Lateral movements in Rayleigh-Taylor instabilities due to frontiers. Experimental study

Lateral movements of the fingers in Rayleigh-Taylor hydrodynamic instabilities at the interface between two fluids are studied. We show that transverse movements appear when a physical boundary is present; these phenomena have not been explained until now. The boundary prevents one of the fluids from crossing it. Such frontiers can be buoyancy driven as, for example, the frontier to the passage of a less dense solution through a denser solution or when different aggregation states coexist (liquid and gaseous phases). An experimental study of the lateral movement velocity of the fingers was performed for different Rayleigh numbers (Ra), and when oscillations were detected, their amplitudes were studied. Liquid-liquid (L-L) and gas-liquid (G-L) systems were analysed. Aqueous HCl and Bromocresol Green (sodium salt, NaBCG) solutions were used in L-L experiments, and CO₂ (gas) and aqueous NaOH, NaHCO₃, and CaCl₂ solutions were employed for the G-L studies. We observed that the lateral movement of the fingers and finger collapses near the interface are more notorious when Ra increases. The consequences of this, for each experience, are a decrease in the number of fingers and an increase in the velocity of the lateral finger movement close to the interface as time evolves. We found that the amplitude of the oscillations did not vary significantly within the considered Ra range. These results have an important implication when determining the wave number of instabilities in an evolving system. The wave number could be strongly diminished if there is a boundary.

Lateral movements in Rayleigh-Taylor instabilities due to frontiers. Numerical analysis

Numerical simulations were performed for Rayleigh-Taylor (RT) hydrodynamic instabilities when a frontier is present. The frontier formed by the interface between two fluids prevents the free movement of the fingers created by the instability. As a consequence, transversal movements at the rear of the fingers are observed in this area. These movements produce collapse of the fingers (two or more fingers join in one finger) or oscillations in the case that there is no collapse. The transversal velocity of the fingers, the amplitude of the oscillations, and the wave number of the RT instabilities as a function of the Rayleigh number (Ra) were studied near the frontier. We verified numerically that in classical RT instabilities, without a frontier, these lateral movements do not occur; only with a physical frontier, the transversal displacements of the fingers appear. The transverse displacement velocity and the initial wave number increase with Ra. This leads to the collapse of the fingers, diminishing the wave number of the instabilities at the interface. Instead, no significant changes in the amplitude of the oscillations are observed modifying Ra. The numerical results are independent of the type or origin of the frontier (gas-liquid, liquid-liquid, or solid-liquid). The numerical results are in good agreement with the experimental results reported by Binda et al. [Chaos 28, 013107 (2018)]. Based on these results, it was possible to determine the cause of the transverse displacements, which had not been explained until now.

Experimental analysis of density fingering instability modified by precipitation

We analyze the effect of precipitate formation on the development of density induced hydrodynamic instabilities. In this case, the precipitate is BaCO₃, obtained by reaction of CO₂ with aqueous BaCl₂. CO₂(g) dissolution increases the local density of the aqueous phase, triggering Rayleigh-Taylor instabilities and BaCO₃ formation. It was observed that at first the precipitate was formed at the finger front. As the particles became bigger, they began to fall down from the front. These particles were used as tracers using PIV technique to visualize the particle streamlines and to obtain the velocity of that movement. This falling produced a downward flow that might increase the mixing zone. Contrary to expectations, it was observed that the finger length decreased, indicating that for the mixing zone development, the consumption of CO₂ to form the precipitate is more important than the downward flow. The mixing zone length was recovered by increasing the availability of the reactant (higher CO₂ partial pressure), compensating the CO₂ used for BaCO₃ formation. Mixing zone development rates reached constant values at shorter times when the precipitate is absent than when it is present. An analysis of the nonlinear regime with and without the precipitate is performed.

Experimental study of linear and nonlinear regimes of density-driven instabilities induced by CO(2) dissolution in water

Density driven instabilities produced by CO2 (gas) dissolution in water containing a color indicator were studied in a Hele Shaw cell. The images were analyzed and instability patterns were characterized by mixing zone temporal evolution, dispersion curves, and the growth rate for different CO2 pressures and different color indicator concentrations. The results obtained from an exhaustive analysis of experimental data show that this system has a different behaviour in the linear regime of the instabilities (when the growth rate has a linear dependence with time), from the nonlinear regime at longer times. At short times using a color indicator to see the evolution of the pattern, the images show that the effects of both the color indicator and CO2 pressure are of the same order of magnitude: The growth rates are similar and the wave numbers are in the same range (0-30 cm(-1)) when the system is unstable. Although in the linear regime the dynamics is affected similarly by the presence of the indicator and CO2 pressure, in the nonlinear regime, the influence of the latter is clearly more pronounced than the effects of the color indicator.

Pattern formation driven by an acid-base neutralization reaction in aqueous media in a gravitational field

We report the hydrodynamic instabilities found in a simple exothermic neutralization reaction. Although the heavier aqueous NaOH solution was put below the lighter layer of aqueous HCl solution, fingering at the interface in a Hele-Shaw cell was observed. The reaction front, which propagates downward, becomes buoyantly unstable in the gravity field. The mixing zone length and wave number depend on the reactant concentrations. The mixing zone length increases and the wave number decreases when the reactant concentrations decrease.

A response time model for judging order relationship between two symbolic stimuli

The response time to judge the order relationship between two symbolic stimuli is frequently modeled as the time spent in a (constant-rate) accumulative sampling process until a threshold is reached. We will show that empirical descriptions of observed effects in number comparisons suggest an accrual process that reaches the threshold at an exponential rate. The model accrual equations and stopping conditions have an immediate interpretation in terms of a simple quantitative connectionist network. The encoded stimuli and thresholds are inputs to the network. The former are considered to result from the participant's learning history, and the latter modulate the rearrangement of the network parts; each arrangement models a different task. We have found a good correlation between model predictions and other authors' experimental data, both in number comparisons and in experiments in which the ordering of the symbolic stimuli has been artificially induced. Incorrect answers are discussed, and predictions are compared with data. We will explore differences and similarities with other approaches, such as random walk and the symbolic comparison model. In a limit case, our model becomes identical to the discriminability model.