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Daniel M. Kroll, Principal Investigator

Mesoscopic Models for Solvent Dynamics and Complex Fluids

Hydrodynamic interactions play a central role in determining dynamical and nonequilibrium phenomena in self-assembling amphiphilic systems and molecular aggregates in flow. In self-assembling fluids, correlated mesoscopic structures exist even far from criticality. It has recently been shown that this structure leads to anomalous scaling behavior in the dynamic structure factor as well as anomalies in the shear viscosity and attenuation and dispersion of sound. In flow, the deformation of these correlated domains gives rise to excess stresses that result in rheological behavior 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 (and incompletely understood) influence on both the shape of these networks as well as the rheology of suspensions. For example, the deformation of polymers in hydrodynamic flows is a fundamental and still incompletely resolved problem in polymer physics, and the rheology and shape of red blood cells flowing in narrow capillaries is of great importance in medicine. Excess shear stress at the endothelial wall can lead to life threatening lesions called dissecting aneurysms. The shear stress at vessel walls also influences many other vascular functions, such as the permeability of the vascular walls to large molecules, the biosynthetic activity of the endothelial cells, and the coagulation of the blood.

While there has been some success understanding these problems using analytic methods, progress has been hindered by the lack of efficient simulation techniques. What is required is a sufficiently coarse-grained description of the solvent degrees of freedom. A promising approach being currently explored is to describe the hydrodynamic degrees of freedom using a Boltzmann equation, discretized in velocity, space, and time.

Extended lattice Boltamann (LB) methods have been developed to study these systems. Thomas Ihle, a current Supercomputing Institute Research Scholar, has developed a LB scheme capable of describing the dynamics of all the hydrodynamic modes of a normal non-ideal fluid. He has also implemented a simpler LB scheme for ideal fluids and binary mixtures that includes the effect of thermal fluctuations.

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Unfortunately, the discrete nature of the velocity field in the LB approximation leads to instabilities that 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, a closely related mesoscopic model for solvent dynamics is being studied. This model utilizes a synchronous, discrete-time dynamics with continuous velocities and local multiparticle collisions. The fluid is modeled by "particles" whose positions and velocities are continuous variables. The system is coarse grained onto the cells of a regular lattice, and the dynamics is carried out synchronously at discrete time steps. Particle streaming is treated exactly while the cells are the collision volumes for a multiparticle collision dynamics. The dynamics satisfies mass, momentum, and energy conservation and yields the correct hydrodynamics equations. Since it is a particle model, collision coupling to other microscopic degrees of freedom is easily incorporated and its application to complex geometries is straightforward. The method can also be extended to model binary mixtures and more complex mixtures.

This information is available in alternative formats upon request by individuals with disabilities. Please send email to alt-format@msi.umn.edu or call 612-624-0528.

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