The main focus of my research is on modeling of complex and biological fluids and the development of multiscale methods suitable for such systems. The modeling of complex fluids mainly involves polymer suspensions ranging from dilute and semi-dilute solutions to melts, and includes numerical rheological measurements of their properties and fluid flow simulations. My research on biological fluids is focused on the modeling of red blood cells, vesicles, blood flow, and rheology in health and disease. I also work on the development of methods for efficient multiscale algorithms which couple together atomistic, mesoscopic, and continuum descriptions.

Research projects

Coarse-grained modeling of red blood cells, vesicles, blood flow, and rheology

Red blood cells (RBCs) and vesicles are modeled as coarse-grained membranes using the Dissipative Particle Dynamics method. The cell surface is triangulated as shown in the figure, where each vertex corresponds to a DPD particle and each edge to a spring. The membrane properties can be successfully specified through an in-plane visco-elastic energy, bending energy, area, and volume constraints. The model is compared to available experimental results on the red blood cell stretching response and RBC microrheology and dynamics. Blood is modeled as a suspension of RBCs. Blood flow in arterioles yields to the cell-free layer near the vessel wall as RBCs separate from the plasma and migrate to the center of the vessel. The cell-free layer contributes significantly to the effective blood viscosity and vessel-wall shear-stresses.

Related publications:

1. D. A. Fedosov, B. Caswell and G. E. Karniadakis, "General coarse-grained red blood cell models: I. Mechanics", Biophysical Journal, submitted, [preprint].
2. D. A. Fedosov, B. Caswell and G. E. Karniadakis, "General coarse-grained red blood cell models: II. Rheology and dynamics", in preparation.
3. D. A. Fedosov, B. Caswell and G. E. Karniadakis, "Dissipative Particle Dynamics Simulation of Polymer- and Cell-Wall Depletion in Micro-Channels", Proceedings of the XV International Congress on Rheology: The Society of Rheology 80th Annual Meeting, AIP Conference Proceedings, 1027(1), 612-614, 2008.

The Triple-Decker algorithm: interfacing atomistic-mesoscale-continuum flow regimes

The Triple-Decker algorithm is a hybrid multiscale method based on coupling the Molecular Dynamics (MD) method, the Dissipative Particle Dynamics (DPD) method, and the incompressible Navier-Stokes (NS) equations. MD, DPD, and NS are formulated in separate sub-domains and are coupled via communication of state information at the sub-domain boundaries. The Triple-Decker multiscale method is able to cover a broad range of spatio-temporal scales starting from molecular to mesoscopic and to continuum, and it provides an efficient space and time decoupling.

Related publications:

1. D. A. Fedosov and G. E. Karniadakis, "Triple-Decker: Interfacing Atomistic-Mesoscopic-Continuum Flow Regimes", Journal of Computational Physics, 228(4), 1157-1171, 2009.

Modeling blood flow in cerebral malaria

The main characteristics of the malaria disease are progressing changes in red blood cell (RBC) mechanical properties and geometry, and its cytoadhesion to the vascular endothelium. Malaria-infected RBCs become considerably stiff compared to healthy ones, and may bind to the vascular endothelium of arterioles and venules. This leads to a significant reduction of blood flow, and eventual vessel obstruction. Blood flow in cerebral malaria is simulated using a coarse-grained RBC model in combination with the stochastic bond formation/breakage adhesion model. Adhered RBCs in a flow may be stationary or move in a rolling or flipping fashion with a nonzero velocity depending on the adhesion forces. In case of weak adhesion interactions, RBCs may detach from the vessel wall.

Numerical rheometry

Steady-state rheological properties (shear-dependent viscosity and normal stresses) are derived from simulations of plane reverse-Poiseuille flow (RPF) where a body force drives the flow in opposite directions in the left and right halves of a box. Periodic boundary conditions ensure the macro velocity to be zero on the walls without density fluctuations. Properties of solutions at different concentrations satisfy the time-concentration superposition principle. In addition, properties at several temperatures satisfy the time-temperature superposition principle. The RPF arrangement is generally more efficient and spans a greater range of shear rates than its Couette counterparts such as Lees-Edwards boundary conditions.

Related publications:

1. D. A. Fedosov, B. Caswell and G. E. Karniadakis, "Reverse Poiseuille Flow - The Virtual Rheometer", Soft Matter, submitted, preprint available upon request.
2. D. A. Fedosov, B. Caswell and G. E. Karniadakis, "Reverse Poiseuille Flow: the Numerical Viscometer", Proceedings of the XV International Congress on Rheology: The Society of Rheology 80th Annual Meeting, AIP Conference Proceedings, 1027(1), 1432-1434, 2008.

Polymers in solutions; depletion and migration in a flow

Polymers in solutions are simulated using a bead-spring model. Their properties are characterized through the radius of gyration and polymer diffusivity. Polymers in solutions are subject to wall depletion when placed in confined geometries. In micro- and nano-channels the depletion layer is often of the same order as the channel width, and greatly affects polymer distribution across the channel. In the presence of flow (e.g. Poiseuille, Couette) polymers experience across-stream migration, which changes polymer distribution across the channel.

Related publications:

1. D. A. Fedosov, B. Caswell and G. E. Karniadakis, "DPD Simulation of Depletion Layer and Polymer Migration in Micro- and Nano-Channels for Dilute Polymer Solutions", Journal of Chemical Physics, 128(14), 144903, 2008. Selected for publication in Virtual Journal of Nanoscale Science & Technology, 17(17), April 28 2008.

Dissipative Particle Dynamics: hydrodynamics, limits, boundary conditions

Dissipative Particle Dynamics (DPD) is a mesoscale method used in simulations of complex and biological fluids. Hydrodynamic interactions in DPD simulations are often of great importance due to a low Reynolds number of simulated flows. On the other side of the Re number range, the DPD method applicability is limited such that at high shear rates the DPD thermostat may not be able to keep the specified temperature, or a fluid must be considered compressible. In addition, in wall-bounded flows we need to correctly impose boundary conditions, and exclude erroneous effects such as near-wall density fluctuations.

Related publications:

1. W. Pan, D. A. Fedosov, B. Caswell and G. E. Karniadakis, "Hydrodynamic Interactions for Single DPD Particles, and their Clusters and Filaments", Physical Review E, 78(4), 046706, 2008.
2. D. A. Fedosov, I. V. Pivkin and G. E. Karniadakis, "Velocity Limit in DPD Simulations of Wall-Bounded Flows", Journal of Computational Physics, 227(4), 2540-2559, 2008.