|Vivek Narsimhan |
B.S., Chemical Engineering,
California Institute of Technology, 2008
Cert. Adv. Study, Applied Mathematics,
University of Cambridge, 2009
M.S., Chemical Engineering,
Stanford University, 2011
1. Coarse-grained theory to predict concentration distribution of red blood cells in Couette flow
When red blood cells move throughout our microcirculation, they do not flow with a uniform distribution across the blood vessel, but instead leave a significant layer of clarified fluid near the vessel wall, a phenomenon famously coined the “Fahraeus-Lindqvist effect.’’ The size and shape of this clarified layer plays an important role in reducing blood's effective viscosity in the microcirculation, mediating plasma skimming at channel bifurcations, and controlling oxygen and nitric oxide transport in the arterioles. We develop a coarse-grained model to predict the concentration distribution of red blood cells (and hence the Fahraeus-Lindqvist effect) in wall-bounded shear flows. This model balances the wall-induced hydrodynamic lift on deformable particles with the flux due to binary collisions, which we represent via a second-order kinetic master equation. Our theory is not self-sufficient, as it requires data (simulation or experimental) on the details of a binary collision process and the hydrodynamic lift of a single particle in a wall-bounded shear flow. Nevertheless, it represents a significant improvement in terms of time savings and predictive power over current large-scale numerical simulations of suspension flows.
Fig 1: Schematic of Fahraeus-Lindqvist effect
Fig 2: Probability Density of Red Blood Cells in Channel Flow. Dots represent results from 3D boundary
integral simulations of a suspension of red blood cells in Couette flow, while the other curves are results
from our coarse-grained theory (R is a hydrodynamic screening length that is an input to the model).
The volume fraction is 10 percent, and channel height is 12 times the particle radius.
2. Instability of Vesicles under Extensional Flow
Recently, several researchers have observed that biological particles such as vesicles undergo
asymmetric shape transitions under strong extensional flows (Fig 3). These shape transitions are very
different than what is observed for standard droplet breakup, and we believe that this instability is
driven by the dynamics of the complex interface on these particles. We focus our attention on vesicles as a model system, which are particles that possess area-preserving membranes as well as bending resistance. We develop a simple, analytical
theory to predict the onset of shape-change. This model will help us understand the mechanism
behind this instability, as well as the seemingly unrelated phenomenon of pearling (see Fig 4).
Fig 3: Asymmetric shape change of a vesicle under planar extensional flow. Pictures are from Spjut
and Muller, 2008. The scale bar is 5 microns.
Fig 4: Pearling Instability. In this picture (reproduced from Kantsler et al (2008)), a long, cylindrical
vesicle under extensional flow undergoes an instability where satellite “pearls” form in the middle of the
1. Spjut, J. & Muller, S. 2008 Phospholipid vesicle: stagnation point flow studies. ''Private
2. Kantsler, V., Segre, E. & V., Steinberg 2008. “Critical dynamics of vesicle stretching transition
in elongational flow.” Phys. Rev. Lett. 101, 048101.