Particle dispersion in synthetic turbulent flows

We study particle dispersion advected by a synthetic turbulent flow from a Lagrangian perspective and focus on the two-particle and cluster dispersion by the flow. It has been recently reported that Richardson¿s law for the two-particle dispersion can stem from different dispersion mechanisms, and can be dominated by either diffusive or ballistic events. The nature of the Richardson dispersion depends on the parameters of our flow and is discussed in terms of the values of a persistence parameter expressing the relative importance of the two above-mentioned mechanisms. We support this analysis by studying the distribution of interparticle distances, the relative velocity correlation functions, as well as the relative trajectories.

Reaction-diffusion fronts under stochastic advection

We study front propagation in stirred media using a simplified modelization of the turbulent flow. Computer simulations reveal the existence of the two limiting propagation modes observed in recent experiments with liquid phase isothermal reactions. These two modes respectively correspond to a wrinkled although sharp propagating interface and to a broadened one. Specific laws relative to the enhancement of the front velocity in each regime are confirmed by our simulations.

Dispersion of passive particles by a quasi-two-dimensional turbulent flow

Using the experimental data of Paret and Tabeling [Phys. Rev. Lett. 79, 4162 (1997)] we consider in detail the dispersion of particle pairs by a two-dimensional turbulent flow and its relation to the kinematic properties of the velocity field. We show that the mean square separation of a pair of particles is governed by rather rare, extreme events and that the majority of initially close pairs are not dispersed by the flow. Another manifestation of the same effect is the fact that the dispersion of an initially dense cluster is not the result of homogeneously spreading the particles within the whole system. Instead it proceeds through a splitting into smaller but also dense clusters. The statistical nature of this effect is discussed.

Nonequilibrium orientational patterns in two-component Langmuir monolayers

A model of a phase-separating two-component Langmuir monolayer in the presence of a photoinduced reaction interconverting two components is formulated. An interplay between phase separation, orientational ordering, and reaction is found to lead to a variety of nonequilibrium self-organized patterns, both stationary and traveling. Examples of the patterns, observed in numerical simulations, include flowing droplets, traveling stripes, wave sources, and vortex defects.

Velocity fluctuations of fracturelike disruptions of associating polymer solutions

Velocity has been measured as a function of time for propagating crack tips as water is injected into solutions of end-capped associating polymers in a rectanguar Hele-Shaw cell. Measurements were performed for flows with different values of cell gap, channel width, polymer molecular weight, and polymer concentration. The condition for the onset of fracturelike behavior is well described by a Deborah number which uses the shear-thinning shear rate of the polymer solution as a characteristic frequency for network relaxation. At low molecular weight, the onset of fracturelike pattern evolution is accompanied by an abrupt jump in tip velocity, followed by a lower and approximately constant acceleration. At high molecular weight, the transition to fracturelike behavior involves passing through a regime that may be understood in terms of stick-slip dynamics. The crack-tip wanders from side to side and fluctuates (in both speed and velocity along the channel) with a characteristic frequency which depends linearly on the invading fluid injection rate.

Velocity-jump instabilities in Hele-Shaw flow of associating polymer solutions

We study fracturelike flow instabilities that arise when water is injected into a Hele-Shaw cell filled with aqueous solutions of associating polymers. We explore various polymer architectures, molecular weights, and solution concentrations. Simultaneous measurements of the finger tip velocity and of the pressure at the injection point allow us to describe the dynamics of the finger in terms of the finger mobility, which relates the velocity to the pressure gradient. The flow discontinuities, characterized by jumps in the finger tip velocity, which are observed in experiments with some of the polymer solutions, can be modeled by using a nonmonotonic dependence between a characteristic shear stress and the shear rate at the tip of the finger. A simple model, which is based on a viscosity function containing both a Newtonian and a non-Newtonian component, and which predicts nonmonotonic regions when the non-Newtonian component of the viscosity dominates, is shown to agree with the experimental data.

Chemoconvection patterns in the Methylene-blue-glucose system: Weakly nonlinear analysis

The oxidation of solutions of glucose with methylene-blue as a catalyst in basic media can induce hydrodynamic overturning instabilities, termed chemoconvection in recognition of their similarity to convective instabilities. The phenomenon is due to gluconic acid, the marginally dense product of the reaction, which gradually builds an unstable density profile. Experiments indicate that dominant pattern wavenumbers initially increase before gradually decreasing or can even oscillate for long times. Here, we perform a weakly nonlinear analysis for an established model of the system with simple kinetics, and show that the resulting amplitude equation is analogous to that obtained in convection with insulating walls. We show that the amplitude description predicts that dominant pattern wavenumbers should decrease in the long term, but does not reproduce the aforementioned increasing wavenumber behavior in the initial stages of pattern development. We hypothesize that this is due to horizontally homogeneous steady states not being attained before pattern onset. We show that the behavior can be explained using a combination of pseudo-steady-state linear and steady-state weakly nonlinear theories. The results obtained are in qualitative agreement with the analysis of experiments.

Influence of ohmic heating on the flow field in thin-layer electrodeposition

In thin-layer electrodeposition the dissipated electrical energy leads to a substantial heating of the ion solution. We measured the resulting temperature field by means of an infrared camera. The properties of the temperature field correspond closely with the development of the concentration field. In particular, we find that the thermal gradients at the electrodes act similar to a weak additional driving force to the convection rolls driven by concentration gradients.

Experiments on anisotropic radial viscous fingering

We observe dendritic patterns in fluid flow in an anisotropic Hele-Shaw cell and measure the tip shapes and trajectories of individual dendritic branches under conditions where the pattern growth appears to be dominated by surface tension anisotropy and also under conditions where kinetic effects appear dominant. In each case, the tip position depends on a power law in the time, but the exponent of this power law can vary significantly among flow realizations. Averaging many growth exponents a yields a =0.640.09 in the surface tension dominated regime and a =0.660.09 in the kinetic regime. Restricting the analysis to realizations when a is very close to 0.6 shows great regularity across pattern regimes in the coefficient of the temporal dependence of the tip trajectory.

The effect of lattice defects on Hele-Shaw flow over an etched lattice

We examine the patterns formed by injecting nitrogen gas into the center of a horizontal, radial Hele-Shaw cell filled with paraffin oil. We use smooth plates and etched plates with lattices having different amounts of defects (010 %). In all cases, a quantitative measure of the pattern ramification shows a regular trend with injection rate and cell gap, such that the dimensionless perimeter scales with the dimensionless time. By adding defects to the lattice, we observe increased branching in the pattern morphologies. However, even in this case, the scaling behavior persists. Only the prefactor of the scaling function shows a dependence on the defect density. For different lattice defect densities, we examine the nature of the different morphology phases.

Nonlinear chemoconvection in the Methylene-blue-glucose system

Interfacial hydrodynamic instabilities arise in a range of chemical systems. One mechanism for instability is the occurrence of unstable density gradients due to the accumulation of reaction products. In this paper we conduct two-dimensional nonlinear numerical simulations for a member of this class of system: the methylene-blue¿glucose reaction. The result of these reactions is the oxidation of glucose to a relatively, but marginally, dense product, gluconic acid, that accumulates at oxygen permeable interfaces, such as the surface open to the atmosphere. The reaction is catalyzed by methylene-blue. We show that simulations help to disassemble the mechanisms responsible for the onset of instability and evolution of patterns, and we demonstrate that some of the results are remarkably consistent with experiments. We probe the impact of the upper oxygen boundary condition, for fixed flux, fixed concentration, or mixed boundary conditions, and find significant qualitative differences in solution behavior; structures either attract or repel one another depending on the boundary condition imposed. We suggest that measurement of the form of the boundary condition is possible via observation of oxygen penetration, and improved product yields may be obtained via proper control of boundary conditions in an engineering setting. We also investigate the dependence on parameters such as the Rayleigh number and depth. Finally, we find that pseudo-steady linear and weakly nonlinear techniques described elsewhere are useful tools for predicting the behavior of instabilities beyond their formal range of validity, as good agreement is obtained with the simulations.

Langevin approach to generate synthetic turbulent flows

We present an analytical scheme, easily implemented numerically, to generate synthetic Gaussian turbulent flows by using a linear Langevin equation, where the noise term acts as a stochastic stirring force. The characteristic parameters of the velocity field are well introduced, in particular the kinematic viscosity and the spectrum of energy. As an application, the diffusion of a passive scalar is studied for two different energy spectra. Numerical results are compared favorably with analytical calculations.

Front dynamics in turbulent media

A study of a stable front propagating in a turbulent medium is presented. The front is generated through a reaction-diffusion equation, and the turbulent medium is statistically modeled using a Langevin equation. Numerical simulations indicate the presence of two different dynamical regimes. These regimes appear when the turbulent flow either wrinkles a still rather sharp propagating interfase or broadens it. Specific dependences of the propagating velocities on stirring intensities appropriate to each case are found and fitted when possible according to theoretically predicted laws. Different turbulent spectra are considered.

Diffusion of passive scalars under stochastic convection

The diffusion of passive scalars convected by turbulent flows is addressed here. A practical procedure to obtain stochastic velocity fields with well¿defined energy spectrum functions is also presented. Analytical results are derived, based on the use of stochastic differential equations, where the basic hypothesis involved refers to a rapidly decaying turbulence. These predictions are favorable compared with direct computer simulations of stochastic differential equations containing multiplicative space¿time correlated noise.

Spatial patterns mediated by subcritical and supercritical thermal fluctuations in the splay Fréedericksz transition

The magnetically induced splay Fréedericksz transition is reexamined to look for pattern forming phenomena slightly above or below criticality. By using our traditional scheme of stochastic nematodynamic equations, situations are, respectively, found of transient and permanent predominance of transversal periodicities (wave numbers) along the direction perpendicular to the initial orientation within the sample. The relevance of these predictions in relation with recent observations in the electrically driven splay Fréedericksz transition, and in general with other pattern forming phenomena, is stressed.