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.

Phase separation dynamics under stirring

Phase separation dynamics in the presence of externally imposed stirring is studied. The stirring is assumed independent of the concentration and it is generated with a well-defined energy spectrum. The domain growth process is either favored or frozen depending on the intensity and correlation length of this advective flow. This behavior is explained by analytical arguments.

Bernoulli correction to viscous losses: Radial flow between two parallel discs

For a massless fluid (density = 0), the steady flow along a duct is governed exclusively by viscous losses. In this paper, we show that the velocity profile obtained in this limit can be used to calculate the pressure drop up to the first order in density. This method has been applied to the particular case of a duct, defined by two plane-parallel discs. For this case, the first-order approximation results in a simple analytical solution which has been favorably checked against numerical simulations. Finally, an experiment has been carried out with water flowing between the discs. The experimental results show good agreement with the approximate solution

Radial displacement of a fluid annulus in a rotating Hele-Shaw cell

The radial displacement of a fluid annulus in a rotating circular HeleShaw cell has been investigated experimentally. It has been found that the flow depends sensitively on the wetting conditions at the outer interface. Displacements in a prewet cell are well described by Darcy"s law in a wide range of experimental parameters, with little influence of capillary effects. In a dry cell, however, a more careful analysis of the interfacemotion is required; the interplay between a gradual loss of fluid at the inner interface, and the dependence of capillary forces at the outer interface on interfacial velocity and dynamic contact angle, result in a constant velocity for the interfaces. The experimental results in this case correlate in the form of an empirical scaling relation between the capillary number Ca and a dimensionless group, related to the ratio of centrifugal to capillary forces, which spans about three orders of magnitude in both quantities. Finally, the relative thickness of the coating film left by the inner interface is obtained as a function of Ca.

Developing discontinuous Galerkin methods for the resolution of the incompressible Navier-Stokes equations

Informe de investigación elaborado a partir de una estancia en el Laboratorio de Diseño Computacional en Aeroespacial en el Massachusetts Institute of Technology (MIT), Estados Unidos, entre noviembre de 2006 y agosto de 2007. La aerodinámica es una rama de la dinámica de fluidos referida al estudio de los movimientos de los líquidos o gases, cuya meta principal es predecir las fuerzas aerodinámicas en un avión o cualquier tipo de vehículo, incluyendo los automóviles. Las ecuaciones de Navier-Stokes representan un estado dinámico del equilibrio de las fuerzas que actúan en cualquier región dada del fluido. Son uno de los sistemas de ecuaciones más útiles porque describen la física de una gran cantidad de fenómenos como corrientes del océano, flujos alrededor de una superficie de sustentación, etc. En el contexto de una tesis doctoral, se está estudiando un flujo viscoso e incompresible, solucionando las ecuaciones de Navier- Stokes incompresibles de una manera eficiente. Durante la estancia en el MIT, se ha utilizado un método de Galerkin discontinuo para solucionar las ecuaciones de Navier-Stokes incompresibles usando, o bien un parámetro de penalti para asegurar la continuidad de los flujos entre elementos, o bien un método de Galerkin discontinuo compacto. Ambos métodos han dado buenos resultados y varios ejemplos numéricos se han simulado para validar el buen comportamiento de los métodos desarrollados. También se han estudiado elementos particulares, los elementos de Raviart y Thomas, que se podrían utilizar en una formulación mixta para obtener un algoritmo eficiente para solucionar problemas numéricos complejos.

Desenvolupament de codis numèrics per a la resolució de fluxos turbulents en ordinadors paral·lels emprant discretitzacions tipus symmetry-preserving

Projecte de recerca elaborat a partir d’una estada a la University of Groningen, Holanda, entre 2007 i 2009. La simulació directa de la turbulència (DNS) és una eina clau dins de la mecànica de fluids computacional. Per una banda permet conèixer millor la física de la turbulència i per l'altra els resultats obtinguts són claus per el desenvolupament dels models de turbulència. No obstant, el DNS no és una tècnica vàlida per a la gran majoria d'aplicacions industrials degut al elevats costos computacionals. Per tant, és necessari cert grau de modelització de la turbulència. En aquest context, s'han introduïts importants millores basades en la modelització del terme convectiu (no lineal) emprant symmetry-preserving regularizations. En tracta de modificar adequadament el terme convectiu a fi de reduir la producció d'escales més i més petites (vortex-stretching) tot mantenint tots els invariants de les equacions originals. Fins ara, aquest models s'han emprat amb èxit per nombres de Rayleigh (Ra) relativament elevats. En aquest punt, disposar de resultats DNS per a configuracions més complexes i nombres de Ra més elevats és clau. En aquest contexte, s'han dut a terme simulacions DNS en el supercomputador MareNostrum d'una Differentially Heated Cavity amb Ra=1e11 i Pr=0.71 durant el primer any dels dos que consta el projecte. A més a més, s'ha adaptat el codi a fi de poder simular el fluxe al voltant d'un cub sobre una pared amb Re=10000. Aquestes simulacions DNS són les més grans fetes fins ara per aquestes configuracions i la seva correcta modelització és un gran repte degut la complexitat dels fluxes. Aquestes noves simulacions DNS estan aportant nous coneixements a la física de la turbulència i aportant resultats indispensables per al progrés de les modelitzacións tipus symmetry-preserving regularization.

Dynamics of turing patterns under spatiotemporal forcing

We study, both theoretically and experimentally, the dynamical response of Turing patterns to a spatiotemporal forcing in the form of a traveling-wave modulation of a control parameter. We show that from strictly spatial resonance, it is possible to induce new, generic dynamical behaviors, including temporally modulated traveling waves and localized traveling solitonlike solutions. The latter make contact with the soliton solutions of Coullet [Phys. Rev. Lett. 56, 724 (1986)] and generalize them. The stability diagram for the different propagating modes in the Lengyel-Epstein model is determined numerically. Direct observations of the predicted solutions in experiments carried out with light modulations in the photosensitive chlorine dioxide-iodine-malonic acid reaction are also reported.

Dynamics of domain walls in pattern formation under traveling-wave forcing

We study dynamics of domain walls in pattern forming systems that are externally forced by a moving space-periodic modulation close to 2:1 spatial resonance. The motion of the forcing induces nongradient dynamics, while the wave number mismatch breaks explicitly the chiral symmetry of the domain walls. The combination of both effects yields an imperfect nonequilibrium Ising-Bloch bifurcation, where all kinks (including the Ising-like one) drift. Kink velocities and interactions are studied within the generic amplitude equation. For nonzero mismatch, a transition to traveling bound kink-antikink pairs and chaotic wave trains occurs.

Diffusion in spatially and temporarily inhomogeneous media: Effects of turbulent mixing

We consider diffusion of a passive substance C in a phase-separating nonmiscible binary alloy under turbulent mixing. The substance is assumed to have different diffusion coefficients in the pure phases A and B, leading to a spatially and temporarily dependent diffusion ¿coefficient¿ in the diffusion equation plus convective term. In this paper we consider especially the effects of a turbulent flow field coupled to both the Cahn-Hilliard type evolution equation of the medium and the diffusion equation (both, therefore, supplemented by a convective term). It is shown that the formerly observed prolonged anomalous diffusion [H. Lehr, F. Sagués, and J.M. Sancho, Phys. Rev. E 54, 5028 (1996)] is no longer seen if a flow of sufficient intensity is supplied.

Dynamical scaling of imbibition in columnar geometries

compatible with the usual nonlocal model governed by surface tension that results from a macroscopic description. To explore this discrepancy, we exhaustively analyze numerical integrations of a phase-field model with dichotomic columnar disorder. We find that two distinct behaviors are possible depending on the capillary contrast between the two values of disorder. In a high-contrast case, where interface evolution is mainly dominated by the disorder, an inherent anomalous scaling is always observed. Moreover, in agreement with experimental work, the interface motion has to be described through a local model. On the other hand, in a lower-contrast case, the interface is dominated by interfacial tension and can be well modeled by a nonlocal model. We have studied both spontaneous and forced-flow imbibition situations, giving a complete set of scaling exponents in each case, as well as a comparison to the experimental results.

Inertial effects on reactive particles advected by turbulence

We study the problem of the advection of passive particles with inertia in a two-dimensional, synthetic, and stationary turbulent flow. The asymptotic analytical result and numerical simulations show the importance of inertial bias in collecting the particles preferentially in certain regions of the flow, depending on their density relative to that of the flow. We also study how these aggregates are affected when a simple chemical reaction mechanism is introduced through a Eulerian scheme. We find that inertia can be responsible for maintaining a stationary concentration pattern even under nonfavorable reactive conditions or destroying it under favorable ones.

Excitability transitions and wave dynamics under spatiotemporal structured noise

We present an analytic and numerical study of the effects of external fluctuations in active media. Our analytical methodology transforms the initial stochastic partial differential equations into an effective set of deterministic reaction-diffusion equations. As a result we are able to explain and make quantitative predictions on the systematic and constructive effects of the noise, for example, target patterns created out of noise and traveling or spiral waves sustained by noise. Our study includes the case of realistic noises with temporal and spatial structures.

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.

Interface dynamics in Hele-Shaw flows with centrifugal forces. Preventing cusp singularities with rotation

A class of exact solutions of Hele-Shaw flows without surface tension in a rotating cell is reported. We show that the interplay between injection and rotation modifies the scenario of formation of finite-time cusp singularities. For a subclass of solutions, we show that, for any given initial condition, there exists a critical rotation rate above which cusp formation is suppressed. We also find an exact sufficient condition to avoid cusps simultaneously for all initial conditions within the above subclass.