Supplementary Information Theoretical and experimental analysis of the core sampling method: reducing diffusional losses in aerosol sampling line

where n is the concentration of diffusive species as a function of the spatial position in a cylindrical coordinate, n(r, θ, z); D is the diffusivity of the sampled diffusive species; u is the fluid speed which is a vector function of spatial position, u(r, θ, z); ∇ is the nabla operator; ∇n is the gradient of n(r, θ, z); and ∇ is the Laplace operator. According to symmetry, u and n is independent of the angle θ. When Assumptions 1~2 are valid, convection diffusion can be reformulated into the Graetz problem: