Cardiff University | Prifysgol Caerdydd ORCA
Online Research @ Cardiff 
WelshClear Cookie - decide language by browser settings

Particle trapping by an external body force in the limit of large Peclet number: applications to magnetic targeting in the blood flow

Richardson, G., Kaouri, Katerina and Byrne, H. M. 2010. Particle trapping by an external body force in the limit of large Peclet number: applications to magnetic targeting in the blood flow. European Journal of Applied Mathematics 21 (01) , pp. 77-107. 10.1017/S0956792509990155

[img]
Preview
PDF - Accepted Post-Print Version
Download (274kB) | Preview

Abstract

Motivated by the technology of magnetically targeted drug and gene delivery, in which a magnetic field is used to direct magnetic carrier particles from the circulation to a target site, we develop a continuum model for the motion of particles (magnetic carriers) subject to an external body force (magnetic field) in a flow of a concentrated suspension of a species of neutrally buoyant particles (blood). An advection–diffusion equation describes the evolution of the carrier particles as they advect in the flow under the action of an external body force, and diffuse as a result of random interactions with the suspension of neutrally buoyant particles (shear-induced diffusion). The model is analysed for the case in which there is steady Poiseuille flow in a cylindrical vessel, the diffusive effects are weak and there is weak carrier uptake along the walls of the vessel. The method of matched asymptotic expansions is used to show that carriers are concentrated in a boundary layer along the vessel wall and, further, that there is a carrier flux along this layer which results in a sub-layer, along one side of the vessel, in which carriers are even more highly concentrated. Three distinguished limits are identified: they correspond to cases for which (i) the force is sufficiently weak that most particles move through the vessel without entering the boundary layers along the walls of the vessel and (ii) and (iii) to a force which is sufficiently strong that a significant fraction of the particles enter the boundary layers and, depending upon the carrier absorption from the vessel walls, there is insignificant/significant axial carrier flux in these layers.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: Cambridge University Press
ISSN: 0956-7925
Funders: BBSRC; The University of Nottingham; University of Southampton
Date of First Compliant Deposit: 17 May 2018
Date of Acceptance: 4 November 2009
Last Modified: 04 Jun 2018 16:34
URI: http://orca.cf.ac.uk/id/eprint/111529

Citation Data

Cited 4 times in Google Scholar. View in Google Scholar

Cited 3 times in Scopus. View in Scopus. Powered By Scopus® Data

Actions (repository staff only)

Edit Item Edit Item

Downloads

Downloads per month over past year

View more statistics