arXiv subjects

Prateek Anand

Publications and source records attributed to Prateek Anand.

8 recordsLinked to original sources

arXiv2026

Dynamics of an internally actuated elastic particle in a plane Poiseuille flow

We analytically analyse the dynamics of an internally actuated particle, modelled as a compressible elastic sphere embedded with a magnetic bead at its undeformed centre, translating in a plane Poiseuille flow in the Stokes limit. The particle is constrained to translate with a prescribed velocity while remaining at an arbitrary position within the flow by applying an external point force and external point torque at its undeformed centre. The governing equations for the fluid and particle are the Stokes and Navier elasticity equations, respectively. We use the series solutions to the governing equations and the domain perturbation method to capture the deformed shape of the particle, assuming $\alpha \ll 1$. Here, $\alpha$ quantifies the elastic strain induced in the particle due to the viscous stress from the fluid. The external force and external torque are obtained until O($\alpha^2$). The particle translating along the channel length experiences an elastic-induced hydrodynamic lift as well as hydrodynamic torque both at O($\alpha$) and O($\alpha^2$). The leading-order lift depends linearly on the local shear rate and on the combined effects of slip velocity and flow curvature, where the slip velocity is defined as the particle velocity relative to the local ambient flow. The particle reaches a stable equilibrium position away from the centreline, where the net lift vanishes. We show that the direction of deformation-induced lateral migration of the internally actuated particle is qualitatively distinct from that of drops, capsules, and vesicles in the Stokes limit and from that of rigid spheres undergoing inertial migration.

physics.flu-dyn↗

arXiv2025

The dynamics of thermalisation in the Galerkin-truncated, three-dimensional Euler equation

The inviscid, partial differential equations of hydrodynamics when projected via a Galerkin-truncation on a finite-dimensional subspace spanning wavenumbers $-{\bf K}_{\rm G} \le {\bf k} \le {\bf K}_{\rm G}$, and hence retaining a finite number of modes $N_{\rm G}$, lead to absolute equilibrium states. We review how the Galerkin-truncated, three-dimensional, incompressible Euler equation thermalises and its connection to questions in turbulence. We also discuss an emergent pseudo-dissipation range in the energy spectrum and the time-scales associated with thermalisation.

physics.flu-dyn↗

arXiv2025

Inertial migration of slender prolate and thin oblate spheroids in plane Poiseuille flow

We theoretically examine the inertial migration of a neutrally buoyant spheroid of aspect ratio $\kappa$ in wall-bounded plane Poiseuille flow at small particle Reynolds number ($Re_p$) and small confinement ratio ($\lambda$), with channel Reynolds number $Re_c = Re_p/\lambda^2$ arbitrary. For $\lambda \ll 1$, inertia rapidly drives the spheroid to the tumbling orbit ($C = \infty$), with migration governed by the time-averaged lift over orientations sampled in this orbit. Spheroids with $\kappa = O(1)$ follow Jeffery rotation closely, while deviations for slender rods and thin disks yield equilibrium positions distinct from the classical Segre-Silberberg result. Above a threshold $Re_c$, both rods and disks can undergo rotation arrest near walls, with these arrested regions expanding toward the centerline as $Re_c$ increases. Unlike spheres, the resulting equilibrium positions shift inward with increasing $Re_c$; for disks, these positions themselves become arrested beyond a threshold $Re_c$. The $\kappa$-dependence of equilibrium locations suggests passive shape-sorting strategies in microfluidic devices.

physics.flu-dyn↗

arXiv2024

Pair statistics of oblate spheroids settling in a turbulent flow

We perform direct numerical simulations of sub-Kolmogorov, inertial spheroids settling under gravity in homogeneous, isotropic turbulence and find that small-scale clustering, measured via the correlation dimension, depends sensitively on their aspect ratios. In particular, such particles are shown to cluster more as their anisotropy increases. Further, the approach rate for pairs of spheroids are calculated and found to deviate significantly from the spherical-particle limit. Our study, spanning a range of Stokes numbers and aspect ratios, provides critical inputs for developing collision models to understand the dynamics of sedimenting, anisotropic particles in general and ice crystals in clouds in particular.

physics.flu-dyn↗

arXiv2023

Inertial migration of a neutrally buoyant spheroid in plane Poiseuille flow

We study the cross-stream inertial migration of a torque-free neutrally buoyant spheroid, of an arbitrary aspect ratio $κ$, in wall-bounded plane Poiseuille flow for small particle Reynolds numbers\,($Re_p\ll1$) and confinement ratios\,($λ\ll1$), with the channel Reynolds number, $Re_c = Re_p/λ^2$, assumed to be arbitrary; here, $λ=L/H$ where $L$ is the semi-major axis of the spheroid and $H$ denotes the separation between the channel walls. In the Stokes limit\,($Re_p =0)$ and for $λ\ll 1$, a spheroid rotates along any of an infinite number of Jeffery orbits parameterized by an orbit constant $C$, while translating with a time dependent speed along a given ambient streamline. Weak inertial effects stabilize either the spinning\,($C=0$) or the tumbling orbit\,($C=\infty$), or both, depending on $κ$. The separation of the Jeffery-rotation and orbital drift time scales, from that associated with cross-stream migration, implies that the latter occurs due to a Jeffery-averaged lift velocity. Although the magnitude of this averaged lift velocity depends on $κ$ and $C$, the shape of the lift profiles are identical to those for a sphere, regardless of $Re_c$. In particular, the equilibrium positions for a spheroid remain identical to the classical Segre-Silberberg ones for a sphere, starting off at a distance of about $0.6(H/2)$ from the channel centerline for small $Re_c$, and migrating wallward with increasing $Re_c$. For spheroids with $κ\sim O(1)$, the Jeffery-averaged analysis is valid for $Re_p\ll1$; for extreme aspect ratio spheroids, the regime of validity becomes more restrictive being given by $Re_p\,κ/\ln κ\ll 1$ and $Re_p/κ^2 \ll 1$ for $κ\rightarrow \infty$\,(slender fibers) and $κ\rightarrow 0$\,(flat disks), respectively.

physics.flu-dyn↗

arXiv2023

Inertial migration in pressure-driven channel flow: beyond the Segre-Silberberg pinch

We examine theoretically the inertial migration of a neutrally buoyant rigid sphere in pressure-driven channel flow, accounting for its finite size relative to the channel width (the confinement ratio). For sufficiently large channel Reynolds numbers\,($Re_c$), a small but finite confinement ratio qualitatively alters the inertial lift velocity profiles obtained using a point-particle formulation. Finite size effects are shown to lead to new equilibria, in addition to the well known Segre-Silberberg pinch locations. Consequently, a sphere can migrate to either the near-wall Segre-Silberberg equilibria, or the new stable equilibria located closer to the channel centerline, depending on $Re_c$ and its initial position. Our findings are in accord with recent experiments and simulations, and have implications for passive sorting of particles based on size, shape and other physical characteristics, in microfluidic applications.

physics.flu-dyn↗

arXiv2022

Inertial migration of a sphere in plane Couette flow

We study the inertial migration of a torque-free neutrally buoyant sphere in wall-bounded plane Couette flow over a wide range of channel Reynolds numbers, $Re_c$, in the limit of small particle Reynolds number\,($Re_p\ll1$) and confinement ratio\,($λ\ll1$). Here, $Re_c = V_\text{wall}H/ν$ where $H$ denotes the separation between the channel walls, $V_\text{wall}$ denotes the speed of the moving wall, and $ν$ is the kinematic viscosity of the Newtonian suspending fluid; $λ= a/H$, $a$ being the sphere radius, with $Re_p=λ^2 Re_c$. The channel centerline is found to be the only (stable)\,equilibrium below a critical $Re_c\,(\approx 148)$, consistent with the predictions of earlier small-$Re_c$ analyses. A supercritical pitchfork bifurcation at the critical $Re_c$ creates a pair of stable off-center equilibria, symmetrically located with respect to the centerline, with the original centerline equilibrium simultaneously becoming unstable. The new equilibria migrate wallward with increasing $Re_c$. In contrast to the inference based on recent computations, the aforementioned bifurcation occurs for arbitrarily small $Re_p$ provided $λ$ is sufficiently small. An analogous bifurcation occurs in the two-dimensional scenario, that is, for a circular cylinder suspended freely in plane Couette flow, with the critical $Re_c$ being approximately $110$.

physics.flu-dyn↗

arXiv2020

Orientation Dynamics of Sedimenting Anisotropic Particles in Turbulence

We examine the dynamics of small anisotropic particles (spheroids) sedimenting through homogeneous isotropic turbulence using direct numerical simulations and theory. The gravity-induced inertial torque acting on sub-Kolmogorov spheroids leads to pronouncedly non-Gaussian orientation distributions localized about the broadside-on(to gravity) orientation. Orientation distributions and average settling velocities are obtained over a wide range of spheroid aspect ratios, Stokes and Froude numbers. Orientational moments from the simulations compare well with analytical predictions in the inertialess rapid-settling limit, with both exhibiting a non-monotonic dependence on spheroid aspect ratio. Deviations arise at Stokes numbers of order unity due to a spatially inhomogeneous particle concentration field resulting from a preferential sweeping effect; as a consequence, the time-averaged particle settling velocities exceed the orientationally averaged estimates.

physics.ao-ph↗