explain this change in the fingering pattern caused by the chemical reaction is proposed.

Pattern formation during air injection into granular materials confined in a circular Hele-Shaw cell

We investigate the dynamics of granular materials confined in a radial Hele-Shaw cell, during central air injection. The behavior of this granular system, driven by its interstitial fluid, is studied both experimentally and numerically. This allows us to explore the associated pattern formation process, characterize its features and dynamics. We classify different hydrodynamic regimes as function of the injection pressure. The numerical model takes into account the interactions between the granular material and the interstitial fluid, as well as the solid-solid interactions between the grains and the confining plates. Numerical and experimental results are comparable, both to reproduce the hydrodynamical regimes experimentally observed, as well as the dynamical features associated to fingering and compacting.

Numerical simulations of a viscous-fingering instability in a fluid with a temperature-dependent viscosity

We have performed numerical simulations of the flow of hot glycerine as it displaces colder, more viscous glycerine in a radial Hele–Shaw cell. We find that fingering occurs for sufficiently high inlet velocities and viscosity ratios. The wavelength of the instability is independent of inlet velocity and viscosity ratio, but depends weakly on cell width. The growth rate of the fingers is found to increase with inlet velocity and decrease with the cell width. We compare our results with those from experiments.PACS No.: 47.54.–r

Viscous fingering with a single fluid

We study fingering that occurs when hot glycerine displaces cooler, more viscous glycerine in a radial Hele-Shaw cell. We find that fingering occurs for a sufficiently large initial viscosity contrast and for sufficiently high flow rates of the displacing fluid. The wavelength of the fingering instability is proportional to the cell width for thin cells, but the ratio of wavelength to cell width decreases for our thickest cell. Similar fingering is seen in numerical simulations of this system.PACS Nos.: 47.54.+r, 68.15.+e, 47.20.–k

Magnetic field effects on viscous fingering of a ferrofluid in a radial Hele–Shaw cell

We have studied the effects of a magnetic field on viscous fingering when a ferrofluid is pushed in a more viscous liquid in a circular Hele–Shaw cell. The main effect of the magnetic field, as already known, is to stabilize interfaces parallel to the field and to destabilize interfaces normal to the field. Depending on the growth regime (quasi static, fingering, dendritic growth), which depends on parameters like the cell thickness and oil viscosity, the combination of field effect and anisotropy is analyzed through the various observed patterns.

Viscous fingering instabilities in an oil in water emulsion

Viscous fingering of an emulsion in which silicone oil is dispersed in aqueous polymer solution was investigated in a radial Hele-Shaw cell by the injection of water and the aqueous polymer solution as a function of the injection rate. The pressure imposed at the finger tip was simultaneously monitored. The crack-like fingering patterns are observed at the lower injection rates and they start to grow when the imposed pressure attains the maximum value. An increase in the injection rate causes the pattern transition from the crack pattern to ramified ones. Such a pattern transition is strongly related to rheological properties of the emulsion.

Scaling anomalies in the coarsening dynamics of fractal viscous fingering patterns.

We analyze a recent experiment of Sharon et al. (2003) on the coarsening, due to surface tension, of fractal viscous fingering patterns (FVFPs) grown in a radial Hele-Shaw cell. We argue that an unforced Hele-Shaw model, a natural model for that experiment, belongs to the same universality class as model B of phase ordering. Two series of numerical simulations with model B are performed, with the FVFPs grown in the experiment and with diffusion limited aggregates as the initial conditions. We observed Lifshitz-Slyozov scaling t(1/3) at intermediate distances and slow convergence to this scaling at small distances. Dynamic scale invariance breaks down at large distances.

Low viscosity contrast fingering in a rotating Hele-Shaw cell

We study the fingering instability of a circular interface between two immiscible liquids in a radial Hele-Shaw cell. The cell rotates around its vertical symmetry axis, and the instability is driven by the density difference between the two fluids. This kind of driving allows studying the interfacial dynamics in the particularly interesting case of an interface separating two liquids of comparable viscosity. An accurate experimental study of the number of fingers emerging from the instability reveals a slight but systematic dependence of the linear dispersion relation on the gap spacing. We show that this result is related to a modification of the interface boundary condition which incorporates stresses originated from normal velocity gradients. The early nonlinear regime shows nearly no competition between the outgrowing fingers, characteristic of low viscosity contrast flows. We perform experiments in a wide range of experimental parameters, under conditions of mass conservation (no injection), and characterize the resulting patterns by data collapses of two characteristic lengths: the radius of gyration of the pattern and the interface stretching. Deep in the nonlinear regime, the fingers which grow radially outwards stretch and become gradually thinner, to a point that the fingers pinch and emit drops. We show that the amount of liquid emitted in the first generation of drops is a constant independent of the experimental parameters. Further on there is a sharp reduction of the amount of liquid centrifugated, punctuated by periods of no observable centrifugation.

Systematic weakly nonlinear analysis of radial viscous fingering.

We present a weakly nonlinear analysis of the interface dynamics in a radial Hele-Shaw cell driven by both injection and rotation. We extend the systematic expansion introduced in [E. Alvarez-Lacalle et al., Phys. Rev. E 64, 016302 (2001)] to the radial geometry, and compute explicitly the first nonlinear contributions. We also find the necessary and sufficient condition for the uniform convergence of the nonlinear expansion. Within this region of convergence, the analytical predictions at low orders are compared satisfactorily to exact solutions and numerical integration of the problem. This is particularly remarkable in configurations (with no counterpart in the channel geometry) for which the interplay between injection and rotation allows that condition to be satisfied at all times. In the case of the purely centrifugal forcing we demonstrate that nonlinear couplings make the interface more unstable for lower viscosity contrast between the fluids.

Room‐Temperature Synthesis of Aragonite Crystals at an Expanding Liquid–Liquid Interface in a Radial Hele–Shaw Cell

Large quantities of extremely fine aragonite needles (see Figure, top image) have been synthesized at room temperature at an expanding liquid–liquid interface in a radial Hele–Shaw cell. By simple variation of the experimental conditions, hollow, cylindrical aragonite/calcite crystals (see Figure, bottom image) may also be obtained. It is believed that this method can be extended to other materials and nanostructures.

BaSO4 Crystals Grown at an Expanding Liquid−Liquid Interface in a Radial Hele-Shaw Cell Show Spontaneous Large-Scale Assembly into Filaments

Control over the crystallography, morphology, and spontaneous organization of ceramic crystals are important goals in advanced materials engineering with important application potential. Most studies hitherto have concentrated on static charged interfaces as templates for the controlled nucleation and growth of ceramic crystals. In this communication, we show that BaSO4 crystals grown at a steadily expanding liquid−liquid interface populated by fatty acid molecules spontaneously organize themselves into highly linear superstructures over large length-scales. This experiment is realized in a radial Hele-Shaw cell where the liquid−liquid interfacial growth rate and consequently time scales such as arrival of surfactant molecules to the interface etc. may be readily modulated. Possible reasons for the regular assembly of barite crystals are discussed.

Viscous fingering with chemical reaction: effect of in-situ production of surfactants

Viscous fingering experiments are performed in a radial Hele-Shaw cell for a liquid–liquid system in the presence of a well-characterized interfacial reaction capable of changing the surface tension on the time scale of the experiments. The reaction is a neutralization of a fatty acid by an alkaline material to form a surfactant, which exhibits first-order kinetics for the surface tension as a function of time. The experiments are carried out for capillary numbers, , the reactive fingering patterns are similar to the fingers with no reaction: the fractal dimension is found to be the same for both systems. These effects are consistent with the hypothesis that Marangoni stresses are present and produce wider fingers.

Mode-coupling approach to non-Newtonian Hele-Shaw flow.

The Saffman-Taylor viscous fingering problem is investigated for the displacement of a non-Newtonian fluid by a Newtonian one in a radial Hele-Shaw cell. We execute a mode-coupling approach to the problem and examine the morphology of the fluid-fluid interface in the weak shear limit. A differential equation describing the early nonlinear evolution of the interface modes is derived in detail. Owing to vorticity arising from our modified Darcy's law, we introduce a vector potential for the velocity in contrast to the conventional scalar potential. Our analytical results address how mode-coupling dynamics relates to tip splitting and sidebranching in both shear-thinning and shear-thickening cases. The development of non-Newtonian interfacial patterns in rectangular Hele-Shaw cells is also analyzed.

Flow Patterns of Polymer Solutions Injected into Dispersions of Bentonite

Abstract The flow behaviour of colloidal dispersions is largely influenced by the interactions between the dispersed particles. We studied the influence of either natural or synthetic polyelectrolytes solutions on flow patterns within colloidal clay dispersion. For this purpose, highly diluted aqueous polymer solutions were intruded into a radial Hele-Shaw cell filled with montmorillonite dispersions. The developing flow patterns were recorded with a high resolution digital camera. The morphological parameters: fractal dimension, total number of branching, branching density of the patterns, compactness and form were obtained by digital image analysis. The results show that the patterns are largely affected by the different polymers.

Periodic forcing in viscous fingering of a nematic liquid crystal

Viscous fingering of an air-nematic interface in a radial Hele-Shaw cell is studied when periodically switching on and off an electric field, which reorients the nematic and thus changes its viscosity, as well as the surface tension and its anisotropy (mainly enforced by a single groove in the cell). Undulations at the sides of the fingers are observed that correlate with the switching frequency and with tip oscillations that give maximal velocity to smallest curvatures. These lateral undulations appear to be decoupled from spontaneous (noise induced) side branching. It is concluded that the lateral undulations are generated by successive relaxations between two limiting finger widths. The change between these two selected pattern scales is mainly due to the change in the anisotropy. This scenario is confirmed by numerical simulations in the channel geometry, using a phase-field model for anisotropic viscous fingering.