Pre-asymptotic dispersion of active particles through a vertical pipe: the origin of hydrodynamic focusing

This paper investigates the transport of drugs delivered by direct injection into the cerebrospinal fluid (CSF) that fills the intrathecal space surrounding the spinal cord. Because of the small drug diffusivity, the dispersion of neutrally buoyant drugs has been shown in previous work to rely mainly on the mean Lagrangian flow associated with the CSF oscillatory motion. Attention is given here to effects of buoyancy, arising when the drug density differs from the CSF density. For the typical density differences found in applications, the associated Richardson number is shown to be of order unity, so that the Lagrangian drift includes a buoyancy-induced component that depends on the spatial distribution of the drug, resulting in a slowly evolving cycle-averaged flow problem that can be analysed with two-time scale methods. The asymptotic analysis leads to a nonlinear integro-differential equation for the spatiotemporal solute evolution that describes accurately drug dispersion at a fraction of the cost involved in direct numerical simulations of the oscillatory flow. The model equation is used to predict drug dispersion of positively and negatively buoyant drugs in an anatomically correct spinal canal, with separate attention given to drug delivery via bolus injection and constant infusion.

Section: Discussionmentioning

confidence: 99%

“…For example, for

1

1

, diffusion rapidly uniformizes the composition in the transverse direction, so that the concentration becomes independent of

.…”

Section: Solute Transport In the Presence Of Buoyancymentioning

confidence: 99%

Effects of buoyancy on the dispersion of drugs released intrathecally in the spinal canal

Alaminos-Quesada,

Gutiérrez-Montes,

Coenen

et al. 2024

“…We hope that the streamwise perspective can offer an exemplary framework for the theoretical analysis of active suspensions (Jiang & Chen 2019; Guan et al. 2023), analogous to its application for passive particles (Guo, Jiang & Chen 2020; Guo & Chen 2022).…”

Section: Literature Reviewmentioning

confidence: 99%

“…2022 b ) and self-propelling swimmers (Bearon, Hazel & Thorn 2011; Bearon & Hazel 2015; Jiang & Chen 2021; Fung, Bearon & Hwang 2022; Wang, Jiang & Chen 2022 a , 2023; Guan et al. 2023). The wide-ranging applicability of dispersion encompasses diverse disciplines, from physics to biology and ecology, addressing issues such as cargo transport (Yasa et al.…”

Section: Introductionmentioning

confidence: 99%

Streamwise dispersion of soluble matter in solvent flowing through a tube

Guan,

Chen

2024

Self Cite

For the dispersion of soluble matter in solvent flowing through a tube as investigated originally by G.I. Taylor, a streamwise dispersion theory is developed from a Lagrangian perspective for the whole process with multi-scale effects. By means of a convected coordinate system to decouple convection from diffusion, a diffusion-type governing equation is presented to reflect superposable diffusion processes with a multi-scale time-dependent anisotropic diffusivity tensor. A short-time benchmark, complementing the existing Taylor–Aris solution, is obtained to reveal novel statistical and physical features of mean concentration for an initial phase with isotropic molecular diffusion. For long times, effective streamwise diffusion prevails asymptotically corresponding to the overall enhanced diffusion in Taylor's classical theory. By inverse integral expansions of local concentration moments, a general streamwise dispersion model is devised to match the short- and long-time asymptotic solutions. Analytical solutions are provided for most typical cases of point and area sources in a Poiseuille tube flow, predicting persistent long tails and skewed platforms. The theoretical findings are substantiated through Monte Carlo simulations, from the initial release to the Taylor dispersion regime. Asymmetries of concentration distribution in a circular tube are certified as originated from (a) initial non-uniformity, (b) unidirectional flow convection, and (c) non-penetration boundary effect. Peculiar peaks in the concentration cloud, enhanced streamwise dispersivity and asymmetric collective phenomena of concentration distributions are illustrated heuristically and characterised to depict the non-equilibrium dispersion. The streamwise perspective could advance our understanding of macro-transport processes of both passive solutes and active suspensions.

Migration of confined micro-swimmers subject to anisotropic diffusion

Guan,

Jiang,

Tao

et al. 2024

Self Cite

Shear-induced migration of elongated micro-swimmers exhibiting anisotropic Brownian diffusion at a population scale is investigated analytically in this work. We analyse the steady motion of confined ellipsoidal micro-swimmers subject to coupled diffusion in a general setting within a continuum homogenisation framework, as an extension of existing studies on macro-transport processes, by allowing for the direct coupling of convection and diffusion in local and global spaces. The analytical solutions are validated successfully by comparison with numerical results from Monte Carlo simulations. Subsequently, we demonstrate from the probability perspective that symmetric actuation does not yield net vertical polarisation in a horizontal flow, unless non-spherical shapes, external fields or direct coupling effects are harnessed to generate steady locomotion. Coupled diffusivities modify remarkably the drift velocity and vertical migration of motile micro-swimmers exposed to fluid shear. The interplay between stochastic swimming and preferential alignment could explain the diverse concentration and orientation distributions, including rheological formations of depletion layers, centreline focusing and surface accumulation. Results of the analytical study shed light on unravelling peculiar self-propulsion strategies and dispersion dynamics in active-matter systems, with implications for various transport problems arising from the fluctuating shape, size and other external or inter-particle interactions of swimmers in confined environments.