L. Ramírez-Piscina

Modeling of spatiotemporal patterns in bacterial colonies.

A diffusion-reaction model for the growth of bacterial colonies is presented. The often observed cooperative behavior developed by bacteria which increases their motility in adverse growth conditions is here introduced as a nonlinear diffusion term. The presence of this mechanism depends on a response which can present hysteresis. By changing only the concentrations of agar and initial nutrient, numerical integration of the proposed model reproduces the different patterns shown by Bacillus subtilis OG-01.

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.

Initial front transients in directional solidification of thin samples of dilute alloys

Abstract We study the dynamics of recoil of a planar front in a directional solidification process, following a sudden jump from rest to a constant pulling velocity V . To this end, we solve numerically the full integral equation describing the front dynamics in the one-sided model. We find, in particular, that the asymptotic (respectively initial) regimes, for which we derive analytical expressions for the front position, are restricted to such long (respectively short) times that they are in practice irrelevant for the analysis of experiments. We show that the results obtained from the heuristic approximation recently proposed by Warren and Langer are in remarkably good agreement with the exact ones in the regimes relevant to planar recoil experiments. Equally good agreement is found for the velocity threshold and the critical wavelength of the cellular instability after a large velocity jump, as calculated in the adiabatic approximation.

Generation of a Monodisperse Microbubble Jet in Microgravity

A new method to create a jet of a virtually monodisperse microbubble suspension of prescribed bubble size into a quiescent cavity is proposed. The method is insensitive to gravity and is based on the creation of a slug flow at a T junction in a capillary tube before injection. We develop a theoretical analysis that establishes the validity and efficiencyofthe method,ascontrolledbythecrossflowWebernumber,andyields asimple explicitprediction forthe bubble size in terms of the injection parameters. The method operates efficiently for small Weber numbers, yet it generates small bubbles of very uniform size. The reduced size dispersion is also explained within the theoretical model. The method of bubble formation, injection, and spreading by the resulting turbulent jet is validated experimentally in 4.7 s of free fall in the drop tower at the University of Bremen. Experiments demonstrate the physical principle behind the method of bubble formation and allow us to explore the dynamics of the resulting bubble jet after injection of the slug flow into a quiescent cavity in microgravity conditions as an efficient method of bubblespreadingandtransport.Detailed measurements of averagelocal velocities show thatbubblesare essentially passivewithrespecttothecarriermean flow,andtheinherentturbulenceofthe flowiscrucialforoptimalspreading of the bubbledistribution andreduction of bubble coalescence. Theshape of the bubblejet isstudied asa function of the Reynolds number. Finally, the degree of coalescence is also characterized and found to be remarkably small.

Spontaneous formation of nanometric multilayers of metal-carbon films by up-hill diffusion during growth

We report the spontaneous formation of multilayer structures with nanometric periodicity during Ti–C thin-film growth by reactive magnetron sputtering. Their characterization was performed by transmission electron microscopy, x-ray photoelectron spectroscopy, x-ray diffraction, and secondary ion mass spectrometry. We discuss film structure and morphology as a function of metal content, and propose surface-directed spinodal decomposition as the mechanism responsible for the segregation of species in separated layers by up-hill diffusion.

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...

Interface roughening in Hele-Shaw flows with quenched disorder: Experimental and theoretical results

We study the forced fluid invasion of an air-filled model porous medium at constant flow rate, in 1+1 dimensions, both experimentally and theoretically. We focus on the nonlocal character of the interface dynamics, due to liquid conservation, and its effect on the scaling properties of the interface upon roughening. Specifically, we study the limit of large flow rates and weak capillary forces. Our theory predicts a roughening behaviour characterized at short times by a growth exponent β1 = 5/6, a roughness exponent α1 = 5/2, and a dynamic exponent z1 = 3, and by β2 = 1/2, α2 = 1/2, and z2 = 1 at long times, before saturation. This theoretical prediction is in good agreement with the experiments at long times. The ensemble of experiments, theory, and simulations provides evidence for a new universality class of interface roughening in 1+1 dimensions.

Phase-field simulations and experiments of faceted growth in liquid crystals

We present numerical simulations directed at the description of smectic-B germs growing into the supercooled nematic phase for two different liquid crystalline substances. The simulations are done by means of a phase-field model appropriate to study strong anisotropy and also faceted interfaces. The most important ingredient is the angle-dependent surface energy, but kinetic effects are also relevant. The simulations reproduce qualitatively a rich variety of morphologies observed in the experiments for different value of undercooling, extending from the faceted equilibrium shape to fully developed dendrites.

Effective diffusion in a stochastic velocity field

Analytical results are derived for the effective dispersion of a passive scalar in a stochastic velocity field evolving in a fast time scale. These results are favorably compared with direct computer simulation of stochastic differential equations containing multiplicative space-time correlated noise.

A nonequilibrium phase transition with colored noise

Abstract A Langevin equation for the Φ4 scalar continuum field model is studied. Fluctuations are modeled by a Gaussian additive noise, white in space and colored in time. A computer simulation evidences the presence of a nonequilibrium phase transition when the correlation time of the noise is used as control parameter.