Jaume Casademunt

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.

Collective Dynamics of Interacting Molecular Motors

O. Campàs, 2 Y. Kafri, 3 K. B. Zeldovich, J. Casademunt, and J.-F. Joanny Institut Curie, UMR CNRS 168, 26 rue d’Ulm 75248 Paris Cedex 05 France. Departament d’ECM, Universitat de Barcelona, Avinguda Diagonal 647, E-08028 Barcelona, Spain. Physics Department, Technion, Haifa 32000, Israel. Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford St., Cambridge, MA 02138 USA. (Dated: February 9, 2008)

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.

Dynamical organization of the cytoskeletal cortex probed by micropipette aspiration

Bleb-based cell motility proceeds by the successive inflation and retraction of large spherical membrane protrusions (“blebs”) coupled with substrate adhesion. In addition to their role in motility, cellular blebs constitute a remarkable illustration of the dynamical interactions between the cytoskeletal cortex and the plasma membrane. Here we study the bleb-based motions of Entamoeba histolytica in the constrained geometry of a micropipette. We construct a generic theoretical model that combines the polymerization of an actin cortex underneath the plasma membrane with the myosin-generated contractile stress in the cortex and the stress-induced failure of membrane-cortex adhesion. One major parameter dictating the cell response to micropipette suction is the stationary cortex thickness, controlled by actin polymerization and depolymerization. The other relevant physical parameters can be combined into two characteristic cortex thicknesses for which the myosin stress (i) balances the suction pressure and (ii) provokes membrane-cortex unbinding. We propose a general phase diagram for cell motions inside a micropipette by comparing these three thicknesses. In particular, we theoretically predict and experimentally verify the existence of saltatory and oscillatory motions for a well-defined range of micropipette suction pressures.

Coordination of Kinesin motors pulling on fluid membranes.

Intracellular transport relies on the action of motor proteins, which work collectively to either carry small vesicles or pull membranes tubes along cytoskeletal filaments. Although the individual properties of kinesin-1 motors have been extensively studied, little is known on how several motors coordinate their action and spatially organize on the microtubule when pulling on fluid membranes. Here we address these questions by studying, both experimentally and numerically, the growth of membrane tubes pulled by molecular motors. Our in vitro setup allows us to simultaneously control the parameters monitoring tube growth and measure its characteristics. We perform numerical simulations of membrane tube growth, using the experimentally measured values of all parameters, and analyze the growth properties of the tube considering various motor cooperation schemes. The comparison of the numerical results and the experimental data shows that motors use simultaneously several protofilaments of a microtubule to pull a single tube, as motors moving along a single protofilament cannot generate the forces required for tube extraction. In our experimental conditions, we estimate the average number of motors pulling the tube to be approximately nine, distributed over three contiguous protofilaments. Our results also indicate that the motors pulling the tube do not step synchronously.

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.

Viscous fingering as a paradigm of interfacial pattern formation: recent results and new challenges.

We review recent results on dynamical aspects of viscous fingering. The Saffman-Taylor instability is studied beyond linear stability analysis by means of a weakly nonlinear analysis and the exact determination of the subcritical branch. A series of contributions pursuing the idea of a dynamical solvability scenario associated to surface tension in analogy with the traditional selection theory is put in perspective and discussed in the light of the asymptotic theory of Tanveer and co-workers. The inherently dynamical singular effects of surface tension are clarified. The dynamical role of viscosity contrast is explored numerically. We find that the basin of attraction of the Saffman-Taylor finger depends on viscosity contrast, and that the sensitivity to this parameter is maximal in the usual limit of high viscosity contrast. The competing attractors are identified as closed bubble solutions. We briefly report on recent results and work in progress concerning rotating Hele-Shaw flows, topological singularities and wetting effects, and also discuss future directions in the context of viscous fingering.

Study of the parametric oscillator driven by narrow‐band noise to model the response of a fluid surface to time‐dependent accelerations

A stochastic formulation is introduced to study the large amplitude and high‐frequency components of residual accelerations found in a typical microgravity environment (or g‐jitter). The linear response of a fluid surface to such residual accelerations is discussed in detail. The analysis of the stability of a free fluid surface can be reduced in the underdamped limit to studying the equation of the parametric harmonic oscillator for each of the Fourier components of the surface displacement. A narrow‐band noise is introduced to describe a realistic spectrum of accelerations, that interpolates between white noise and monochromatic noise. Analytic results for the stability of the second moments of the stochastic parametric oscillator are presented in the limits of low‐frequency oscillations, and near the region of subharmonic parametric resonance. Based upon simple physical considerations, an explicit form of the stability boundary valid for arbitrary frequencies is proposed, which interpolates smoothly between the low frequency and the near resonance limits with no adjustable parameter, and extrapolates to higher frequencies. A second‐order numerical algorithm has also been implemented to simulate the parametric stochastic oscillator driven with narrow‐band noise. The simulations are in excellent agreement with our theoretical predictions for a very wide range of noise parameters. The validity of previous approximate theories for the particular case of Ornstein–Uhlenbeck noise is also checked numerically. Finally, the results obtained are applied to typical microgravity conditions to determine the characteristic wavelength for instability of a fluid surface as a function of the intensity of residual acceleration and its spectral width.

Intrinsic noise-induced phase transitions: Beyond the noise interpretation

We discuss intrinsic noise effects in stochastic multiplicative-noise partial differential equations, which are qualitatively independent of the noise interpretation (Itô vs Stratonovich), in particular in the context of noise-induced ordering phase transitions. We study a model which, contrary to all cases known so far, exhibits such ordering transitions when the noise is interpreted not only according to Stratonovich, but also to Itô. The main feature of this model is the absence of a linear instability at the transition point. The dynamical properties of the resulting noise-induced growth processes are studied and compared in the two interpretations and with a reference Ginzburg-Landau-type model. A detailed discussion of a different numerical algorithm valid for both interpretations is also presented.

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.