Residence-time dispersion modeling: a Peclet number (Pe) of zero represents which idealized flow behavior in a reactor or conduit?

Introduction / Context:
The Peclet number (Pe) is a dimensionless group that compares advective transport to diffusive (dispersive) transport. In reactor engineering and mixing, Pe helps classify flow patterns between the two extremes of ideal plug flow and complete back mixing (continuous stirred-tank behavior). Understanding Pe guides scale-up, prediction of conversion, and interpretation of tracer tests.

Given Data / Assumptions:

• Peclet number defined as Pe = u * L / D_ax, where u is superficial velocity, L is a characteristic length, and D_ax is axial dispersion coefficient.
• Idealized limits are considered.

Concept / Approach:
As Pe → ∞, advection dominates and dispersion is negligible, corresponding to plug flow (no axial mixing). As Pe → 0, dispersion dominates over advection, yielding complete back mixing akin to a CSTR, where concentration becomes uniform along the flow direction due to very strong mixing.

Step-by-Step Solution:

Verification / Alternative check:
RTD models show that the variance of exit age distribution for CSTRs is high, consistent with strong axial mixing and the limit of Pe → 0 for dispersion models.

Why Other Options Are Wrong:

• Laminar flow (a) is not uniquely defined by Pe; laminar plug flow can still have high Pe.
• Plug flow (c) corresponds to Pe → ∞, not zero.
• Eddy diffusivity equals zero (d) implies no dispersion; the opposite of Pe = 0.

Common Pitfalls:
Confusing Reynolds number (laminar/turbulent) with Peclet number (advection/dispersion).

Final Answer:
Complete back mixing