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A Hernández-Machado

Publications and source records attributed to A Hernández-Machado.

At least 19 recordsLinked to original sources
PubMed2006

Intrinsic versus superrough anomalous scaling in spontaneous imbibition.

We study spontaneous imbibition using a phase field model in a two-dimensional system with a dichotomic quenched noise. By imposing a constant pressure mu(a)<0 at the origin, we study the case when the interface advances at low velocities, obtaining the scaling exponents z=3.0+/-0.1, alpha=1.50+/-0.02, and alpha(loc)=0.95+/-0.03 within the intrinsic anomalous scaling scenario. These results are in quite good agreement with experimental data recently published. Likewise, when we increase the interface velocity, the resulting scaling exponents are z=4.0+/-0.1, alpha=1.25+/-0.02, and alpha(loc)=0.95+/-0.03. Moreover, we observe that the local properties of the interface change from a superrough to an intrinsic anomalous description when the contrast between the two values of the dichotomic noise is increased. From a linearized interface equation we can compute analytically the global scaling exponents which are comparable to the numerical results, introducing some properties of the quenched noise.

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PubMed2006

Phase field approach to spatial perturbations in normal Saffman-Taylor fingers.

We make a numerical study of the effect that spatial perturbations have in normal Saffman-Taylor fingers driven at constant pressure gradients. We use a phase field model that allows for spatial variations in the Hele-Shaw cell. We find that, regardless of the specific way in which spatial perturbations are introduced, a lateral instability develops on the sides of the propagating Saffman-Taylor finger. Moreover, the instability exists regardless of the intensity of spatial perturbations in the cell as long as the perturbations are felt by the finger tip. If, as the finger propagates, the spatial perturbations felt by the tip change, the instability is nonperiodic. If, as the finger propagates, the spatial perturbations felt by the tip are persistent, the instability developed is periodic. In the later case, the instability is symmetrical or asymmetrical depending on the intensity of the perturbation.

Journal Article↗
PubMed2006

Dynamic model and stationary shapes of fluid vesicles.

A phase-field model that takes into account the bending energy of fluid vesicles is presented. The Canham-Helfrich model is derived in the sharp-interface limit. A dynamic equation for the phase-field has been solved numerically to find stationary shapes of vesicles with different topologies and the dynamic evolution towards them. The results are in agreement with those found by minimization of the Canham-Helfrich free energy. This fact shows that our phase-field model could be applied to more complex problems of instabilities.

Computer Simulation↗
PubMed2006

Fluctuations in Saffman-Taylor fingers with quenched disorder.

We make an experimental characterization of the effect that static disorder has on the shape of a normal Saffman-Taylor finger. We find that static noise induces a small amplitude and long wavelength instability on the sides of the finger. Fluctuations on the finger sides have a dominant wavelength, indicating that the system acts as a selective amplifier of static noise. The dominant wavelength does not seem to be very sensitive to the intensity of static noise present in the system. On the other hand, at a given flow rate, rms fluctuations of the finger width, decrease with decreasing intensity of static noise. This might explain why the sides of the fingers are flat for typical Saffman-Taylor experiments. Comparison with previous numerical studies of the effect that temporal noise has on the Saffman-Taylor finger, leads to conclude that the effect of temporal noise and static noise are similar. The behavior of fluctuations of the finger width found in our experiments, is qualitatively similar to one recently reported, in the sense that, the magnitude of the width fluctuations decays as a power law of the capillary number, at low flow rates, and increases with capillary number for larger flow rates.

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PubMed2005

Anomalous roughening of viscous fluid fronts in spontaneous imbibition.

We report experiments on spontaneous imbibition of a viscous fluid by a model porous medium in the absence of gravity. The average position of the interface satisfies Washburn's law. Scaling of the interface fluctuations suggests a dynamic exponent z approximately 3, indicative of global dynamics driven by capillary forces. The complete set of exponents clearly shows that interfaces are not self-affine, exhibiting distinct local and global scaling, both for time (beta = 0.64 +/- 0.02, beta(*) = 0.33 +/- 0.03) and space (alpha = 1.94 +/- 0.20, alpha(loc) = 0.94 +/- 0.10). These values are compatible with an intrinsic anomalous scaling scenario.

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PubMed2005

Side-branch growth in two-dimensional dendrites. II. Phase-field model.

The development of side-branching in solidifying dendrites in a regime of large values of the Peclet number is studied by means of a phase-field model. We have compared our numerical results with experiments of the preceding paper and we obtain good qualitative agreement. The growth rate of each side branch shows a power-law behavior from the early stages of its life. From their birth, branches which finally succeed in the competition process of side-branching development have a greater growth exponent than branches which are stopped. Coarsening of branches is entirely defined by their geometrical position relative to their dominant neighbors. The winner branches escape from the diffusive field of the main dendrite and become independent dendrites.

Journal Article↗
PubMed2005

Side-branch growth in two-dimensional dendrites. I. Experiments.

The dynamics of growth of dendrites' side branches is investigated experimentally during the crystallization of solutions of ammonium bromide in a quasi-two-dimensional cell. Two regimes are observed. At small values of the Peclet number a self-affine fractal forms. In this regime it is known that the mean lateral front grows as t(0.5). Here the length of each individual branch is shown to grow (before being screened off) with a power-law behavior t (alpha(n)). The value of the exponent alpha(n) (0.5< or = alpha(n) < or =1) is determined from the start by the strength of the initial disturbance. Coarsening then takes place, when the branches of small alpha(n) are screened off by their neighbors. The corresponding decay of the growth of a weak branch is exponential and defined by its geometrical position relative to its dominant neighbors. These results show that the branch structure results from a deterministic growth of initially random disturbances. At large values of the Peclet number, the faster of the side branches escape and become independent dendrites. The global structure then covers a finite fraction of the two-dimensional space. The crossover between the two regimes and the spacing of these independent branches are characterized.

Journal Article↗
PubMed2005

Lateral instability in normal viscous fingers.

We study a low-amplitude, long-wavelength lateral instability of the Saffman-Taylor finger by means of a phase-field model. We observe such an instability in two situations in which small dynamic perturbations are overimposed to a constant pressure drop. We first study the case in which the perturbation consists of a single oscillatory mode and then a case in which the perturbation consists of temporal noise. In both cases the instability undergoes a process of selection.

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PubMed2003

Phase-field model of Hele-Shaw flows in the high-viscosity contrast regime.

A one-sided phase-field model is proposed to study the dynamics of unstable interfaces of Hele-Shaw flows in the high viscosity contrast regime. The corresponding macroscopic equations are obtained by means of an asymptotic expansion from the phase-field model. Numerical integrations of the phase-field model in a rectangular Hele-Shaw cell reproduce finger competition with the final evolution to a steady-state finger.

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PubMed2003

Anomalous roughening in experiments of interfaces in Hele-Shaw flows with strong quenched disorder.

We report experimental evidence of anomalous kinetic roughening in the stable displacement of an oil-air interface in a Hele-Shaw cell with strong quenched disorder. The disorder consists of a random modulation of the gap spacing that is transverse to the growth direction (tracks). Experiments were performed by varying the average interface velocity and the gap spacing, and measuring the scaling exponents. The following values of the scaling exponents were obtained; beta approximately 0.50, beta* approximately 0.25, alpha approximately 1.0, alpha(loc) approximately 0.5, and z approximately 2. When there is no fluid injection, the interface is driven solely by capillary forces, and a higher value of beta of approximately beta=0.65 is measured. The presence of multiscaling and the particular morphology of the interfaces, characterized by large height differences that follow a Lévy distribution, confirms the existence of anomalous scaling. From a detailed study of the motion of the oil-air interface, we show that the anomaly is a consequence of different local velocities on the tracks plus the coupling in the motion between neighboring tracks. The anomaly disappears at high interface velocities, weak capillary forces, or when the disorder is not sufficiently persistent in the growth direction. We have also observed the absence of scaling when the disorder is very strong or when a regular modulation of the gap spacing is introduced.

Journal Article↗
PubMed2002

Experiments of interfacial roughening in Hele-Shaw flows with weak quenched disorder.

We have studied the kinetic roughening of an oil-air interface in a forced imbibition experiment in a horizontal Hele-Shaw cell with quenched disorder. Different disorder configurations, characterized by their persistence length in the direction of growth, have been explored by varying the average interface velocity v and the gap spacing b. Through the analysis of the rms width as a function of time, we have measured a growth exponent beta approximately 0.5 that is almost independent of the experimental parameters. The analysis of the roughness exponent alpha through the power spectrum has shown different behaviors at short (alpha(1)) and long (alpha(2)) length scales, separated by a crossover wave number q(c). The values of the measured roughness exponents depend on experimental parameters, but at large velocities we obtain alpha(1) approximately 1.3 independently of the disorder configuration. The dependence of the crossover wave number with the experimental parameters has also been investigated, measuring q(c) approximately v(0.47) for the shortest persistence length, in agreement with theoretical predictions.

Journal Article↗
PubMed2002

Anomalous roughening of Hele-Shaw flows with quenched disorder.

The kinetic roughening of a stable oil-air interface moving in a Hele-Shaw cell that contains a quenched columnar disorder (tracks) has been studied. A capillary effect is responsible for the dynamic evolution of the resulting rough interface, which exhibits anomalous scaling. The three independent exponents needed to characterize the anomalous scaling are determined experimentally. The anomalous scaling is explained in terms of the initial acceleration and subsequent deceleration of the interface tips in the tracks coupled by mass conservation. A phenomenological model that reproduces the measured global and local exponents is introduced.

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PubMed2001

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.

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PubMed2001

Sidebranching induced by external noise in solutal dendritic growth.

We have studied sidebranching induced by fluctuations in dendritic growth. The amplitude of sidebranching induced by internal (equilibrium) concentration fluctuations in the case of solidification with solutal diffusion is computed. This amplitude turns out to be significantly smaller than values reported in previous experiments. The effects of other possible sources of fluctuations (of an external origin) are examined by introducing nonconserved noise in a phase-field model. This reproduces the characteristics of sidebranching found in experiments. Results also show that sidebranching induced by external noise is qualitatively similar to that of internal noise, and it is only distinguished by its amplitude.

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PubMed1999

Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. I. Theoretical approach.

We present a phase-field model for the dynamics of the interface between two inmiscible fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. With asymptotic matching techniques we check the model to yield the right Hele-Shaw equations in the sharp-interface limit, and compute the corrections to these equations to first order in the interface thickness. We also compute the effect of such corrections on the linear dispersion relation of the planar interface. We discuss in detail the conditions on the interface thickness to control the accuracy and convergence of the phase-field model to the limiting Hele-Shaw dynamics. In particular, the convergence appears to be slower for high viscosity contrasts.

Journal Article↗
PubMed1999

Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. II. Numerical study.

We implement a phase-field simulation of the dynamics of two fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. We demonstrate the use of this technique in different situations including the linear regime, the stationary Saffman-Taylor fingers, and the multifinger competition dynamics, for different viscosity contrasts. The method is quantitatively tested against analytical predictions and other numerical results. A detailed analysis of convergence to the sharp interface limit is performed for the linear dispersion results. We show that the method may be a useful alternative to more traditional methods.

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