#### 1) Spatiotemporal stability of viscoelastic flows

Understanding the hydrodynamic stability and transition of flows of polymer solutions is paramount to both the fundamental theory of viscoelastic liquids and their industrial applications, especially those arising in micro-fluidic mixing and viscoelastic stabilization via polymer addition. Classical approaches to the viscoelastic stability studies involve identifying an equilibrium state, linearizing the governing equations around that state and representing the perturbations through generalized waves: e ^{i(k y)}. In contrast with the *temporal stability theory* (the case with disturbance having spatial wavenumber, *k* , and temporal frequency,), the spatial development of perturbations resulting from a pointwise harmonic forcing can be ill-posed. The effective response of the system to an external forcing can be overshadowed by the natural unforced growth, a situation that is captured via the *spatiotemporal theory* (i.e., when (*k*, ) ). In this method, we search for *absolute ins*tabilities (perturbations which ill-posed and grow exponentially in time at the point of excitation), *convective instabilities* (disturbances which are swept downstream from the source and decay at any fixed position in space) and *evanescent modes* (the non-propagating or false modes), the latter is distinguished from the former two using the Briggs contour integral method, by counting the number of intersections of the line drawn from the cusp point to the zero-contour curve, as shown below:

which leads to flow-material phase diagram for various setups.

#### Publications

- T. Chauhan, D. Bansal and S. Sircar, ‘Spatiotemporal linear stability of viscoelastic slender jets’, submitted (2021).
- D. Bansal, T. Chauhan and S. Sircar, ‘Spatiotemporal linear stability of viscoelastic Saffman-Taylor flows’, submitted (2021).
- D. Bansal, D. Ghosh and S. Sircar, ‘Spatiotemporal linear stability of viscoelastic free shear flows: Nonaffine response regime’, Phys. Fluids
**33**, 054106 (2021): Weblink - S. Singh, D. Bansal, G. Kaur and S. Sircar, ‘Implicit-explicit-compact methods for advection diffusion reaction equations’, Comput. and Fluids
**212**, 104709 (2020): Weblink - S. Sircar and D. Bansal, ‘Spatiotemporal linear stability of viscoelastic free shear flows: Dilute regime’, Phys. Fluids
**31**, 084104 (2019): Weblink

#### 2) Particle adhesion and fragmentation

The adhesion and fragmentation of particles aggregates is ubiquitous in biological and colloidal process, including cancer cell metastasis, thrombosis, study of phytoplankton accumulation in shallow water bodies and in the development of products in paper and pulp making industries. However, in many population models studying these processes, the rate of adhesion is described as a simple product between aggregate sizes, e.g., xy, where is a coefficient fit to experimental data. This rate is an extremely imprecise characterization of the multitude of factors influencing adhesion (e.g. fluid flow, effect of charges, surface deformation). Therefore, we study this problem in detail using multi-scale models.

- S. Sircar, G. Nguyen, A. Kotousov and A. J. Roberts, ‘Ligand mediated adhesive mechanics of two deformed spheres’, Eur. Phys. J. E
**39**:95 (2016): Weblink - S. Sircar and A. J. Roberts, ‘Surface deformation and shear flow in ligand mediated cell adhesion’, J. Math. Bio.,
**73**(4), pg 1035-52 (2016): Weblink - S.Sircar, J.G. Younger and D.M.Bortz, ‘Sticky Surfaces: Sphere-Sphere Adhesion Dynamics’, J. Biol. Dynamics, DOI: http://dx.doi.org/10.1080/17513758.2014.942394 (2014): Weblink
- S.Sircar and D.M.Bortz, ‘Impact of flow on ligand mediated bacterial flocculation’, Math. Biosci.,
**245**, pg 314-321 (2013): Weblink

#### 3) Hydrodynamic stability of gels, mucus, liquid crystals, active materials

The hydrodynamics of ionic gels has numerous applications in biomechanics, including contraction of actin-myosin networks, propulsion of myxobacteria via swelling of slime, biofilm formation and environments for artificial cartilage production. In this problem, we explore, using a multi scale model for (a) artificial cartilage and (b) mucus, how the various physiochemical factors (e.g. fixed charge density of the polymer, pH, micro-structure elasticity) effects the polymer structure and production.

Similarly, active materials are ubiquitous in biological contexts such as bacterial swimmers, living cells moving on a substrate, ion pumps, self-propelled colloids and cells associated with the cytoskeleton. I have developed an initial mesoscopic kinetic theory for semi-dilute active suspensions with arbitrary particle, which is used to study a variety of biological systems, including self-organization of motor proteins of eukaryotic cells and pattern-formation in flocking animals.

#### Publications

- S. Sircar, ‘Chap 9: Tissue Engineering’, in Biofluid Mechanics second edition, by J. N. Mazumdar, World Scientific, Singapore (2015): Weblink
- S. Sircar and A. J. Roberts, ‘Ion mediated crosslink driven mucous swelling kinetics’, DCDS-B,
**21**(6) pg 1937-51 (2016): Weblink - S.Sircar, E.Aisenbrey, S.Bryant & D.M.Bortz, ‘Determining average osmolarity in Poly (ethyleneglycol)-Ch sulfate gels mimicking cartillage’, J. Theo. Biol.
**364**, 397 (2015): Weblink - S. Sircar, J. P. Keener and A. Fogelson, ‘The effect of divalent vs. monovalent ions on the swelling of mucin-like polyelectrolyte gels’, J. Chem. Phys.,
**138**, 014901 (2013): Weblink - J. P. Keener, S. Sircar and A.Fogelson, ‘Kinetics of swelling gels’, SIAM J. Appl. Math.
**71**(3), pg 854-875 (2011): Weblink - J.P.Keener, S.Sircar and A.Fogelson, ‘Influence of free energy on swelling kinetics of gels’, Phys. Rev. E,
**83**(4-1), 041802 (2011): Weblink - S. Sircar, ‘A hydrodynamical kinetic theory for self-propelled ellipsoidal suspensions’, Int. J. Emerg. Multi. Fluid Sci.,
**2**(4), pg 255-268 (2011): Weblink - S.Sircar, Jun Li and Q. Wang, ‘Biaxial phases of bent-core lcps in shear flows’, Comm. Math. Sci.,
**8**(3), pg 697-720 (2010): Weblink - J. Li, S.Sircar and Q. Wang, ‘Transient rheological responses in sheared blcps’, Rheol. Acta 49(7), pg 699-717 (2010): Weblink
- J. Li, S. Sircar and Q. Wang, ‘A note on the kinematics of rigid molecules in linear flow fields and kinetic theory of biaxial liquid crystal polymers’, Int. J. Emerg. Multi. Fluid Sci.
**1**(2), pg 115-126 (2009): Weblink - S.Sircar and Q.Wang, ‘Dynamics and rheology of blcps in shear flow’, J. Rheol.,
**53**(4), pg 819-858 (2009): Weblink - S. Sircar and Q. Wang, ‘Shear induced mesostructures in blcps’, Phys. Rev. E,
**78**, 061702 (2008): Weblink - M. G. Forest, S. Sircar, Q. Wang and R. Zhou, ‘Monodomain dynamics for rigid rod and platelet suspensions in strongly coplanar linear flow & magnetic field-II’, Phys. Fluids,
**18**, 103102 (2006): Weblink - T. K. Sengupta and S.Sircar, ‘High accuracy schemes DNS & acoustics’, J. Sci. Comp.,
**26**(2), 151-193 (2006): Weblink - Q. Wang, S.Sircar and H. Zhou, ‘Steady solutions of the Smoluchowski equation for nematic polymers under imposed fields’, Comm. Math. Sci.,
**3**(4), pg 605-620 (2005): Weblink