Computational study of drop deformation in systems with two immiscible liquids

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This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).The project is devoted to development and implementation of new algorithms for the modeling and computational investigation of deformation and breakup of interfaces that separate two immiscible liquids. The majority of the effort is focused on the following four themes: (i) Differential constitutive models for viscoelastic liquids such as the Giesekus model will be used to study drops suspended in a matrix liquid and deformed by simple shear, cessation of shear, and large strain jumps. (ii) The recent development of microscale apparatuses has spawned new modeling and simulation challenges for droplet evolution in physical devices that are as small as the droplet itself. The project will investigate the effect of walls closing in on viscoelastic systems, for which novel breakup scenarios have been discovered experimentally. (iii) The motion of contact lines in liquid-liquid-solid systems will be investigated. A combination of the phase-field formulation and the volume-of-fluid height function method will be pursued. The former is more suited for resolving the physics of the contact line, but too resource intensive for use in the entire flow field. A challenge in contact line problems is how to obtain mesh independent results. Recent work has suggested the existence of a 'master curve' which can be used to determine a mesh dependent 'imposed' contact angle as a function of the desired 'macroscopic' contact angle. A specific computational application is electrowetting, which is perhaps the most widely used technique for drop actuation because of lower power consumption and because an applied voltage moves the drop without the need for pumps and valves. In this context, moving contact lines for the coupled system of hydrodynamic and Maxwell equations will be studied. (iv) Magnetic drug targeting involves using a ferrofluid drop as a drug carrier, which is guided through biological tissue to a specific location. An important quantity for feasibility is the transit time. Direct numerical simulations will be carried out for the motion of ferrofluid drops in viscous media under non-uniform magnetic fields. This project involves the mentoring of a postdoctoral research associate and the training of graduate students. Results will be disseminated at national and international conferences on mathematics, physics and engineering, and through journal publications. Cross-disciplinary and international partnerships will take place with scientists who obtain experimental data for comparison with numerical results.The advantages in combining the desired properties of two different liquids to produce a new blended mixture are well known. The quality of the blend is strongly dependent on its microstructure, such as the size of the dispersed droplets and their distribution in the final product. Therefore, it is of practical importance to understand how a droplet evolves in the surrounding liquid and to predict how this is influenced by the rheological properties of each constituent fluid. This will be accomplished by performing direct numerical simulations with in-house state-of-the-art parallelized algorithms that are optimized for scalability and computational cost. The topics in this project contribute to the understanding of complex multi-scale systems that arise in recycling plastics, environmental sustainability, biomedical drug delivery, and droplet manipulation in microfluidic devices. Intensive use of computational infrastructures such as the TeraGrid will allow for quantitative comparison of mathematical models with raw experimental data.