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Multiphase fluid flows are encountered in a wide array of industrial operations in the petrochemical industry. Depending upon the process, the multiphase mixture may be a concentrated oil-water suspension, a liquid-liquid foam or even a three phase mixture of oil, gas and water. Multiphase fluid mixtures are also utilized in many manufacturing operations involving flow through pipelines, capillaries, packed beds and porous media. The macroscopic properties of multiphase fluid mixtures of greatest interest include the relative permeabilities (or transport rates) of the individual phases for flow through porous media and the effective rheological properties of the mixture for processing operations. On a macroscopic level, emulsions and foams exhibit a range of non- Newtonian rheological behavior including shear dependent viscosity, normal stresses, viscoelasticity and yield stresses. Theoretical predictions for these properties require analysis on the microscale viscous multiphase flows governed by the Stokes equations.

In this research program, we seek to execute large scale three dimensional hydrodynamic simulations with up to 500-1000 droplets to study highly concentrated emulsions and foams. The research focuses on two distinct thrusts: (1) to characterize the rheology and phase behavior of the suspensions in linear shear flows and (2) to analyze the multiphase transport through three dimensional model porous media. For the rheology studies, the phenomena include (i) shear thinning/shear thickening behavior,(ii) disorder-order phase transitions, (iii) phase segregation in bidisperse suspensions,(iv) non-uniform shear fields leading to shear bands and wall slip. For the transport in porous media, attention will focus on the relative transport of the two phases and the effect of pore-constriction geometries on transport properties. Special efforts will focus on the effects of random disordered microstructures on phenomena such as pore blocking, and preferential flow behavior for individual phases.

In the past year, our efforts have focused on our asymptotic model based on suspensions with mixtures of deformable spheres and rigid spheres. This model may be used be used to characterize the behavior of emulsions with strong surface tension yielding low capillary numbers. Suspensions with a monodisperse collection of deformable spheres may be used to model emulsions in unbounded shear flows, while suspensions with mixtures of freely suspended deformable spheres and rigid spheres at fixed positions may be employed to study droplet motion through porous media. Large scale simulations with this model will allow rapid exploration of the phase transitions occurring in concentrated emulsions and provide comparisons for the more complex spectral boundary integral simulations. The primary challenge in this effort has been the development of an accurate low order discretization of the elastohydrodynamic interactions in the near contact region. The resolution of these contact interactions in the droplet approach stage proved straightforward, however the dynamics in the droplet withdrawal stage proved quite a bit more complex. During the past year, we have successfully completed the algorithms for the asymptotic interaction model with robust solutions over the full range of deformability from soft spheres through asymptotically small capillary number. This provides the foundation for efficient simulations on the dynamics of concentrated emulsions in both unbounded and bounded domains.

The support provided by the Petroleum Research Fund will assist in the successful implementation and dissemination of these new, innovative computational algorithms. This will provide a computational toolbox of great utility for both academic and industrial researchers. The support is of significant benefit to the principal investigator as it provides critical early support for a novel computational approach without which the final application to industrial problems could not be achieved. The support for the graduate research assistant is of significant educational benefit as it allows him to develop skills in the complementary areas of asymptotic analysis, large scale computation, physical modeling and statistical analysis of disordered systems.