RT Journal Article
T1 Buoyancy-modulated Lagrangian drift in wavy-walled vertical channels as a model problem to understand drug dispersion in the spinal canal
A1 Alaminos Quesada, J.
A1 Coenen, Wilfried
A1 Gutiérrez-Montes, C.
A1 Sánchez, A. L.
AB 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.
PB Cambridge University Press
SN 0022-1120
YR 2022
FD 2022-10-25
LK https://hdl.handle.net/10016/37170
UL https://hdl.handle.net/10016/37170
LA eng
NO This work was supported by the National Institute of Neurological Disorders and Stroke through contract number 1R01NS120343-01 and by the National Science Foundation through grant number 1853954. The work of WC was partially supported by the Comunidad de Madrid through contract CSFFLOW-CM-UC3M and by the Spanish MICINN through the coordinated project PID2020-115961RB, whereas that of CGM was partially supported by Junta de Andalucía and European Funds through grant P18-FR-4619 and by the Spanish MICINN through the coordinated project PID2020-115961RB.
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RD 18 jul. 2024