Emulsion flows occur in polymer blending, mass-transfer equipment, food and beverage processing, oil recovery and other applications. Describing these flows is made difficult by complex rheological features of the emulsions (drop deformation and interactions, surfactant elasticity, etc.). The problem is even more difficult when the flow is through narrow channels or a porous medium such as a packed bed. This project is focused on the development of a comprehensive modeling strategy for the rheology of highly-concentrated emulsions based on rigorous microstructural dynamical simulations. Realistic features affecting the rheological behavior are included, such as an arbitrary type of macroscopic flow, three-dimensionality, random arrangement, drop deformation, hydrodynamical interactions, the presence of surfactants, and the possibility of dynamical phase transition to a partially-ordered state. The specific tasks of the project are:
(i) Prediction of the rheology of concentrated emulsions in extensional flows. A new algorithm for many drops is based on a combination of highly-efficient, 3D multipole-accelerated boundary-integral tools with periodic conditions to predict the average stress tensor in planar-extensional flows and its dependence on drop volume fraction, deformability and viscosity ratio.
(ii) Determination of the effect of surfactants on the emulsion rheology. A model of an insoluble surfactant is incorporated into 3D simulations for many deformable drops to study the additional effect of surfactant elasticity on the emulsion rheology. At high drop volume fractions, a prominent effect of surfactants is expected near the jamming limit, where the drops become less deformable and the role of interactions and surface mobility greatly increases.
(iii) Construction of a constitutive equation for a concentrated emulsion. A novel constitutive model from this work is based on matching a generalized Oldroyd-type rheological equation to shear and planar-extension simulations. The resulting constitutive equation, with parameters based exclusively on microstructural modeling, incorporates the effects of drop volume fraction, deformability, viscosity ratio and surfactant elasticity.
(iv) Simulations of emulsion flow through a packed bed. The microstructure-based constitutive equations are employed in a novel, multipole-accelerated boundary-integral algorithm to study 3D viscoelastic flow of a concentrated emulsion through a randomly packed bed. When the drops are comparable in size with the particles, so that the drop and continuous phases have different permeabilities and must be treated separately, a complementary, fully-microstructural approach is used for comprehensive modeling based on multidrop-multiparticle simulations.
Intellectual Merit: The project provides substantially new information about the rheology of realistic, concentrated emulsions obtained by rigorous simulations from first principles. The new approach to constitutive modeling, not limited to emulsions, is expected to apply for broad classes of flows. The novel method for emulsion flow through packed beds bridges emulsion rheology and non-Newtonian hydrodynamics; the algorithm for the solution is not be limited to emulsions and can accommodate any constitutive equation of differential type.
Broader Impacts: An important feature of the project is the development of interactive eduational modules to provide animations for multiphase flow through porous media. The web-based modules can be distributed to K-12 students via the TeachEngineering digital library and via NSF Graduate K-12 Fellows to the University of Colorado and local schools, in partnership with the Integrated Teaching and Learning Program at the University of Colorado. The project also provides training for at least one graduate student and three undergraduates through the research and module work.
