To interested graduate and undergraduate students:

Below is a summary of our projects with a broad range of industrial, biophysical and biomedical applications . Other projects are also available; please feel free to contact me for further information.

(Note that experience with programming languages, such as C or Fortran, and numerical analysis is an advantage but not a requirement.)

Dynamics of Multiphase Flows: Flow in Porous Media
The dynamics of three-dimensional droplets, bubbles and fluid bridges in restricted geometries under low-Reynolds-number steady or oscillatory flows and gravity is a problem of great technological and fundamental interest. Efforts will be made to understand the dynamics of (a) fluid volumes adhering to the inner surface of capillary tubes or channels; (b) fluid droplets and bridges spreading on solid surfaces; and (c) fluid volumes attached to solid substrates under the influence of oscillatory flows. These systems are encountered in a broad range of industrial applications including coating operations, vapor condensation and waste treatment. The project is further motivated by its applicability to the secondary oil recovery. These processes are strongly dependent on the interaction of the immiscible two-phase mixtures and the success of such operations often depends on the displacement of small drops attached to solid surfaces.

Biofluid Dynamics: Blood Flow in Arteries and Microvessels
Blood flow in vivo is a complicated flow of numerous biological cells and inorganic ions and, for this reason, it is still not well understood. Several diseases are associated with abnormal microcirculation, including cardiovascular diseases, sickle-cell anemia and cerebral malaria. The cardiovascular disorders are the cause of heart attacks and strokes that are responsible for more than 50% of deaths in the Western world. These disasters are often associated with a blood clot, thrombus or embolus, blocking a key artery that supplies blood to the heart or the brain. Our goal is to develop tools for analyzing blood flow and, in particular, for describing the motion of red cells through blood vessels or bronchial airways.

Biophysics and Microrheology: Dilute Solutions of Biopolymers
During the last few years there has been a great interest in understanding the properties of semiflexible biopolymers, such as DNA, actin filaments, microtubules and very stiff viruses. In contrast to the large amount of work on flexible and rod-like polymers, work on semiflexible biopolymers is extremely limited. This project is concentrated on the dynamics properties of these biopolymers in dilute solutions in unbounded or constrained geometries. One example is the study of a DNA molecule inside a (spherical) virus, i.e. a common method in biomedical engineering to transfer genes.

Biophysics and Microrheology: Concentrated Solutions of Biopolymers
Understanding the dynamic behavior of concentrated solutions and networks of biopolymers remains one of the major challenges of biophysics. Our current understanding of such systems is mainly based on the reptation model for both flexible and rod-like polymers. Unfortunately, comparison of these models with experiments show limited agreement for semiflexible biopolymers like DNA, actin filaments or microtubules. Results from this study will have applications in diverse fields; e.g. this work will provide information on the mechanical stability of the cytoskeleton of the cells.

Numerical Analysis: Development of Novel Computational Techniques
The goal of this project is to develop novel computational algorithms that will facilitate the study of the dynamics of three-dimensional droplets, bubbles, biological cells and artificial capsules under viscous steady and oscillatory flows. The use of the current state of the art algorithms is restricted because (a) they employ low-order interpolation schemes resulting in low accuracy and/or high computational cost due to dense grids; (b) they also employ explicit time integration schemes for determining the interfacial position resulting in small time steps due to stability considerations; and/or (c) show limited scalability on multiprocessor computers. To overcome these obstacles, we propose the development of efficient algorithms based on our Spectral Boundary Element implementation of interfacial dynamics in Stokes flow.

Computational Laboratory
Our computational research includes the utilization of state of the art, efficient algorithms which permit the study of a large number of "objects" and the parallelization of these algorithms, so that we are able to exploit the recent availability of great computational power. These methodologies facilitate the investigation of large-scale dynamic simulations of suspensions of red blood cells, biopolymer chains as well as artificial capsules, drops and solid nanoparticles. Today, a vast array of more realistic and complicated problems, which in the past were regarded as unattainable, can be studied thoroughly. These computations are performed on both local and remote machines. Our group employs a cluster of several multi-core computers as well as multiprocessor computers provided by the Extreme Science and Engineering Discovery Environment (XSEDE)

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