  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 Email: vivekn12 @ stanford . edu

1. Coarsegrained 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 “FahraeusLindqvist 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 coarsegrained model to predict the concentration distribution of red blood cells (and hence the FahraeusLindqvist effect) in wallbounded shear flows. This model balances the wallinduced hydrodynamic lift on deformable particles with the flux due to binary collisions, which we represent via a secondorder kinetic master equation. Our theory is not selfsufficient, 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 wallbounded shear flow. Nevertheless, it represents a significant improvement in terms of time savings and predictive power over current largescale numerical simulations of suspension flows.

Fig 1: Schematic of FahraeusLindqvist 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 coarsegrained 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 areapreserving membranes as well as bending resistance. We develop a simple, analytical
theory to predict the onset of shapechange. 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
tube.
References:
1. Spjut, J. & Muller, S. 2008 Phospholipid vesicle: stagnation point flow studies. ''Private
communication''.
2. Kantsler, V., Segre, E. & V., Steinberg 2008. “Critical dynamics of vesicle stretching transition
in elongational flow.” Phys. Rev. Lett. 101, 048101.