Dispersion characteristics of blood during nanoparticle assisted drug delivery process through a permeable microvessel

Elucidating the rheological implications of adding particles in blood

In the past few decades, nanotechnology has been employed to provide breakthroughs in the diagnosis and treatment of several diseases using drug-carrying particles (DCPs). In such an endeavor, the optimal design of DCPs is paramount, which necessitates the use of an accurate and trustworthy constitutive model in computational fluid dynamics (CFD) simulators. We herein introduce a continuum model for elaborating on the rheological implications of adding particles in blood. The model is developed using non-equilibrium thermodynamics to guarantee thermodynamic admissibility. Red blood cells are modeled as deformed droplets with a constant volume that are able to aggregate, whereas particles are considered rigid spheroids. The model predictions are compared favorably against rheological data for both spherical and non-spherical particles immersed in non-aggregating blood. It is expected that the use of this model will allow for the testing of DCPs in virtual patients and for their tailor-design in treating various diseases.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s00397-021-01289-x.

New regimes of dispersion in microfluidics as mediated by travelling temperature waves

We unveil new regimes of dispersion in miniaturized fluidic devices, by considering fluid flow triggered by a travelling temperature wave. When a temperature wave travels along a channel wall, it alters the density and viscosity of the adjacent fluid periodically. Successive expansion–contraction of the fluid volume through a spatio-temporally evolving viscosity field generates a net fluidic current. Based on the temporal evolution of the axial dispersion coefficient, new regimes of dispersion—such as a short-time ‘oscillating regime’ and a large-time ‘stable regime’—have been identified, which are absent in traditionally addressed flows through miniaturized fluidic devices. Our analysis reveals that the oscillation of axial dispersion persists until the variance of species concentration becomes equal to half of the square of the wavelength of the thermal wave. The time period of oscillation in the dispersion coefficient turns out to be a unique function of the thermal wavelength and net flow velocity induced by thermoviscous pumping. The results of this study are likely to contribute towards the improvement of microscale systems that are subjected to periodic temperature variations, including microreactors and DNA amplification devices.

Unsteady solute dispersion in small blood vessels using a two-phase Casson model

This study explores the transport of a solute in an unsteady blood flow in small arteries with and without absorption at the wall. The Casson fluid model is suitable for blood flow in small vessels. Owing to the aggregation of red cells in the central region of the small vessels, a two-phase model is considered in this investigation. Using the generalized dispersion model (Sankarasubramanian & Gill 1973 Proc. R. Soc. Lond. A 333 , 115–132. (doi:10.1098/rspa.1973.0051)), the convection, dispersion and mean concentration of the solute are analysed at all times in small arteries of different radii. The effects of the yield stress, wall absorption, the amplitude of the fluctuating pressure gradient component, the peripheral layer thickness, the Womersley frequency parameter, the Schmidt number and the Peclet number on the dispersion process are discussed. A comparative study of solute dispersion among single- and two-phase fluid models is presented. For small vessels, a significant difference between these models is observed during the solute dispersion; however, this difference becomes insignificant for large vessels. The mean concentration of solute reduces with increasing radius of the vessels. The present investigation is more realistic for understanding the transportation process of drugs in blood flow in small arteries using the non-Newtonian fluid model.

Shear dispersion in a capillary tube with a porous wall

An analytical expression is presented for the shear dispersion during solute transport in a coupled system comprised of a capillary tube and a porous medium. The dispersion coefficient is derived in a capillary tube with a porous wall by considering an accurate boundary condition, which is the continuity of concentration and mass flux, at the interface between the capillary tube and porous medium. A comparison of the obtained results with that in a non-coupled system identifies three regimes including: diffusion-dominated, transition, and advection-dominated. The results reveal that it is essential to include the exchange of solute between the capillary tube and porous medium in development of the shear dispersion coefficient for the last two regimes. The resulting equivalent transport equation revealed that due to mass transfer between the capillary tube and the porous medium, the dispersion coefficient is decreased while the effective velocity in the capillary tube increases. However, a larger effective advection term leads to faster breakthrough of a solute and enhances mass delivery to the porous medium as compared with the classical double-porosity model with a non-coupled dispersion coefficient. The obtained results also indicate that the finite porous medium gives faster breakthrough of a solute as compared with the infinite one. These results find applications in solute transport in porous capillaries and membranes.