Current and past research:

My research is broadly in soft matter systems, bio-fluid dynamics and bio-locomotion. My Ph.D. work was in granular physics. I worked on visco-elastic fluid flow during my post-doc at MIT. I joined the Applied Math Lab at the Courant Institute NYU in 2009, where I worked on the locomotion of C. elegans in structured environments.

1.    Bio-fluid Dynamics and Bio-Mechanics: Locomotion of C. elegans in structured environments

       Experimental and
            Simulation Schematic           Worm Tracks                 
The focus of my current research is to understand low Reynolds number locomotion 
of microorganisms. Undulatory locomotion of microorganisms in complex environments is 
ubiquitous in nature. For example, a sperm moving through mucus, or a Spirochete moving 
through tissue. Microorganisms navigate complex environments consisting of fluids and 
obstacles, negotiating hydrodynamic effects and geometrical constraints. 
Some of the key questions are:
What role do hydrodynamics and geometrical constraints play?
Do these obstacles help or hinder 
their motion?

To gain insights into these questions, I am studying undulating locomotion of C. elegans in 
PDMS micro-pillar arrays filled with buffer solution. Such a setup allows systematic control over 
geometric constraints, and along with hydrodynamic simulations, determines the role of 
hydrodynamic contributions. 
We have found that the nematode (L ~ 1 mm), while swimming between the pillars, employs a number 
of different locomotory strategies depending on the lattice spacing (q: [0.380 - 0.700] mm). 
Instead of being hindered by the obstacles, it can utilize them to push off and gain speed. 
These regimes of enhanced locomotion depend on the lattice spacing scaled by the length of 
the nematode. In addition, we also observe changes in frequency, velocity, curvature, and the gait 
of the worm as a function of the scaled lattice spacing. Our experimental approach, in conjunction with 
modeling and simulations (Eric Keaveny and Mike Shelley), allow us to disentangle the effects of 
geometry and hydrodynamics on end behavior. We find that the simulations not only reproduce 
locomotory strategies of the real nematode, but also match the experimental measurements of enhanced 
velocity quantitatively. Combining experiments and simulations, we can now establish a regime map of 
changes in locomotory strategies of an undulating swimmer in structured media.

(A comprehensive database about various aspects of C elegans biology is at Wormbase)


 
Experiments and Theory of Undulatory Locomotion in a Simple Structured Medium

Supplementary Material: The Mechanical Worm Model

Supplementary Movies: (combined Zip File: Supplementary Movies )


1) Movie 1    (Experimental Movie)
2) Movie 2    (Experimental Movie)
3) Movie 3    (Experimental Movie)
4) Movie 4    (Simulations Movie)
5) Movie 5    (Simulations Movie)
6) Movie 6    (Simulations Movie)
7) Movie 7    (Simulations Movie)
Here is the movie for DFD Gallery of Fluid Motion: Locomotion of C. elegans in Structured Media

2.    Granular Physics: (Advisor: Bob Behringer, Duke University, Physics)

                              Force chains in
            granular systems

The focus of my graduate research was on understanding the statistical properties of dense, dry 
granular systems under isotropic compression and pure shear. The key feature of granular 
systems is the heterogeneous network of contact forces called the “force-chain” network. 
Understanding these force networks and their spatial correlations is a fundamental goal of 
granular mechanics. Although knowledge of inter-grain contact forces is indispensable 
for a complete understanding of the system, they are exceedingly difficult to measure 
non-destructively in a realistic granular system. I developed a novel method to measure 
both the normal and tangential components of contact forces, in bulk samples, at the grain scale [1]. 
We visualized the stresses by using birefringent circular disks and solved the inverse problem 
of finding the contact forces producing the observed stress patterns. Figure shows an experimental 
image (left) of sheared granular system, and the corresponding "best-fit" image obtained after finding 
the contact forces.

A demo-version of my Ph.D. work is a permanent exhibit at the Museum of Science and Industry in Chicago.
http://www.msichicago.org/whats-here/exhibits/science-storms/the-exhibit/avalanche/force-chains/


3.    Non-Newtonian Fluid Dynamics: Jetting of Viscoelastic Fluids (Advisor: Gareth McKinley, Mech. E. MIT)

(An instructive set of videos about Newtonian, and non-Newtonian fluid dynamics is available here.)
(A good resource for rheology is the Society of Rheology, SOR.)


Jetting
            dynamics of worm-like micellar fluids

Viscoelastic jets with moderate elasticities exhibit a rich array of complex nonlinear dynamics: 
the buckling instability of a steady jet resulting in periodic coiling, and a transition from periodic 
to quasi-periodic dynamics, followed by a transition to multi-frequency, chaotic dynamics. Beyond 
this regime, the jet dynamics smoothly crosses over to exhibit a spectacular ``leaping shampoo" or the 
Kaye effect. We created a regime map of the dynamics of the jet in terms of viscous, elastic, 
gravitational, and inertial effects, allowing us to connect rheology of the fluids to the changes in the 
dynamics of the jets. We examined different dynamical regimes in terms of scaling variables, which 
depend on the geometry (dimensionless height), kinematics (dimensionless flow rate), and the fluid 
properties (elasto-gravity number). This approach allowed us to unify diverse phenomena like dripping, 
coiling, and leaping jets, as a sequence of transitions in the parameter space of scaled flow rate and scaled 
height.  Fluids with higher elasticities predominantly tend to exhibit folding motions (linear oscillations) 
instead of circular coiling. There is also an absence of any ``leaping shampoo" effect, and at larger 
heights, the jet ruptures as it cannot sustain the elastic stresses. The regime map of the dynamics for 
high elasticity fluids was also established along the same lines.