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ABSTRACT
The splitting method used in a previous study for the numerical solution of mass transfer equations in ternary systems is generalized to mixtures with n-components. The diffusion coefficients are considered constant. Theoretical results about the stability of the method are presented, as well as numerical simulations for mixtures with n = 4, 5, and 6. The numerical experiments confirmed the theoretical results and show good numerical performances. Moreover, multicomponent diffusion effects without an imposed concentration gradient are investigated for mixtures with n = 4, 5, and 6 components.
Nomenclature
| c | = | mass fraction of the chemical species, kg/kg |
| d | = | diameter of the sphere, d = 2 R, m |
| D | = | Fick diffusion coefficient, m2/s |
| J | = | diffusion flux (flow), kg/(m2 s) |
| Pe | = | Peclet number, Pe = U0 d/D11, dimensionless |
| r | = | dimensionless radial coordinate, r*/R, in a spherical coordinate system |
| r* | = | radial coordinate in a spherical coordinate system, m |
| R | = | radius of the sphere, m |
| t | = | time, s |
| U0 | = | free stream velocity, m/s |
| VR | = | dimensionless radial velocity component |
| Vθ | = | dimensionless tangential velocity component |
| w | = | mass concentration of the chemical species, kg/m3 |
| W | = | dimensionless concentration of the chemical species |
| Z | = | transformed dimensionless concentration |
| θ | = | polar angle in a spherical coordinate system |
| ρ | = | mass density of the mixture, kg/m3 |
| τ | = | dimensionless time or Fourier number, |
| ψ | = | dimensionless stream function |
| Superscripts | = | |
| R | = | surface of the sphere |
| 0 | = | initial conditions |
Nomenclature
| c | = | mass fraction of the chemical species, kg/kg |
| d | = | diameter of the sphere, d = 2 R, m |
| D | = | Fick diffusion coefficient, m2/s |
| J | = | diffusion flux (flow), kg/(m2 s) |
| Pe | = | Peclet number, Pe = U0 d/D11, dimensionless |
| r | = | dimensionless radial coordinate, r*/R, in a spherical coordinate system |
| r* | = | radial coordinate in a spherical coordinate system, m |
| R | = | radius of the sphere, m |
| t | = | time, s |
| U0 | = | free stream velocity, m/s |
| VR | = | dimensionless radial velocity component |
| Vθ | = | dimensionless tangential velocity component |
| w | = | mass concentration of the chemical species, kg/m3 |
| W | = | dimensionless concentration of the chemical species |
| Z | = | transformed dimensionless concentration |
| θ | = | polar angle in a spherical coordinate system |
| ρ | = | mass density of the mixture, kg/m3 |
| τ | = | dimensionless time or Fourier number, |
| ψ | = | dimensionless stream function |
| Superscripts | = | |
| R | = | surface of the sphere |
| 0 | = | initial conditions |