A subgrid-scale model for reactive concentration boundary layers for 3D mass transfer simulations with deformable fluid interfaces

A VOF-based approach for the detailed computation of reactive mass transfer at rising gas bubbles is presented. Based on a local approximation of the transport equation at the fluid interface, a reactive subgrid-scale model for uncoupled reactions within the concentration boundary layer is derived. For this purpose, the convective term of the boundary layer description is modeled, reducing the governing nonlinear partial differential equation to a one-dimensional nonlinear differential equation. A numerical scheme is developed to solve the remaining differential equation and obtain the concentration gradient at the fluid interface. Mesh convergence for the resulting scheme is shown. The method is validated within the VOF code FS3D by comparing to local and integral Sherwood numbers, and Schmidt numbers up to 1000 for a 3D reactive Stokes flow regime around a rising spherical bubble (Hadamard-Rybczynski flow field). Local Sherwood numbers show significant reactive mass transfer into the liquid phase in the wake region of the rising bubble.