Abstract
The dispersion of intravasculary injected nanoparticles can be efficiently described by introducing an effective diffusion coefficient Deff which quantifies the longitudinal mass transport in blood vessels. Here, the original work of Gill and Sankarasubramanian was modified and extended to include 1) the variati- on over time of Deff; 2) the permeability of the blood vessels and 3) non-Newtonian rheology of blood. A general solution was provided for Deff depending on space (?), time (?), plug radius (?c) and a subset of permeability parameters. It was shown that increasing the vessel plug radius (thus hematocrit) or permeability leads to a reduction in Deff, limiting the transport of nanoparticles across those vessels. It was also shown that the asymptotic time beyond which the solution attains the steady state behaviour is always independent of the plug radius and wall permeability. The analysis presented can more accurately predict the transport of nanoparticles in blood vessels, compared to previously developed models.
Highlights
The study of solute dispersion in capillaries dates back to the celebrated works of Taylor and Aris [1,2], who first studied the effect of shear stress on the transport in laminar flows
It was shown that the asymptotic time beyond which the solution attains the steady state behaviour is always independent of the plug radius and wall permeability
The analysis presented can more accurately predict the transport of nanoparticles in blood vessels, compared to previously developed models
Summary
The study of solute dispersion in capillaries dates back to the celebrated works of Taylor and Aris [1,2], who first studied the effect of shear stress on the transport in laminar flows They provided a solution for the classic advection/diffusion equation C t u C Dm 2C (1). The solution of Taylor and Aris is valid under the simplifying assumptions of 1) quasi-steady dispersion and 2) unidirectional flow It is strictly valid beyond the asymptotic time tst = 1/2 × Re2/Dm. Notice that sub-micrometric particles with a molecular diffusivity Dm typically ranging between 10-11 and 10-9 m2/s, in large vessels (Re 10-2 m) would have tst of the order of 105 -107 s, whereas in small capillaries (Re 10-6 m) tst would fall in the range 10-3-10-1 s
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
