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The CONSERVATION OF CHEMICAL SPECIES (mass fraction Y_α of species α) gives:
A{'text': '$Y_\\alpha = 0$', 'label': 'A'}
B{'text': '$\\rho DY_\\alpha/Dt = -\\nabla\\cdot \\mathbf{j}_\\alpha + \\omega_\\alpha$ — substantial derivative balances diffusive flux $\\mathbf{j}_\\alpha$ and chemical source ω_α', 'label': 'B'}
C{'text': 'Y_α = const', 'label': 'C'}
D{'text': 'Y_α explodes', 'label': 'D'}
Answer & Solution
Correct answer: B. {'text': '$\\rho DY_\\alpha/Dt = -\\nabla\\cdot \\mathbf{j}_\\alpha + \\omega_\\alpha$ — substantial derivative balances diffusive flux $\\mathbf{j}_\\alpha$ and chemical source ω_α', 'label': 'B'}
Species transport: each component's mass fraction obeys an advection-diffusion-reaction equation. Diffusive flux usually approximated by Fick's law $\mathbf{j}_\alpha = -\rho D_\alpha \nabla Y_\alpha$. Sum over all species recovers global mass conservation.
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