Advection-dispersion solute transport through combined activity-driven and pressure-driven flows in a capillary tube

The flow of active fluids is a combination of activity-driven and pressure-driven components. This implies that the solute transport phenomenon in active fluids occurs due to combined activity-driven and pressure-driven flows. While this topic finds many biophysical and industrial applications, it still needs further investigation. In this study, by means of the Reynolds decomposition type cross-sectional averaging and deviating method, a reduced-order model for advection-dispersion solute transport through combined activity-driven and pressure-driven flows in a capillary tube is developed. The effective velocity and dispersion coefficient that depend on the pressure-driven (Poiseuille) contribution fraction (ω) and Peclet number (Pe) are extracted from the obtained model. The solution of the resultant equation provides the concentration profile. The proposed model is validated through the comparison with the two existing classical limiting cases of purely pressure-driven flow (ω = 1) and purely activity-driven flow (ω = 0) in terms of the velocity distribution, effective velocity and dispersion coefficient, and concentration profile. The results reveal that the effective velocity and dispersion coefficient for the case of ω = 1 are larger than those for the case of ω = 0. For 0 < ω < 1, the effective velocity and dispersion coefficient are between those for ω = 0 and ω = 1. It is also indicated that the case of ω = 1 leads to earlier breakthrough compared with the case of ω = 0. For 0 < ω < 1, the breakthrough time is between those for ω = 1 and ω = 0.