CHE 318 Lecture 12

Preparation Before Midterm / Convective Mass Transfer

Author

Dr. Tian Tian

Published

January 30, 2026

Note

Slides 👉 Open presentation🗒️
PDF version of course note 👉 Open in pdf
Handwritten notes 👉 Open in pdf

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!

--- title: "CHE 318 Lecture 12" subtitle: "Preparation Before Midterm / Convective Mass Transfer" author: "Dr. Tian Tian" date: "2026-01-30" format: html: {} revealjs: output-file: slides.html --- ::: {.content-visible when-format="html" unless-format="revealjs"} ::: {.callout-note} - Slides 👉 [Open presentation🗒️](./slides.html) - PDF version of course note 👉 [Open in pdf](./L12.pdf) - Handwritten notes 👉 [Open in pdf](./public/L12_annotated.pdf) ::: ::: ## Recap {.center} - 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 {.center} 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 {.center} - 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 {.center} - Covers up to unsteady state mass transport - Sample questions to be released this week on Canvas - Use our [AI helper](https://gemini.google.com/gem/f2d47200f0bf) 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 ::: {.content-visible when-format="html"} ## A Mindmap For Mass Transfer Part I ```{mermaid} 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 ![](./public/sa-1.png){width="100%"} ## 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 ![](./public/la-1.png){width="100%"} ## 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 ![](./public/la-2.png){width="100%"} ## 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 ![](./public/la-3.png){width="100%"} ## 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!