Prateek Anand

IIT Bombay, Mechanical Engineering, Faculty Member

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Inertial migration of a neutrally buoyant spheroid in plane Poiseuille flow

arXiv (Cornell University), Feb 28, 2023

We study the cross-stream inertial migration of a torque-free neutrally buoyant spheroid, of an a... more 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 1) and confinement ratios (λ 1), with the channel Reynolds number, Re c = Re p /λ 2 , assumed to be arbitrary; here, λ = L/H where L is the semimajor axis of the spheroid and H denotes the separation between the channel walls. In the Stokes limit (Re p = 0) and for λ 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 = ∞), 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 ∼ O(1), the Jeffery-averaged analysis is valid for Re p 1; for extreme aspect ratio spheroids, the regime of validity becomes more restrictive being given by Re p κ/ ln κ 1 and Re p /κ 2 1 for κ → ∞ (slender fibers) and κ → 0 (flat disks), respectively.

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

arXiv (Cornell University), Jan 2, 2023

We examine theoretically the inertial migration of a neutrally buoyant rigid sphere in pressuredr... more We examine theoretically the inertial migration of a neutrally buoyant rigid sphere in pressuredriven channel flow, accounting for its finite size relative to the channel width (the confinement ratio). For sufficiently large channel Reynolds numbers (Rec), 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 Rec 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.

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Inertial migration of a sphere in plane Couette flow

arXiv (Cornell University), Nov 2, 2022

We study the inertial migration of a torque-free neutrally buoyant sphere in wall-bounded plane C... more 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 1) and confinement ratio (λ 1). Here, Re c = V wall H/ν where H denotes the separation between the channel walls, V 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 (≈ 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.

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Stability of a liquid film flowing down an inclined anisotropic and inhomogeneous porous layer: an analytical description

Journal of Fluid Mechanics, 2016

We study the effect of anisotropy and inhomogeneity in the permeability of the porous layer on th... more We study the effect of anisotropy and inhomogeneity in the permeability of the porous layer on the stability of surface waves of an inclined fluid–porous double-layer system. The fluid is assumed to be Newtonian and the porous layer to be Darcian. The porous layer is saturated with the same fluid and the two layers are coupled at the interface via the Beavers–Joseph condition. Linear stability analysis is performed based on a long-wave approximation. The resulting eigenvalue problem is exactly solved up to third order in the wavenumber. The anisotropic behaviour of permeability, cross-stream component of permeability, surface tension and porosity are found to have only higher-order effects on the stability characteristics of the system. On the other hand, the inhomogeneous feature in the streamwise component of permeability play a dominant role in determining the stability of the gravity-driven surface waves; as do other system parameters such as the thickness of the fluid layer rel...

J.71 P. Deepu, P. Anand, S. Basu, Stability in confined porous media flow: Effects of anisotropy and inhomogenity, Physical Review E 92, 023009 (2015); DOI: 10.1103/PhysRevE.92.023009

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

We present the linear stability analysis of horizontal Poiseuille flow in a fluid overlying a por... more We present the linear stability analysis of horizontal Poiseuille flow in a fluid overlying a porous medium with anisotropic and inhomogeneous permeability. The generalized Darcy model is used to describe the flow in the porous medium with the Beavers-Joseph condition at the interface of the two layers and the eigenvalue problem is solved numerically. The effect of major system parameters on the stability characteristics is addressed in detail. It is shown that the anisotropic and inhomogeneous modulation of the permeability of the underlying porous layer provides an effective means for passive control of the flow stability.

Effects of Instabilities and Coherent Structures on the Performance of a Thermocline Based Thermal Energy Storage

Applied Thermal Engineering, 2015

ABSTRACT We investigate the transient dynamics of disturbances inside a thermocline based molten ... more ABSTRACT We investigate the transient dynamics of disturbances inside a thermocline based molten salt thermal energy storage (TES). Numerical simulations were conducted with four inlet flow configurations. The disturbances introduced at the inlet grow via Rayleigh Taylor instability. The formed vortical motions inside the tank propagate downstream and destroy the thermocline. The vortex-thermocline interaction upsets the stratification inside the TES. The disturbance growth rate, penetration length and vortex Reynolds number are measured. The growth of penetration length prior to the vortex-thermocline interaction is quadratic. The vortex Reynolds number of the eddy which causes thermocline breakdown increases with increase in Atwood number. The impingement of vortex on thermocline is studied.

Orientation Dynamics of Sedimenting Anisotropic Particles in Turbulence

Physical Review Letters

We examine the dynamics of small anisotropic particles (spheroids) sedimenting through homogeneou... more 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.

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