arXiv subjects

Sabarish V. Narayanan

Publications and source records attributed to Sabarish V. Narayanan.

4 recordsLinked to original sources

arXiv2026

Simulating the swimming motion of a flagellated bacterium in a microstructured bio-fluid

We develop a numerical framework to simulate the locomotion of a flagellated bacterium with a spheroidal head (such as Escherichia coli) in biological fluids like mucus, which are entangled polymer solutions exhibiting elasto-viscoplastic (EVP) rheology and porous microstructure. To account for the scale disparity between the large bacterial head and the slender flagellar bundle, whose thickness is comparable to the pore size, we employ a two-fluid model in which the bundle directly drives the solvent and exchanges momentum with the polymer phase via drag proportional to their relative velocity. The numerical implementation combines a finite-difference discretization of the two-fluid equations with a slender-body theory (SBT) to model flagellar forcing. A key observation is that the coupled mass and momentum equations for these inertialess flows, together with SBT, are linear in the pressure and velocity fields and in the force distribution along the flagellar bundle. By treating the polymer stress as a body force, we decompose the flow field and hydrodynamic moments into three additive contributions: kinematic (motion), flagellar forcing, and polymer stress. This decomposition allows several components of the flow to be precomputed and enables the determination of swimming velocity via a resistivity formulation driven by polymer-induced forces, which greatly improves computational efficiency during transient calculations of the polymer stress and the resulting flow. We validate the method and use it to analyze how polymer microstructure and its interactions with the bacterial head and tail affect motility in complex biofluids.

physics.flu-dyn↗

arXiv2026

Convective scalar transport from spherical drops in complex shearing flows

We calculate the scalar transport rate, as characterized by the Nusselt number\,($Nu$), from a neutrally buoyant spherical drop in an ambient linear flow, in the absence of inertia and in the strong convection limit. This corresponds to the regime $Re \ll 1, Pe \gg 1$, where $Re$ and $Pe$ are the Reynolds and Péclet numbers, and denote the ratios of the diffusive and convective time scales associated with momentum and scalar transport. The focus is on the exterior problem, with the drop-phase transport resistance assumed negligible, and the scalar field being a constant on the drop surface. While $Nu \propto Pe^{\frac{1}{2}}$ for $Pe \gg 1$, owing to the transport occurring across a thin $O(a Pe^{-\frac{1}{2}})$ boundary layer\,($a$ being the drop radius), the proportionality factor in this relation depends sensitively on ambient flow geometry via the surface-streamline topology. Unlike a rigid sphere, a variety of surface-streamline topologies can drive transport across the boundary layer at widely differing rates. In contrast to earlier studies which almost exclusively focus on axisymmetric ambient flows, we calculate $Nu$ for a pair of non-axisymmetric linear flow families: (i) 3D extensional flows with aligned vorticity and (ii) Axisymmetric extensional flows with inclined vorticity, using a non-orthogonal surface-streamline aligned coordinate system. Taken together, the families span the entire gamut of surface-streamline topologies in the space of incompressible linear flows. Independent numerical simulations of the interior problem reveal the emergence of an $O(aPe^{-\frac{1}{2}})$ boundary layer beneath the drop surface, driven by chaotic streamlines, pointing to the possibility of $Nu \propto Pe^{\frac{1}{2}}$ for the conjugate problem, for sufficiently large $Pe$.

physics.flu-dyn↗

arXiv2024

A viscous drop in a planar linear flow -- the role of deformation on streamline topology

Planar linear flows are a one-parameter family, with the parameter $\hatα\in [-1,1]$ being a measure of the relative magnitudes of extension and vorticity; $\hatα = -1$, $0$ and $1$ correspond to solid-body rotation, simple shear flow and planar extension, respectively. For a neutrally buoyant spherical drop in a hyperbolic planar linear flow with $\hatα\in(0,1]$, the near-field streamlines are closed for $0 \leq \hatα < 1$ and for $λ> λ_c = 2 \hatα / (1 - \hatα)$, $λ$ being the drop-to-medium viscosity ratio; all streamlines are closed for an ambient elliptic linear flow with $\hatα\in[-1,0)$. We use both analytical and numerical tools to show that drop deformation, as characterized by a non-zero capillary number ($Ca$), destroys the aforementioned closed-streamline topology. While inertia has previously been shown to transform closed Stokesian streamlines into open spiraling ones that run from upstream to downstream infinity, the streamline topology around a deformed drop, for small but finite $Ca$, is more complicated. Only a subset of the original closed streamlines transforms to open spiraling ones, while the remaining ones densely wind around a configuration of nested invariant tori. Our results contradict previous efforts pointing to the persistence of the closed streamline topology exterior to a deformed drop and have important implications for transport and mixing.

physics.flu-dyn↗

arXiv2024

A swimming bacterium in a two-fluid model of a polymer solution

We analyse the motion of a flagellated bacterium in a two-fluid medium using slender body theory. The two-fluid model is useful for describing a body moving through a complex fluid with a microstructure whose length scale is comparable to the characteristic scale of the body. This is true for bacterial motion in biological fluids (entangled polymer solutions), where the entanglement results in a porous microstructure with typical pore diameters comparable to or larger than the flagellar bundle diameter but smaller than the diameter of the bacterial head. Thus the polymer and solvent satisfy different boundary conditions on the flagellar bundle and move with different velocities close to it. This gives rise to a screening length $L_B$ within which the fluids exchange momentum and the relative velocity between the two fluids decays. In this work, both the solvent and polymer of the two-fluid medium are modeled as Newtonian fluids with different viscosities $μ_s$ and $μ_p$ (viscosity ratio $λ= μ_p/μ_s$), thereby capturing the effects solely introduced by the microstructure of the complex fluid. From our calculations, we observe an increased drag anisotropy for a rigid, slender flagellar bundle moving through this two-fluid medium, resulting in an enhanced swimming velocity of the organism. The results are sensitive to the interaction between the bundle and the polymer and we discuss two physical scenarios corresponding to two types of interaction. Our model provides an explanation for the experimentally observed enhancement of swimming velocity of bacteria in entangled polymer solutions and motivates further experimental investigations.

physics.flu-dyn↗