Buoyancy-modulated Lagrangian drift in wavy-walled vertical channels as a model problem to understand drug dispersion in the spinal canal
Buoyancy-modulated Lagrangian drift in wavy-walled vertical channels as a model problem to understand drug dispersion in the spinal canal
复制标题
DOI：
10.1017/jfm.2022.799
复制
发表时间：
2022-10-06
影响因子：
3.7
通讯作者：
Sanchez, A. L.
中科院分区：
文献类型：
--
作者：
Alaminos-Quesada, J.;Coenen, W.;Sanchez, A. L.
本文研究了在两端压差振荡作用下细长波壁竖直通道内的流动和输运。当脉动流的冲程长度与通道波长的比率小时，已知所得到的流速包括由对流加速度的效应引起的缓慢的稳定流动分量。我们的研究考虑了引力在非均匀密度分布的结构中的附加效应。特别注意的是缓慢发展的浮力调制流出现后，沉积的有限量的溶质，其密度是不同的，从所包含的流体中的通道，一个相关的问题，与药物分散在鞘内给药（ITDD）的过程，涉及到注射的药物注入到充满椎管的脑脊液。结果表明，当Richardson数是为了团结，ITDD应用程序中的相关限制，所产生的浮力诱导的速度是可比的稳定流。因此，缓慢的时间平均拉格朗日运动的流体，涉及的斯托克斯漂移和时间平均欧拉速度的总和，是密切耦合的溶质的运输，导致在一个缓慢发展的问题，可以用两个时间尺度的方法处理。渐近发展导致一个时间平均的，非线性的积分微分输运方程，描述了缓慢的溶质分散，从而规避了需要描述的小浓度波动与快速振荡运动。这里提出的想法可以找到应用程序在开发减少模型，为未来的定量分析药物在椎管内的分散。
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.