CHE 318 Lecture 12

Preparation Before Midterm / Convective Mass Transfer

Dr. Tian Tian

2026-01-30

Recap

• Several example systems in unsteady state mass transfer regime
• General procedures to identify generation / accumulation terms
• Steady state solution from mass balance equations

Learning Outcomes

After today’s lecture, you will be able to:

• Recall concepts in steady state and unsteady state mass transfer
• Practice step-by-step solution to sample problems
• Analyze typical pitfalls in concepts of mass transfer
• Familiarize with convective mass transfer concepts

Midterm Exam Announcement

• Date: Feb 09, 2026 (Monday)
• Time: 50 min during class
• Question types:
  • Multichoice questions (conceptual, no derivation)
  • Short-answer questions (conceptual, no derivation)
  • Long-answer questions (derivation and / or calculation)
• Formula sheet / calculator policy: refer to course syllabus

Midterm Exam Questions

• Covers up to unsteady state mass transport
• Sample questions to be released this week on Canvas
• Use our AI helper wisely!

Key Concepts of Mass Transfer

• Q: What is mass transfer about?
  • Moving of chemical species through space
• Q: What does mass transfer study?
  • How fast can we move chemicals / materials through space –> Concept of flux
  • What drives species to move? –> Concept of driving force / concentration gradient
  • Resistance of species moving during transport –> Concept of Diffusivity
  • Slow vs fast ways to move species –> diffusion vs convection
• Q: What systems do we study?
  • Steady state: concentration of species do not change over time
  • Unsteady state: concentration of species change over time

A Mindmap For Mass Transfer Part I

mindmap
  root((Mass Transfer))
    Mass Balance
      Steady State
      Unsteady State
        Boundary conditions
        Reaction rate coupling
      Pseudo-steady State

    Flux Equation
      Diffusion
        Fick 1st law
        Diffusive velocity
      Convection
        Convective velocity

    General Systems
      EMCD
      Stagnant B
      General and reaction

    Geometry
      1D slab
      Cylinder
      Sphere
      Varying cross section

    State of Material and Diffusivity
      Gas
        Chapman–Enskog
        Fuller
      Liquid
        Stokes–Einstein
      Solid
        Solubility
        Permeability
        Effective diffusivity

Sample Questions (2019)

• Please check our Canvas examples for solutions.
• We will give a few “what do we look for” and “potential pitfalls”
• Always remember to draw the diagram and list conditions!

Short Answer Question

Short Answer Question 1 – Key Points

• Surface area of droplet – sphere – \(4 \pi r_0^2\)
• Total flux per droplet – \(\overline{N}_A = 4 \pi r_0^2 N_A\) (bonus: the flux is described by stagnant B solution)
• Relation between surface flux \(N_A \propto r_0^{-1}\)
• Number of droplets \(n \propto r_0^{-3}\)
• Total mass transfer for same weight: \(\propto r_0^{-2}\)

Conclusion: - smaller particle \(r_0\) 👉 larger combined area 👉 larger total flux / amount of absorption - (bonus) in practice you want to balance between making smaller droplets, and energy cost for producing the droplets

Long Answer Question 1

Long Answer Question 1 – Key Points

• Sign in \(N_A\) or \(J_{Az}^*\)
• EMCD situation
• Use Fuller method to calibrate \(D_{AB}\) (\(\propto T^{1.5}/P\))

Long Answer Question 2

Long Answer Question 2 – Key Points

• Diagram (a cylinder with in/out diameter & length)
• Solid diffusion 👉 EMCD-like equation (diffusion only)
• DO NOT write \(N_A \propto 1/(d_2 - d_1)\)!
• Steady state flux eq. in cylindrical coordinate
• Governing eq for cylindrical coordinate
• Use of \(\overline{N}_A\) for steady state
• \(c_A\) from solubility

Long Answer Question 3

Long Answer Question 3 – Key Points

• Diagram (convection in axial / z-axis; diffusion in radial / r-axis)
• Mass balance in control volume
• Generation term link to flux-controlled consumption
• Flux boundary conditions in r-axis

Summary

• Good luck with the midterm exam!