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1. Oscillating viscous flow past a streamwise linear array of circular cylinders

   https://doi.org/10.1017/jfm.2023.178  

   Alaminos-Quesada, J.; Lawrence, J.J.; Coenen, W.; Sánchez, A.L. (March 2023, Journal of Fluid Mechanics)

   This paper addresses the viscous flow developing about an array of equally spaced identical circular cylinders aligned with an incompressible fluid stream whose velocity oscillates periodically in time. The focus of the analysis is on harmonically oscillating flows with stroke lengths that are comparable to or smaller than the cylinder radius, such that the flow remains two-dimensional, time-periodic and symmetric with respect to the centreline. Specific consideration is given to the limit of asymptotically small stroke lengths, in which the flow is harmonic at leading order, with the first-order corrections exhibiting a steady-streaming component, which is computed here along with the accompanying Stokes drift. As in the familiar case of oscillating flow over a single cylinder, for small stroke lengths, the associated time-averaged Lagrangian velocity field, given by the sum of the steady-streaming and Stokes-drift components, displays recirculating vortices, which are quantified for different values of the two relevant controlling parameters, namely, the Womersley number and the ratio of the inter-cylinder distance to the cylinder radius. Comparisons with results of direct numerical simulations indicate that the description of the Lagrangian mean flow for infinitesimally small values of the stroke length remains reasonably accurate even when the stroke length is comparable to the cylinder radius. The numerical integrations are also used to quantify the streamwise flow rate induced by the presence of the cylinder array in cases where the periodic surrounding motion is driven by an anharmonic pressure gradient, a problem of interest in connection with the oscillating flow of cerebrospinal fluid around the nerve roots located along the spinal canal. 

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2. Buoyancy-modulated Lagrangian drift in wavy-walled vertical channels as a model problem to understand drug dispersion in the spinal canal

   https://doi.org/10.1017/jfm.2022.799  

   Alaminos-Quesada, J.; Coenen, W.; Gutiérrez-Montes, C.; Sánchez, A.L. (October 2022, Journal of Fluid Mechanics)

   This paper investigates flow and transport in a slender wavy-walled vertical channel subject to a prescribed oscillatory pressure difference between its ends. When the ratio of the stroke length of the pulsatile flow to the channel wavelength is small, the resulting flow velocity is known to include a slow steady-streaming component resulting from the effect of the convective acceleration. Our study considers the additional effect of gravitational forces in configurations with a non-uniform density distribution. Specific attention is given to the slowly evolving buoyancy-modulated flow emerging after the deposition of a finite amount of solute whose density is different from that of the fluid contained in the channel, a relevant problem in connection with drug dispersion in intrathecal drug delivery (ITDD) processes, involving the injection of the drug into the cerebrospinal fluid that fills the spinal canal. It is shown that when the Richardson number is of order unity, the relevant limit in ITDD applications, the resulting buoyancy-induced velocities are comparable to those of steady streaming. As a consequence, the slow time-averaged Lagrangian motion of the fluid, involving the sum of the Stokes drift and the time-averaged Eulerian velocity, is intimately coupled with the transport of the solute, resulting in a slowly evolving problem that can be treated with two-time-scale methods. The asymptotic development leads to a time-averaged, nonlinear integro-differential transport equation that describes the slow dispersion of the solute, thereby circumventing the need to describe the small concentration fluctuations associated with the fast oscillatory motion. The ideas presented here can find application in developing reduced models for future quantitative analyses of drug dispersion in the spinal canal. 

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3. Bending fluctuations in semiflexible, inextensible, slender filaments in Stokes flow: Toward a spectral discretization

   https://doi.org/10.1063/5.0144242  

   Maxian, Ondrej; Sprinkle, Brennan; Donev, Aleksandar (April 2023, The Journal of Chemical Physics)

   Semiflexible slender filaments are ubiquitous in nature and cell biology, including in the cytoskeleton, where reorganization of actin filaments allows the cell to move and divide. Most methods for simulating semiflexible inextensible fibers/polymers are based on discrete (bead-link or blob-link) models, which become prohibitively expensive in the slender limit when hydrodynamics is accounted for. In this paper, we develop a novel coarse-grained approach for simulating fluctuating slender filaments with hydrodynamic interactions. Our approach is tailored to relatively stiff fibers whose persistence length is comparable to or larger than their length and is based on three major contributions. First, we discretize the filament centerline using a coarse non-uniform Chebyshev grid, on which we formulate a discrete constrained Gibbs–Boltzmann (GB) equilibrium distribution and overdamped Langevin equation for the evolution of unit-length tangent vectors. Second, we define the hydrodynamic mobility at each point on the filament as an integral of the Rotne–Prager–Yamakawa kernel along the centerline and apply a spectrally accurate “slender-body” quadrature to accurately resolve the hydrodynamics. Third, we propose a novel midpoint temporal integrator, which can correctly capture the Ito drift terms that arise in the overdamped Langevin equation. For two separate examples, we verify that the equilibrium distribution for the Chebyshev grid is a good approximation of the blob-link one and that our temporal integrator for overdamped Langevin dynamics samples the equilibrium GB distribution for sufficiently small time step sizes. We also study the dynamics of relaxation of an initially straight filament and find that as few as 12 Chebyshev nodes provide a good approximation to the dynamics while allowing a time step size two orders of magnitude larger than a resolved blob-link simulation. We conclude by applying our approach to a suspension of cross-linked semiflexible fibers (neglecting hydrodynamic interactions between fibers), where we study how semiflexible fluctuations affect bundling dynamics. We find that semiflexible filaments bundle faster than rigid filaments even when the persistence length is large, but show that semiflexible bending fluctuations only further accelerate agglomeration when the persistence length and fiber length are of the same order. 

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4. CEREBROSPINAL FLUID FLOW SIMULATIONS IN BRAIN VENTRICLES WITH ELASTIC WALL RESPONSES

   Liou, Willlam W; Yang, Yang; Yamada, Shinya (June 2019, 6th International Conference on Computational and Mathematical Biomedical Engineering)

   The cerebrospinal fluid surrounds the brain and the spinal cord, and is believed to be a potential risk factor to many CNS diseases. The biomechanics of the CSF flow in the brain ventricles is poorly understood due partly to the difficulty in obtaining the flow data in vivo. This paper describes the outcomes of a computational study to examine the elastic response of the walls of the ventricles and its effects on the flow. Comparisons of the simulated results are guided by clinical data obtained with the Time-SLIP MRI, which captures ventricular CSF flows in real time in vivo. 

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5. CEREBROSPINAL FLUID FLOW SIMULATIONS IN BRAIN VENTRICLES WITH ELASTIC WALL RESPONSES

   Liou, William W; Yang, Yang; Yamada, Shinya (June 2019, 6th International Conference on Computational and Mathematical Biomedical Engineering)

   The cerebrospinal fluid surrounds the brain and the spinal cord, and is believed to be a potential risk factor to many CNS diseases. The biomechanics of the CSF flow in the brain ventricles is poorly understood due partly to the difficulty in obtaining the flow data in vivo. This paper describes the outcomes of a computational study to examine the elastic response of the walls of the ventricles and its effects on the flow. Comparisons of the simulated results are guided by clinical data obtained with the Time-SLIP MRI, which captures ventricular CSF flows in real time in vivo. 

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