Periodic forcing in viscous fingering of a nematic liquid crystalView Publication
Interface roughening in Hele-Shaw flows with quenched disorder: experimental and theoretical resultsView Publication
Sidebranching induced by external noise in solutal dendritic growthView Publication
Pattern-forming instabilities of the nematic - smectic B interfaceView Publication
Viscous fingering in liquid crystals: Anisotropy and morphological transitionsView Publication
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 two-fold 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.
Phase-field model for Hele–Shaw flows with arbitrary viscosity contrast. I. Theoretical approachView Publication
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.
Phase-field model for Hele-Shaw flows with arabitrary contrast II: numerical approachView Publication
We implement a phase-field simulation of the dynamics of two fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. We demonstrate the use of this technique in different situations including the linear regime, the stationary Saffman-Taylor fingers and the multifinger competition dynamics, for different viscosity contrasts. The method is quantitatively tested against analytical predictions and other numerical results. A detailed analysis of convergence to the sharp interface limit is performed for the linear dispersion results. We show that the method may be a useful alternative to more traditional methods.
Growth of unstable interfaces in disordered mediaView Publication
Heat diffusion anisotropy in dendritic growth: phase-field simulations and experiments in liquid crystalsView Publication
Pattern forming during mesophase growth in a homologous seriesView Publication
Interfacial instability induced by external fluctuationsView Publication
Scaling relations and exponents in the growth of rough interfaces through random mediaView Publication
The growth of a rough interface through a random media is modelled by a continuous stochastic equation with a quenched noise. By use of the Novikov theorem we can transform the dependence of the noise on the interface height into an effective temporal correlation for different regimes of the evolution of the interface. The exponents characterizing the roughness of the interface can thus be computed by simple scaling arguments showing a good agreement with recent experiments and numerical simulations.