Biomedical subjects

J Casademunt

Publications and source records attributed to J Casademunt.

At least 19 recordsLinked to original sources

PubMed2006

Relevance of dynamic wetting in viscous fingering patterns.

We demonstrate that wetting effects at moving contact lines have a strong impact in viscous fingering patterns. Experiments in a rotating Hele-Shaw (HS) cell, dry or prewetted, show consistent morphological differences. When the wetting fluid invades a dry region, contact angle dynamics yield a kinetic contribution to the interface pressure drop that scales with capillary number as Ca(2/3) but is significantly larger than the Park-Homsy kinetic correction. Numerical results are in very good agreement with experiments and show that standard HS equations work best for prewetted cells.

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PubMed2006

Collective dynamics of interacting molecular motors.

The collective dynamics of N interacting processive molecular motors are considered theoretically when an external force is applied to the leading motor. We show, using a discrete lattice model, that the force-velocity curves strongly depend on the effective dynamic interactions between motors and differ significantly from those of a simple approach where the motors equally share the force. Moreover, they become essentially independent of the number of motors if N is large enough (N> or approximately 5 for conventional kinesin). We show that a two-state ratchet model has a very similar behavior to that of the coarse-grained lattice model with effective interactions. The general picture is unaffected by motor attachment and detachment events.

Computer Simulation↗

PubMed2004

Traveling-stripe forcing generates hexagonal patterns.

We study the response of Turing stripe patterns to a simple spatiotemporal forcing. This forcing has the form of a traveling wave and is spatially resonant with the characteristic Turing wavelength. Experiments conducted with the photosensitive chlorine dioxide-iodine-malonic acid reaction reveal a striking symmetry-breaking phenomenon of the intrinsic striped patterns giving rise to hexagonal lattices for intermediate values of the forcing velocity. The phenomenon is understood in the framework of the corresponding amplitude equations, which unveils a complex scenario of dynamical behaviors.

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PubMed2004

Nonlinear Saffman-Taylor instability.

We show, both theoretically and experimentally, that the interface between two viscous fluids in a Hele-Shaw cell can be nonlinearly unstable before the Saffman-Taylor linear instability point is reached. We identify the family of exact elastica solutions [Nye et al., Eur. J. Phys. 5, 73 (1984)]] as the unstable branch of the corresponding subcritical bifurcation which ends up at a topological singularity defined by interface pinchoff. We devise an experimental procedure to prepare arbitrary initial conditions in a Hele-Shaw cell. This is used to test the proposed bifurcation scenario and quantitatively asses its practical relevance.

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PubMed2003

Systematic weakly nonlinear analysis of radial viscous fingering.

We present a weakly nonlinear analysis of the interface dynamics in a radial Hele-Shaw cell driven by both injection and rotation. We extend the systematic expansion introduced in [E. Alvarez-Lacalle et al., Phys. Rev. E 64, 016302 (2001)] to the radial geometry, and compute explicitly the first nonlinear contributions. We also find the necessary and sufficient condition for the uniform convergence of the nonlinear expansion. Within this region of convergence, the analytical predictions at low orders are compared satisfactorily to exact solutions and numerical integration of the problem. This is particularly remarkable in configurations (with no counterpart in the channel geometry) for which the interplay between injection and rotation allows that condition to be satisfied at all times. In the case of the purely centrifugal forcing we demonstrate that nonlinear couplings make the interface more unstable for lower viscosity contrast between the fluids.

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PubMed2003

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.

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PubMed2003

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.

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PubMed2002

Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study.

We study the singular effects of vanishingly small surface tension on the dynamics of finger competition in the Saffman-Taylor problem, using the asymptotic techniques described by Tanveer [Philos. Trans. R. Soc. London, Ser. A 343, 155 (1993)] and Siegel and Tanveer [Phys. Rev. Lett. 76, 419 (1996)], as well as direct numerical computation, following the numerical scheme of Hou, Lowengrub, and Shelley [J. Comput. Phys. 114, 312 (1994)]. We demonstrate the dramatic effects of small surface tension on the late time evolution of two-finger configurations with respect to exact (nonsingular) zero-surface-tension solutions. The effect is present even when the relevant zero-surface-tension solution has asymptotic behavior consistent with selection theory. Such singular effects, therefore, cannot be traced back to steady state selection theory, and imply a drastic global change in the structure of phase-space flow. They can be interpreted in the framework of a recently introduced dynamical solvability scenario according to which surface tension unfolds the structurally unstable flow, restoring the hyperbolicity of multifinger fixed points.

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PubMed2002

Kinematic reduction of reaction-diffusion fronts with multiplicative noise: derivation of stochastic sharp-interface equations.

We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated with the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-Kardar-Parisi-Zhang universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations and kinetic roughening. We also predict and observe a noise-induced pushed-pulled transition. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.

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PubMed2002

Dynamical systems approach to Saffman-Taylor fingering: dynamical solvability scenario.

A dynamical systems approach to competition of Saffman-Taylor fingers in a Hele-Shaw channel is developed. This is based on global analysis of the phase space flow of the low-dimensional ordinary-differential-equation sets associated with the classes of exact solutions of the problem without surface tension. Some simple examples are studied in detail. A general proof of the existence of finite-time singularities for broad classes of solutions is given. Solutions leading to finite-time interface pinchoff are also identified. The existence of a continuum of multifinger fixed points and its dynamical implications are discussed. We conclude that exact zero-surface tension solutions taken in a global sense as families of trajectories in phase space are unphysical because the multifinger fixed points are nonhyperbolic, and an unfolding does not exist within the same class of solutions. Hyperbolicity (saddle-point structure) of the multifinger fixed points is argued to be essential to the physically correct qualitative description of finger competition. The restoring of hyperbolicity by surface tension is proposed as the key point to formulate a generic dynamical solvability scenario for interfacial pattern selection.

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PubMed2001

Periodic forcing in viscous fingering of a nematic liquid crystal.

Viscous fingering of an air-nematic interface in a radial Hele-Shaw cell is studied when periodically switching on and off an electric field, which reorients the nematic and thus changes its viscosity, as well as the surface tension and its anisotropy (mainly enforced by a single groove in the cell). Undulations at the sides of the fingers are observed that correlate with the switching frequency and with tip oscillations that give maximal velocity to smallest curvatures. These lateral undulations appear to be decoupled from spontaneous (noise induced) side branching. It is concluded that the lateral undulations are generated by successive relaxations between two limiting finger widths. The change between these two selected pattern scales is mainly due to the change in the anisotropy. This scenario is confirmed by numerical simulations in the channel geometry, using a phase-field model for anisotropic viscous fingering.

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PubMed2001

Systematic weakly nonlinear analysis of interfacial instabilities in Hele-Shaw flows.

We develop a systematic method to derive all orders of mode couplings in a weakly nonlinear approach to the dynamics of the interface between two immiscible viscous fluids in a Hele-Shaw cell. The method is completely general: it applies to arbitrary geometry and driving. Here we apply it to the channel geometry driven by gravity and pressure. The finite radius of convergence of the mode-coupling expansion is found. Calculation up to third-order couplings is done, which is necessary to account for the time-dependent Saffman-Taylor finger solution and the case of zero viscosity contrast. The explicit results provide relevant analytical information about the role that the viscosity contrast and the surface tension play in the dynamics of the system. We finally check the quantitative validity of different orders of approximation and a resummation scheme against a physically relevant, exact time-dependent solution. The agreement between the low-order approximations and the exact solution is excellent within the radius of convergence, and is even reasonably good beyond this radius.

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PubMed2001

Universality class of fluctuating pulled fronts.

It has recently been proposed that fluctuating "pulled" fronts propagating into an unstable state should not be in the standard Kardar-Parisi-Zhang (KPZ) universality class for rough interface growth. We introduce an effective field equation for this class of problems, and show on the basis of it that noisy pulled fronts in d+1 bulk dimensions should be in the universality class of the ((d+1)+1)D KPZ equation rather than of the (d+1)D KPZ equation. Our scenario ties together a number of heretofore unexplained observations in the literature, and is supported by previous numerical results.

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PubMed2001

Sidebranching induced by external noise in solutal dendritic growth.

We have studied sidebranching induced by fluctuations in dendritic growth. The amplitude of sidebranching induced by internal (equilibrium) concentration fluctuations in the case of solidification with solutal diffusion is computed. This amplitude turns out to be significantly smaller than values reported in previous experiments. The effects of other possible sources of fluctuations (of an external origin) are examined by introducing nonconserved noise in a phase-field model. This reproduces the characteristics of sidebranching found in experiments. Results also show that sidebranching induced by external noise is qualitatively similar to that of internal noise, and it is only distinguished by its amplitude.

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PubMed2000

Brownian motion of spiral waves driven by spatiotemporal structured noise

Spiral chemical waves subjected to a spatiotemporal random excitability are experimentally and numerically investigated in relation to the light-sensitive Belousov-Zhabotinsky reaction. Brownian motion is identified and characterized by an effective diffusion coefficient which shows a rather complex dependence on the time and length scales of the noise relative to those of the spiral. A kinematically based model is proposed whose results are in good qualitative agreement with experiments and numerics.

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PubMed2000

Viscous fingering in liquid crystals: anisotropy and morphological transitions

We show that a minimal model for viscous fingering with a nematic liquid crystal in which anisotropy is considered to enter through two different viscosities in two perpendicular directions can be mapped to a twofold anisotropy in the surface tension. We numerically integrate the dynamics of the resulting problem with the phase-field approach to find and characterize a transition between tip splitting and side branching as a function of both anisotropy and dimensionless surface tension. This anisotropy dependence could explain the experimentally observed (reentrant) transition as temperature and applied pressure are varied. Our observations are also consistent with previous experimental evidence in viscous fingering within an etched cell and simulations of solidification.

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PubMed2000

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.

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PubMed1999

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.

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