Taylor dispersion in a pulsatile flow of a viscoelastic fluid through an eccentric annular tube

Taylor dispersion of a solute in a pulsatile flow of a viscoelastic fluid, whose constitutive equation follows the Maxwell model, through an eccentric annulus is investigated in this work. To determine the effective dispersion coefficient, Deff , we have used the multiple-scale analysis in conjunction with the homogenization method. The governing equation describing this dispersive phenomenon for solute concentration is the advection-diffusion equation, which depends on the velocity profile. Therefore, the momentum equation must be solved in advance. A hyperbolic partial differential equation in a bipolar coordinate system was derived by combining the Cauchy momentum equation with Maxwell’s constitutive equation. Parameters such as the Womersley number, Wo , and the Deborah number, De , control the time-dependent flow and viscoelasticity, respectively. For low Womersley numbers, i.e. for low frequencies, an increase in the Deborah number, the eccentricity, φ , and gap width, γ , leads to an enhancement of the effective dispersion coefficient. For instance, a fluid with De = 5 could increase Deff by two orders of magnitude compared with a Newtonian fluid with the same settings ( φ = 0.3 and Wo = 0.1 ). However, this enhancement due to the viscoelastic effect is only significant at low frequencies. An advection-diffusion equation for the mean concentration in the cross-section was also derived and evaluated in the same low-frequency limit. It was concluded that pulsatile flow maximises the axial dispersion compared with steady and purely oscillatory flows.