arXiv subjects

R. Folch

Publications and source records attributed to R. Folch.

10 recordsLinked to original sources

arXiv2005

Quantitative phase-field modeling of two-phase solidification

A phase-field model that allows for quantitative simulations of low-speed eutectic and peritectic solidification under typical experimental conditions is developed. Its cornerstone is a smooth free-energy functional, designed so that the stable solutions connecting any two phases are completely free of the third phase. For the simplest choice of this functional, the equations of motion for each of the two solid-liquid interfaces can be mapped to the standard phase-field model of single-phase solidification, and all thin-interface corrections to the dynamics of the solid-liquid interfaces can be eliminated. This means that simulation results become independent of the thickness W of the diffuse interfaces. As a consequence, accurate results can be obtained using values of W much larger than the physical interface thickness, which makes simulations for realistic experimental parameters feasible. Convergence of the simulation outcome with decreasing W is explicitly demonstrated. The results are also compared to a boundary-integral formulation of the corresponding free-boundary problem. Excellent agreement is found, except in the immediate vicinity of bifurcation points, where differences arise. These differences reveal that, in contrast to the standard assumptions of the free-boundary problem, out of equilibrium the diffuse trijunction region of the phase-field model can (i) slightly deviate from Young's law for the contact angles, and (ii) advance in a direction that forms a finite angle with the solid-solid interface at each instant. While the deviation (i) extrapolates to zero in the limit of vanishing interface thickness, the small angle in (ii) remains roughly constant, which indicates that it might be a genuine physical effect, present even for an atomic-scale interface thickness.

cond-mat.mtrl-sci↗

arXiv2004

Spontaneous pinch-off in rotating Hele-Shaw flows

The dynamics of the interface between two immiscible fluids in a rotating Hele-Shaw cell are studied experimentally, theoretically and by phase-field simulations of the H-S equations. As the central, denser fluid is centrifuged, it forms fingering patterns with long, thin radial filaments ended by a droplet, alternating with incoming fingers of the outer fluid. Simulations show the length (width) of the filaments to grow (decay) roughly exponentially, and the incoming finger tips to asymptotically approach a finite radius for n-fold symmetric initial conditions; these thus tend to a stationary-shape, which is calculated. The filament width decays with a time constant which depends only on the viscosity contrast, whereas its length exhibits a completely universal growth rate, related to the run away of an isolated droplet, for which we give an exact solution. The exponential behavior is clear for high, but not low viscosity contrasts A. Both experiments and simulations show systematic pinch-off of the droplets at the tips of the filaments for low and not for high A. A lubrication approximation is derived and successfully accounts for the filament thinning; it explains why pure exponential thinning is not observed for low A, and it could clarify the presence or absence of finite-time pinch-off, since the (morphological) agreement of experiments and simulations suggests that this phenomenon is contained in the Hele-Shaw equations. For low A, the experimental time constant appears to be different from that predicted by standard Hele-Shaw boundary conditions and observed in simulations. An effective slip condition for the Poiseuille flow of inner liquid across the cell gap in the case of two liquids gives a possible explanation of this discrepancy.

physics.flu-dyn↗

arXiv2004

Three-dimensional phase-field simulations of directional solidification

The phase-field method has become in recent years the method of choice for simulating microstructural pattern formation during solidification. One of its main advantages is that time-dependent three-dimensional simulations become feasible. This makes it possible to address long-standing questions of pattern stability. Here, we investigate the stability of hexagonal cells and eutectic lamellae. For cells, it is shown that the geometry of the relevant instability modes is determined by the symmetry of the steady-state pattern, and that the stability limits strongly depend on the strength of the crystalline anisotropy, as was previously found in two dimensions. For eutectics, preliminary investigations of lamella breakup instabilities are presented. The latter are carried out with a newly developed phase-field model of two-phase solidification which offers superior convergence properties.

cond-mat.mtrl-sci↗

arXiv2004

Towards a quantitative phase-field model of two-phase solidification

We construct a diffuse-interface model of two-phase solidification that quantitatively reproduces the classic free boundary problem on solid-liquid interfaces in the thin-interface limit. Convergence tests and comparisons with boundary integral simulations of eutectic growth show good accuracy for steady-state lamellae, but the results for limit cycles depend on the interface thickness through the trijunction behavior. This raises the fundamental issue of diffuse multiple-junction dynamics.

cond-mat.mtrl-sci↗

arXiv2003

Phase-field models in interfacial pattern formation out of equilibrium

The phase-field method is reviewed from the general perspective of converting a free boundary problem into a set of coupled partial differential equations. Its main advantage is that it avoids front tracking by using phase fields to locate the fronts. These fields interpolate between different constant values in each bulk phase through diffuse interfaces of finite thickness. In solidification, the phase fields can be understood as order parameters, and the model is often derived to dynamically minimise a free energy functional. However, this is not a necessary requirement, and both derivations involving a free energy (basic solidification model) and not (first viscous fingering model) are worked out. In any case, the model is required to reproduce the original free boundary problem in the limit of vanishing interface thickness. This limit and its higher order corrections, important to make quantitative contact between simulations and experiments, are discussed for both examples. Applications to fluctuations in solidification, the growth of liquid crystal mesophases, and viscous fingering in Hele-Shaw cells are presented.

cond-mat.mtrl-sci↗

arXiv2002

Phase-field Modeling of Eutectic Solidification: From Oscillations to Invasion

We develop a phase-field model of eutectic growth that uses three phase fields, admits strictly binary interfaces as stable solutions, and has a smooth free energy functional. We use this model to simulate oscillatory limit cycles in two-dimensional lamellar growth, and find a continuous evolution from low-amplitude oscillations to successive invasions of one solid phase by the other when the lamellar spacing is varied.

cond-mat.mtrl-sci↗

arXiv2002

Periodic forcing in viscous fingering of a nematic liquid crystal

We study viscous fingering of an air-nematic interface in a radial Hele-Shaw cell 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). We observe undulations at the sides of the fingers which correlate with the switching frequency and with tip oscillations which give maximal velocity to smallest curvatures. These lateral undulations appear to be decoupled from spontaneous (noise-induced) side branching. We conclude 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.

cond-mat.soft↗

arXiv1999

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 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.

cond-mat.soft↗

arXiv1999

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.

cond-mat.soft↗

arXiv1999

Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. II. Numerical study

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.

cond-mat.soft↗