When a solute such as angiographic contrast is introduced into a solvent such as blood analog fluid flowing in a straight circular tube, it spreads under the combined action of molecule diffusion and the variation of velocity over the cross-section . If two molecules are being carried in the flow, for example, one in the center and one near the wall, the rate of separation caused by the difference in bulk velocity will greatly exceed that caused by molecule motion. Given enough time, any single molecule would wander randomly throughout the cross section of the pipe because of molecular diffusion, and would sample at random all the advective velocities . Therefore, Taylor  adopted the Lagrangian approach to the problem, casting the equations in a coordinate system that moves with the average velocity of the flow and replacing the molecular diffusion coefficient with a dispersion coefficient, and the local concentration with the cross sectional mean concentration. Recasting Taylor’s equation in an inertial coordinate system one obtained the so called advection-dispersion equation.
Computational Investigation on the Dispersive Transport of Angiographic Contrast Injected Antegradely Into Flow in a Tube
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Hao, Q, & Lieber, BB. "Computational Investigation on the Dispersive Transport of Angiographic Contrast Injected Antegradely Into Flow in a Tube." Proceedings of the ASME 2007 Summer Bioengineering Conference. ASME 2007 Summer Bioengineering Conference. Keystone, Colorado, USA. June 20–24, 2007. pp. 567-568. ASME. https://doi.org/10.1115/SBC2007-176423
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