	Continuum-level simulation of multiphase systems
	Research
	Particle-level simulation of multiphase systems
	Experimental investigations

Continuum-level simulation of multiphase systems

Multiphase systems encompass a wide variety of materials found in scientific and engineering processes. Some examples are: ceramic slurries, energetic materials, composite materials, river or ocean sediments, blood. When designing processes that involve multi-phase materials, it is necessary to be able to predict the flow behavior of the fluid under the processing conditions, in order to avoid costly failures of the process.
Generally, interesting multi-phase fluids contain extremely large numbers of particles per unit volume, so that it becomes impossible to treat each particle individually in a simulation. For this reason, the fluid is described as a continuum phase, with variables that describe, for example, the local particle concentration.
Currently, two major models exist to model multiphase flows: the diffusive flux model, and the suspension balance model. Research is ongoing in both areas, however currently the enphasis is on the suspension balance model.

Particle-level simulation of multiphase systems

The formulation of a continuum model for multi-phase system necessitates input from particle-level simulations. For example, the form of the fourth-order tensor which determines the normal stress difference tensor in the suspension balance model is not known. Through numerical experiment, it is possible to examine the normal stress differences that result, and thus obtain the component of the tensor. Other flow properties that are most readily obtained through numerical experiment are individual phase stresses, pair distribution functions, paricle cluster sizes, wall-particle interactions.
The modeling of a flowing multi-phase medium requires the description of a continually evolving geometry. Specification of the inter-phase boundary is the simplest way of describing such geometries. With a specified boundary, it is possible to apply boundary integral equations to the system. By constructing a system of integral equations for a set of points on the boundary, a system of linear equations is set up. Solution of this system yields quantities of interest. For example, if the forces acting on each individual particle are known, the corresponding particles velocities result from the solution of the system of equations. This technique is known as the boundary element method (BEM).
The main drawback that BEM has seen in its application to multi-phase flows is the large, fully populated matrices that must be solved. The operation count scales as N³ in the case of direct solution, or N² in the case of iterative solution, provided that the matrix is well-conditioned. Multipole acceleration can be used to reduce the operation count to scale with N log(N). This makes it possible to perform larger BEM simulation than previosly possible.
The year 1997 saw the birth of BEAVIS (Boundary Element Analysis of VIscous Suspensions), a parallel multipole-accelerated BEM code capable of performing dynamic simulations of systems with large numbers of particles. The code runs primarily at the Maui High Performance Computing Center (MHPCC) and at the Albuquerque High Performance computing center (AHPCC), in both cases on IBM SP2 platforms.

Experimental investigations

The laboratory work is the physical counterpart to the simulation work - in other words, we are interested in both macroscale behavior of complex fluids and what causes this behavior at the mesoscale. The main tools for the measuring macroscale behavior are a strain control Rheometrics RFS 8400 rheometer, and a stress-control Rheologica Stresstech rheometer. Both do a lot of the same measurements, but in some cases, one is better than the other. For example, the strain control rheometer is better for measuring structure formation and breakdown, while the stress control is better suited to measuring yield stresses. Typical work performed on the rheometers involves measuring apparent viscosities of suspensions and emulsions, normal stress difference measurements, apparent slip measurements, as well as more mundane things like characterizing individual fluids that are to be used in various experiments.
At the mesoscale level, the current major experiment is the `flow loop' , where complex fluids of various types are passed through a test sections, where images of the flow are taken for PIV imaging via one or two Kodak Megaplus 1.6i cameras, and stored to computer disk in real time. The steadiness of the flow is ensured by two reservoirs kept at a steady pressure differential, which provides the driving force for the flow. The fluid is returned to the supply reservoir by a peristaltic pump. The experiments that will be performed in the near future with the flow loop include flow of suspensions past various obstacles (to investigate shear and elongational flow behavior), and flow of fine suspensions through coarse porous media. Results will be posted as they become available.