Concentration wave of a solute in an artery: the influence of curvature

Abstract

Mass transport and diffusion phenomena in the arterial lumen are studied through a mathematical model. Blood flow is described by the unsteady Navier–Stokes equation and solute dynamics by an advection–diffusion equation, the convective field being provided by the fluid velocity. A linearization procedure over the steady state solution is carried out and an asymptotic analysis is used to study the effect of a small curvature with respect to the straight tube.

Analytical and numerical solutions are found: the results show the characteristics of the long wave propagation and the role played by the geometry on the solute distribution and demonstrate the strong influence of curvature induced by the fluid dynamics.

Keywords:

• Mass transport
• Diffusion‐advection equation
• Vascular flow
• Curved arteries
• Perturbation methods

Acknowledgements

The authors wish to thank M. Prosi and P. Zunino for many fruitful discussions.

Notes

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Here long means of length much larger than the radius. With such hypothesis the entry effects are disregarded.

is a nondimensional parameter corresponding to the Stokes number (or to the square of Womersley number) for solute dynamics, with the fluid viscosity replaced by .

Here long means of length much larger than the radius. With such hypothesis the entry effects are disregarded.

The problem was solved with the aid of the symbolic computing tool Mathematica^®.

Additional information

Notes on contributors

Amabile Tatone

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