Giuseppe Gonnella

A LATTICE BOLTZMANN MODEL OF TERNARY FLUID MIXTURES

A lattice Boltzmann model is introduced which simulates oil-water-surfactant mixtures. The model is based on a Ginzburg-Landau free energy with two scalar order para meters. Diffusive and hydrodynamic transport is included. Results are presented showing how the surfactant diffuses to the oil-water interfaces thus lowering the surface tension and leading to spontaneous emulsification. The rate of emulsification depends on the viscosity of the ternary fluid.

SPINODAL DECOMPOSITION TO A LAMELLAR PHASE: EFFECTS OF HYDRODYNAMIC FLOW

Results are presented for the kinetics of domain growth of a two-dimensional fluid quenched from a disordered to a lamellar phase. At early times when a Lifshitz-Slyozov mechanism is operative the growth process proceeds logarithmically in time to a frozen state with locked-in defects. However, when hydrodynamic modes become important, or the fluid is subjected to shear, the frustration of the system is alleviated and the size and orientation of the lamellae attain their equilibrium values.

Finite-difference lattice Boltzmann model with flux limiters for liquid-vapor systems

In this paper we apply a finite difference lattice Boltzmann model to study the phase separation in a two-dimensional liquid-vapor system. Spurious numerical effects in macroscopic equations are discussed and an appropriate numerical scheme involving flux limiter techniques is proposed to minimize them and guarantee a better numerical stability at very low viscosity. The phase separation kinetics is investigated and we find evidence of two different growth regimes depending on the value of the fluid viscosity as well as on the liquid-vapor ratio.

Phase-separating binary fluids under oscillatory shear.

We apply the lattice Boltzmann methods to study the segregation of binary fluid mixtures under oscillatory shear flow in two dimensions. The algorithm allows to simulate systems whose dynamics is described by the Navier-Stokes and the convection-diffusion equations. The interplay between several time scales produces a rich and complex phenomenology. We investigate the effects of different oscillation frequencies and viscosities on the morphology of the phase separating domains. We find that at high frequencies the evolution is almost isotropic with growth exponents 2/3 and 1/3 in the inertial (low viscosity) and diffusive (high viscosity) regimes, respectively. When the period of the applied shear flow becomes of the same order of the relaxation time T(R) of the shear velocity profile, anisotropic effects are clearly observable. In correspondence with nonlinear patterns for the velocity profiles, we find configurations where lamellar order close to the walls coexists with isotropic domains in the middle of the system. For particular values of frequency and viscosity it can also happen that the convective effects induced by the oscillations cause an interruption or a slowing of the segregation process, as found in some experiments. Finally, at very low frequencies, the morphology of domains is characterized by lamellar order everywhere in the system resembling what happens in the case with steady shear.

Two-Scale Competition in Phase Separation with Shear

The behavior of a phase separating binary mixture in uniform shear flow is investigated by numerical simulations and in a renormalization group (RG) approach. Results show the simultaneous existence of domains of two characteristic scales. Stretching and cooperative ruptures of the network produce a rich interplay where the recurrent prevalence of thick and thin domains determines log-time periodic oscillations. A power law growth

Phase separation of incompressible binary fluids with Lattice Boltzmann Methods

R(t) \sim t^{\alpha}

Scaling and hydrodynamic effects in lamellar ordering

of the average domain size, with

Switching dynamics in cholesteric blue phases

\alpha =4/3

Hybrid lattice Boltzmann model for binary fluid mixtures

and

Morphologies and flow patterns in quenching of lamellar systems with shear

\alpha = 1/3