Axial mixing metric: in a continuous mixer, the dimensionless group v·L/D (longitudinal velocity * mixer length / axial diffusivity) is known as which number?

Introduction / Context:
Dimensionless numbers help compare convective transport to diffusive transport. In axial mixing of granular or liquid streams, the Peclet number (Pe) gauges the relative importance of plug-flow convection to back-mixing by dispersion/diffusion.

Given Data / Assumptions:

• v = axial (superficial) velocity through the mixer.
• L = characteristic length (mixer length).
• D = axial dispersion coefficient (analog of diffusivity).

Concept / Approach:
Peclet number Pe = v·L/D. High Pe indicates convection-dominated transport (plug-flow-like), while low Pe implies significant axial mixing (approaching a CSTR behavior in limits). Other numbers: Weber relates inertia to surface tension; Schmidt compares momentum and mass diffusivity; Brinkman appears in porous media flow modeling.

Step-by-Step Solution:
Identify the group: v·L/D.Recall definition: that is Peclet number for axial dispersion models.Match to option: Peclet.

Verification / Alternative check:
Axially dispersed plug flow reactor (ADPFR) models and residence-time-distribution analyses routinely use Pe to characterize axial mixing intensity.

Why Other Options Are Wrong:
Weber: inertia vs surface tension (sprays, jets).Schmidt: ν/D_m (momentum vs mass diffusivity).Brinkman: extends Darcy’s law for viscous effects in porous media.

Common Pitfalls:
Confusing Peclet with Reynolds; Reynolds uses hydraulic diameter and kinematic viscosity and relates to turbulence onset.

Final Answer:
Peclet