Geometric control of asymmetries for passive tracer transport in domains with triangular and rounded triangular cross-sections

We investigate the dispersion of passive tracers in laminar pressure-driven shear flows through triangular and ``trefoil'' capillary pipes, characterized as near-triangular cross-sections with smoothed corners and concave sides. We show through asymptotic analyses and Monte-Carlo simulations how the longitudinal asymmetry of the tracer distribution changes in time. For triangular cross-sections, varying from equilateral to isosceles, we observe a loading shift in the concentration profile from back-loaded to front-loaded, corresponding to a sign-change (from positive to negative) in the cross-sectionally averaged skewness. This change becomes more striking as the isosceles domains flatten. For the trefoil domains we explore, behavior aligns with previous studies: bulky cross-sections with aspect ratio ∼1 maintain the same back-loaded concentration profile (and positive skewness) throughout their time-evolution, while flatter cross-sections with aspect ratio «1 present a sign-change in the skewness corresponding to a back- to front-loading shift before symmetrizing on the longest timescales. Open questions and future directions will be discussed.