No abstract

Two separate models were developed to solve the dimensionless partial differential equation: one using Crank-Nicolson discretization and the other using the implicit Euler method. Both methods will be covered in the following sections. A.1 Numerical Model using the Crank-Nicolson MethodTo implement Crank-Nicolson, the domain of the dilution chamber of the UAC was divided into a grid as shown in Figure S1. Given that the solution is expected to rapidly change near the entrance of the dilution chamber, a logarithmic mesh was used in the axial direction, ζ, to capture the concentration profile more efficiently. The mesh spacing in the radial direction, ρ, was kept linear.