Daniel M. Kroll, Principal Investigator

Mesoscopic Models for Solvent Dynamics and Complex Fluids

  In self-assembling fluids, correlated mesoscopic structures exist even far from critical points. This structure leads to anomalous scaling behavior in the dynamic structure factor as well as anomalies in the shear viscosity and the attenuation and dispersion of sound. In flow, the deformation of these correlated domains gives rise to excess stresses which result in rheological behavior that is quite different from that of simple Newtonian fluids. Near phase boundaries, shear can lead to dynamical instabilities and new structures in these systems. Similarly, flow induced hydrodynamic stress on polymers or vesicles has a dramatic influence on both the shape of these networks as well as the rheology of suspensions. The objective of this project was to obtain a better understanding of the dynamics of complex liquids and the dynamical behavior of polymers and membranes in solvent. An essential component of this research was to develop and implement new algorithms based on generalizations of the lattice-Boltzmann method for the numerical simulation of the equilibrium and non-equilibrium dynamics to these systems. Unfortunately, the discrete nature of the velocity field in the lattice-Boltzmann approximation led to instabilities, which severely limit the usefulness of this method in a number of applications. This is particularly true when the method is extended to incorporate thermal fluctuations. For this reason studies were performed using a closely related mesoscopic model for solvent dynamics. This model utilized a synchronous, discrete-time dynamics with continuous velocities and local multiparticle collisions. The method is Galilean invariant, stable, and easy to implement on parallel architectures. Furthermore, all conservation laws were obeyed exactly, with fluctuations included. It can also be extended to model binary mixtures and more complex mixtures. The algorithms were developed for a wide range of applications in basic science and engineering.

  Another study undertaken by these researchers focused on the statistical mechanics of the freezing, undulations, and topology fluctuations of membranes. These are two-dimensional sheets of molecules that are embedded and fluctuate in three-dimensional space. The shape and out-of-plane fluctuations of tensionless membranes are controlled by their bending rigidity. Due to their out-of-plane fluctuations, flexible membranes exhibit very different behavior to flat two-dimensional systems.

  Three properties of membranes were considered:

1. the renormalization of the bending rigidity in fluid membranes due to undulations on short length scales;

2. the suppression of the crystalline phase, and the hexatic-to-fluid transition; and

3. the lamellar-to-sponge transition in systems with variable topology.

  The researchers focused on simulation studies, which are based on the numerical analysis of dynamically triangulated surface models.

  The researchers also performed pore-scale simulations of dispersion. In these simulations, tracer dispersion was simulated in three-dimensional models of regular and random sphere packings for a range of Peclet numbers. A random-walk particle-tracking (PT) method was used to simulate tracer movement within pore-scale flow fields computed with the lattice-Boltzmann (LB) method. The simulation results illustrated the time evolution of dispersion, and they corroborated a number of theoretical and empirical results for the scaling of asymptotic longitudinal and transverse dispersion with Peclet number.

  Comparisons with NMR spectroscopy experiments showed agreement on transient, as well as asymptotic, dispersion rates. These results support NMR findings that longitudinal dispersion rates are significantly lower than reported in earlier experimental literature, as well as the fact that asymptotic rates are observed in relatively short times by techniques that employ a uniform initial distribution of tracers, like NMR.