Coarsening of solid-liquid mixtures in a random acceleration field

The effects of flow induced by a random acceleration field (g-jitter) are considered in two related situations that are of interest for microgravity fluid experiments: the random motion of isolated buoyant particles, and diffusion driven coarsening of a solid-liquid mixture. We start by analyzing in detail actual accelerometer data gathered during a recent microgravity mission, and obtain the values of the parameters defining a previously introduced stochastic model of this acceleration field. The diffusive motion of a single solid particle suspended in an incompressible fluid that is subjected to such random accelerations is considered, and mean squared velocities and effective diffusion coefficients are explicitly given. We next study the flow induced by an ensemble of such particles, and show the existence of a hydrodynamically induced attraction between pairs of particles at distances large compared with their radii, and repulsion at short distances. Finally, a mean field analysis is used to estimate the effect of g-jitter on diffusion controlled coarsening of a solid-liquid mixture. Corrections to classical coarsening rates due to the induced fluid motion are calculated, and estimates are given for coarsening of Sn-rich particles in a Sn-Pb eutectic fluid, an experiment to be conducted in microgravity in the near future.

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

The radial displacement of a fluid annulus in a rotating circular Hele-Shaw 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 interface motion 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, alpha i, is obtained as a function of Ca.

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.

Bifurcations and chaos in single-roll natural convection with low Prandtl number

Convective flows of a small Prandtl number fluid contained in a two-dimensional cavity subject to a lateral thermal gradient are numerically studied by using different techniques. The aspect ratio (length to height) is kept at around 2. This value is found optimal to make the flow most unstable while keeping the basic single-roll structure. Two cases of thermal boundary conditions on the horizontal plates are considered: perfectly conducting and adiabatic. For increasing Rayleigh numbers we find a transition from steady flow to periodic oscillations through a supercritical Hopf bifurcation that maintains the centrosymmetry of the basic circulation. For a Rayleigh number of about ten times that of the Hopf bifurcation the system initiates a complex scenario of bifurcations. In the conductive case these include a quasiperiodic route to chaos. In the adiabatic one the dynamics is dominated by the interaction of two Neimark-Sacker bifurcations of the basic periodic solutions, leading to the stable coexistence of three incommensurate frequencies, and finally to chaos. In all cases, the complex time-dependent behavior does not break the basic, single-roll structure.

Interfacial instabilities of a fluid annulus in a rotating Hele-Shaw cell

We have studied the interfacial instabilities experienced by a liquid annulus as it moves radially in a circular Hele-Shaw cell rotating with angular velocity Omega. The instability of the leading interface (oil displacing air) is driven by the density difference in the presence of centrifugal forcing, while the instability of the trailing interface (air displacing oil) is driven by the large viscosity contrast. A linear stability analysis shows that the stability of the two interfaces is coupled through the pressure field already at a linear level. We have performed experiments in a dry cell and in a cell coated with a thin fluid layer on each plate, and found that the stability depends substantially on the wetting conditions at the leading interface. Our experimental results of the number of fingers resulting from the instability compare well with the predictions obtained through a numerical integration of the coupled equations derived from a linear stability analysis. Deep in the nonlinear regime we observe the emission of liquid droplets through the formation of thin filaments at the tip of outgrowing fingers.

Three-dimensional aspects of fluid flows in channels. II. Effects of meniscus and thin film regimes on viscous fingers

We perform a three-dimensional study of steady state viscous fingers that develop in linear channels. By means of a three-dimensional lattice-Boltzmann scheme that mimics the full macroscopic equations of motion of the fluid momentum and order parameter, we study the effect of the thickness of the channel in two cases. First, for total displacement of the fluids in the channel thickness direction, we find that the steady state finger is effectively two-dimensional and that previous two-dimensional results can be recovered by taking into account the effect of a curved meniscus across the channel thickness as a contribution to surface stresses. Second, when a thin film develops in the channel thickness direction, the finger narrows with increasing channel aspect ratio in agreement with experimental results. The effect of the thin film renders the problem three-dimensional and results deviate from the two-dimensional prediction.

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.

Three-dimensional aspects of fluid flows in channels. I. Meniscus and thin film regimes

We study the forced displacement of a fluid-fluid interface in a three-dimensional channel formed by two parallel solid plates. Using a lattice-Boltzmann method, we study situations in which a slip velocity arises from diffusion effects near the contact line. The difference between the slip and channel velocities determines whether the interface advances as a meniscus or a thin film of fluid is left adhered to the plates. We find that this effect is controlled by the capillary and Péclet numbers. We estimate the crossover from a meniscus to a thin film and find good agreement with numerical results. The penetration regime is examined in the steady state. We find that the occupation fraction of the advancing finger relative to the channel thickness is controlled by the capillary number and the viscosity contrast between the fluids. For high viscosity contrast, lattice-Boltzmann results agree with previous results. For zero viscosity contrast, we observe remarkably narrow fingers. The shape of the finger is found to be universal.

New experimental apparatus for the study of the Bénard-Rayleigh problem

A new experimental system to measure the equivalent thermal conductivity of a liquid with regard to the Bénard-Rayleigh problem was constructed. The liquid is enclosed within walls of polymethylmethacrylate between two copper plates in which there are thermocouples to measure the difference in temperature between the lower and upper surfaces of the layer of liquid. Heat flux is measured by means of a linear heat fluxmeter consisting of 204 thermocouples in series. The fluxmeter was calibrated and the linear relationship that exists between the heat flux and the emf generated was verified. The thermal conductivity of the polymethylmethacrylate employed was measured and measurements of the equivalent conductivity in cylindrical boundaries of two silicone oils were made. The critical value of the temperature difference and the contribution of the convective process to the transmission of heat were determined.

Dynamics of driven three-dimensional thin films: from hdrophilic to superhydrophobic substrates

We study the forced displacement of a thin film of fluid in contact with vertical and inclined substrates of different wetting properties, that range from hydrophilic to hydrophobic, using the lattice-Boltzmann method. We study the stability and pattern formation of the contact line in the hydrophilic and superhydrophobic regimes, which correspond to wedge-shaped and nose-shaped fronts, respectively. We find that contact lines are considerably more stable for hydrophilic substrates and small inclination angles. The qualitative behavior of the front in the linear regime remains independent of the wetting properties of the substrate as a single dispersion relation describes the stability of both wedges and noses. Nonlinear patterns show a clear dependence on wetting properties and substrate inclination angle. The effect is quantified in terms of the pattern growth rate, which vanishes for the sawtooth pattern and is finite for the finger pattern. Sawtooth shaped patterns are observed for hydrophilic substrates and low inclination angles, while finger-shaped patterns arise for hydrophobic substrates and large inclination angles. Finger dynamics show a transient in which neighboring fingers interact, followed by a steady state where each finger grows independently.

Perturbing Hele-Shaw flow with a small gap gradient

A controlled perturbation is introduced into the Saffman-Taylor flow problem by adding a gradient to the gap of a Hele-Shaw cell. The stability of the single-finger steady state was found to be strongly affected by such a perturbation. Compared with patterns in a standard Hele-Shaw cell, the single Saffman-Taylor finger was stabilized or destabilized according to the sign of the gap gradient. While a linear stability analysis shows that this perturbation should have a negligible effect on the early-stage pattern formation, the experimental data indicate that the characteristic length for the initial breakup of a flat interface has been changed by the perturbation.

Lifetime of an ocean island volcano feeder zone: constraints from U-Pb dating on coexisting zircon and baddeleyite, and 40Ar/39Ar age determinations, Fuerteventura, Canary Islands

High-precision isotope dilution - thermal ionization mass spectrometry (ID-TIMS) U-Pb zircon and baddeleyite ages from the PX1 vertically layered mafic intrusion Fuerteventura, Canary Islands, indicate initiation of magma crystallization at 22.10 +/- 0.07 Ma. The magmatic activity lasted a minimum of 0.52 Ma. Ar-40/Ar-39 amphibole dating yielded ages from 21.9 +/- 0.6 to 21.8 +/- 0.3, identical within errors to the U-Pb ages, despite the expected 1% theoretical bias between Ar-40/Ar-39 and U-Pb dates. This overlap could result from (i) rapid cooling of the intrusion (i. e., less than the 0.3 to 0.6 Ma 40Ar/39Ar age uncertainties) from closure temperatures (T-c) of zircon (699-988 degrees C) to amphibole (500-600 degrees C); (ii) lead loss affecting the youngest zircons; or (iii) excess argon shifting the plateau ages towards older values. The combination of the Ar-40/Ar-39 and U/Pb datasets implies that the maximum amount of time PX1 intrusion took to cool below amphibole T-c is 0.8 Ma, suggesting PX1 lifetime of 520 000 to 800 000 Ma. Age disparities among coexisting baddeleyite and zircon (22.10 +/- 0.07/0.08/0.15 Ma and 21.58 +/- 0.15/0.16/0.31 Ma) in a gabbro sample from the pluton margin suggest complex genetic relationships between phases. Baddeleyite is found preserved in plagioclase cores and crystallized early from low silica activity magma. Zircon crystallized later in a higher silica activity environment and is found in secondary scapolite and is found close to calcite veins, in secondary scapolite that recrystallised from plagioclase. close to calcite veins. Oxygen isotope delta O-18 values of altered plagioclase are high (+7.7), indicating interaction with fluids derived from host-rock carbonatites. The coexistence of baddeleyite and zircon is ascribed to interaction of the PX1 gabbro with CO2-rich carbonatite-derived fluids released during contact metamorphism.

Fingerlike aggregates in thin-layer electrodeposition

Electrodeposition experiments conducted in a thin-layer horizontal cell containing a nonbinary aqueous electrolyte prepared with cupric sulfate and sodium sulfate gave rise to fingerlike deposits, a novel and unexpected growth mode in this context. Both the leading instability from which fingers emerge and some distinctive features of their steady evolution are interpreted in terms of a simple model based on the existing theory of fingering in fluids.

Time-resolved imaging of the laser forward transfer of liquids

Time-resolved imaging is carried out to study the dynamics of the laser-induced forward transfer of an aqueous solution at different laser fluences. The transfer mechanisms are elucidated, and directly correlated with the material deposited at the analyzed irradiation conditions. It is found that there exists a fluence range in which regular and well-defined droplets are deposited. In this case, laser pulse energy absorption results in the formation of a plasma, which expansion originates a cavitation bubble in the liquid. After the further expansion and collapse of the bubble, a long and uniform jet is developed, which advances at a constant velocity until it reaches the receptor substrate. On the other hand, for lower fluences no material is deposited. In this case, although a jet can be also generated, it recoils before reaching the substrate. For higher fluences, splashing is observed on the receptor substrate due to the bursting of the cavitation bubble. Finally, a discussion of the possible mechanisms which lead to such singular dynamics is also provided.