Direct numerical simulation of a rising CO2 bubble dissolving in quiescent water at high Schmidt number

Three-dimensional direct numerical simulation (DNS) was performed to investigate mass transfer at high Schmidt numbers, focusing on a rising, dissolving gas bubble in a liquid. The objectives are (i) to develop a numerical method based on the volume-of-fluid (VOF) approach for simulating a dissolving gas bubble and (ii) to determine the mesh resolution required to accurately capture the underlying physical phenomena. A sharp-interface phase-change model is employed, in which the species concentration gradient at the gas–liquid interface is calculated using an irregular stencil that accounts for the local interface geometry. The method was first validated against benchmark cases at low Schmidt numbers, and then applied to a 9 mm CO₂ bubble rising in quiescent water. The simulation was performed on grids ranging from 128³ to 2048³, with the finest case using 8192 cores over 15 days. The total simulated physical time was 1.2 s, including the grid-refinement stages up to the finest resolution. The grid-dependence study indicates that the evaluated grid resolutions remain outside the fully asymptotic regime; nevertheless, the 2048³ grid result underestimates the Sherwood number by only about 7 % relative to the empirical correlation. The CO₂ concentration isosurface from the 2048³ case reveals a complex wake structure with elongated filaments and rolled-up sheets, indicative of shear-induced vortices and strong entrainment. The grid-dependence study suggests that even finer grids (e.g., 4096³) may be necessary, highlighting the need for future exascale computing to fully resolve mass transfer at a high Schmidt number (∼530).