Research

Semiflexible Biopolymers

An important class of mechanical organs that render the capabilities of locomotion, growth and reproduction to biological cells are semiflexible biopolymers. They are present in the form of structural elements (F-actin, microtubules), locomotive organs (flagella, cilia) or carriers of information (double-stranded DNA). I use slender-body theory for Stokes flow to model the dynamics of such filaments, and try to quantitatively describe the physics involved by developing efficient numerical algorithms. We have derived a theory for the stretch-coil transition of semiflexible polymers, and have studied in detail the anomalous transport properties of polymers in patterned flows.

Sedimentation of Flexible Fibers

Unlike the case of sedimentation of rigid fibers in a viscous fluid, the complex shape and orientation dynamics during the sedimentation of elastic filaments has received but limited attention. In the case of a single flexible filament, the loss of symmetry due to bending during sedimentation (or equivalently, due to an electric/magnetic force) already leads to the translational and rotational motions being coupled, and a non-trivial trajectory can be anticipated. Furthermore, more flexible filaments may be subject to a buckling instability due to the tension induced in the filament. These could lead to interesting consequences for applications involving suspensions of such fibers, and we seek to explore the dynamics, instability and rheology in such a suspension. We have so far developed a model to incorporate the effects of gravity along with viscous and elastic forces, and have successfully described the trajectory of sedimentation and the buckling instability of single filaments analytically, results of which agree very well with our non-linear simulations.

Watch my Gallery of Fluid Motion 2014 submission on the sedimentation of flexible filaments here.

Suspension Dynamics

Settling of a suspension of particles is a rich and well-studied subject. Even the seemingly simple case of a sedimenting suspension of spheres in a viscous fluid is complicated by the slowly decaying nature of hydrodynamic interactions, which leads to strong velocity fluctuations. When the suspended particles are non-spherical in shape (say, ellipsoids or rods), the settling velocity depends on particle geometry and, coupled with hydrodynamic interactions, this can lead to a concentration instability. We use our theory from weakly flexible fibers to take this a step further, and develop a kinetic theory for suspensions of weakly flexible sedimenting fibers. A linear stability analysis reveals a key dependence on the anisotropy of the base-state, and the direct effects of particle flexibility as well. Highly accurate numerical simulations validate our predictions, and also illustrate the microstructural mechanisms behind the effect of flexibility and reorientation on suspension stability.

Interfacial Rheology

Complex fluid-fluid interfaces are just about everywhere, with applications in various multiphase engineering flows as well as biological materials. In many of these cases, the interphase is populated by particles, surfactants, or macromolecules which render a non-trivial rheological response to the interface. My recent efforts have been directed at theoretically approaching this problem from the point of view of particle-particle and particle-wall interactions on such an interface. Such studies forms the basis for '2-D suspension' mechanics, which is particularly rich in scope given the success of recent microrheological efforts in exploring interfaces using embedded probe particles. Such fundamental studies are crucial for better understanding interfacial physics in biology (e.g. lung surfactants) to engineering products (e.g. foams, oil recovery).