CHE 318 Lecture 13

Introduction To Mass Transfer Coefficients

Author

Dr. Tian Tian

Published

February 2, 2026

Note

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

Recap

Review of part I of mass transfer
Mindmap in mass transfer part I
Sample questions from previous exams

Learning Outcomes

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

Recall motivations for study convective mass transfer
Describe key assumptions in simplifying mass transfer coefficients in multiple phases and turbulent flow
Analyze the units for mass transfer coefficients

Example Questions (Continued)

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

Convective Mass Transfer

Remaining Questions From Unsteady State Mass Transfer

Our current knowledge cannot answer questions like this:

If chemical species A is transferred between two difference phases, what is the concentration in each phase?
How do we solve the mass transfer when $c$ is not uniform? (See long answer question 2)
What if fluid becomes turbulent?

What We Want To Solve In Part II: A Real Engineering Problem

You work in a pipeline maintenance team in Enbridge and need to remove a sticky, unwanted coating from the inner wall of a pipeline. There are a few design questions:

Which flushing liquid works best?
- solvent / water mixture
- solubility of the coating
How fast should the fluid flow?
- required mean velocity $v_m$
What concentration remains in the liquid?
- outlet concentration of the contaminant
How fast is the coating removed?
- removal rate vs. $v_m$

What you want to report:

Total volume of flushing liquid required
Total flushing time to reach acceptable cleanliness

Mass Transfer Between Phases: Unsteady State Analysis

We will first look at the first problem, $c_A$ between phase boundaries. This is something we in theory can solve using U.S.S. But what are the boundary conditions?

Question: a polymer membrane of thickness $2Δ$ contains a chemical with uniform concentration $c_0$ initially. At $t=0$, it is suddenly submerged into a solution containing the same chemical with concentration $c_1$. The volume of liquid is very large that concentration remains $c_1$ far away from the membrane-liquid interface. Model the concentration profile $c(z)$ inside the membrane, and calculate the total chemical absorption rate.

Solving The Polymer Membrane Mass Transfer Problem

Use the standard procedure for the polymer phase, ignore convection inside

\[ D_{AB} \frac{\partial^2 c_A}{\partial z^2} = \frac{\partial c_A}{\partial t} \]

Initial conditions:

Inside polymer $c_A(z, t=0) = c_0$
Outside polymer $c_A(z, t=0) = c_1$

Boundary conditions?

How do we know $c_A(z)$ at the interface?
They can actually take any value!

Summary

In this lecture, we talked about

Solving long-answer questions in midterm
The difficulty of studying boundary problems in mass transfer
The rise of equilibrium distribution coefficient $K$ and mass transfer coefficient $k$

What To Learn Next

We will introduce the mass transfer coefficient $k$ as a general parameter for convective mass transfer

How to use mass transfer coefficients for different phases (gas, liquid, solid)
How convective fluid transport is expressed using coefficients
How to perform mass transfer analysis based on transfer coefficients

--- title: "CHE 318 Lecture 13" subtitle: "Introduction To Mass Transfer Coefficients" author: "Dr. Tian Tian" date: "2026-02-02" format: html: {} revealjs: output-file: slides.html pdf: output-file: L13.pdf --- ::: {.content-visible when-format="html" unless-format="revealjs"} ::: {.callout-note} - Slides 👉 [Open presentation🗒️](./slides.html) - PDF version of course note 👉 [Open in pdf](./L13.pdf) - Handwritten notes 👉 [Open in pdf](./public/L13_annotated.pdf) ::: ::: ## Recap {.center} - Review of part I of mass transfer - Mindmap in mass transfer part I - Sample questions from previous exams ## Learning Outcomes {.center} After today's lecture, you will be able to: - **Recall** motivations for study convective mass transfer - **Describe** key assumptions in simplifying mass transfer coefficients in multiple phases and turbulent flow - **Analyze** the units for mass transfer coefficients # Example Questions (Continued) ## 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 # Convective Mass Transfer ## Remaining Questions From Unsteady State Mass Transfer Our current knowledge cannot answer questions like this: - If chemical species A is transferred between two difference phases, what is the concentration in each phase? - How do we solve the mass transfer when $c$ is not uniform? (See long answer question 2) - What if fluid becomes turbulent? ## What We Want To Solve In Part II: A Real Engineering Problem You work in a pipeline maintenance team in Enbridge and need to remove a sticky, unwanted coating from the inner wall of a pipeline. There are a few design questions: - Which flushing liquid works best? - solvent / water mixture - solubility of the coating - How fast should the fluid flow? - required mean velocity $v_m$ - What concentration remains in the liquid? - outlet concentration of the contaminant - How fast is the coating removed? - removal rate vs. $v_m$ **What you want to report:** - Total volume of flushing liquid required - Total flushing time to reach acceptable cleanliness ## Mass Transfer Between Phases: Unsteady State Analysis We will first look at the first problem, $c_A$ between phase boundaries. This is something we _in theory_ can solve using U.S.S. But what are the boundary conditions? Question: a polymer membrane of thickness $2Δ$ contains a chemical with uniform concentration $c_0$ initially. At $t=0$, it is suddenly submerged into a solution containing the same chemical with concentration $c_1$. The volume of liquid is very large that concentration remains $c_1$ far away from the membrane-liquid interface. Model the concentration profile $c(z)$ inside the membrane, and calculate the total chemical absorption rate. ## Solving The Polymer Membrane Mass Transfer Problem Use the standard procedure for the polymer phase, ignore convection inside $$ D_{AB} \frac{\partial^2 c_A}{\partial z^2} = \frac{\partial c_A}{\partial t} $$ Initial conditions: - Inside polymer $c_A(z, t=0) = c_0$ - Outside polymer $c_A(z, t=0) = c_1$ Boundary conditions? - How do we know $c_A(z)$ at the interface? - They can actually take any value! ## Summary In this lecture, we talked about - Solving long-answer questions in midterm - The difficulty of studying boundary problems in mass transfer - The rise of equilibrium distribution coefficient $K$ and mass transfer coefficient $k$ ## What To Learn Next - We will introduce the **mass transfer coefficient** $k$ as a general parameter for convective mass transfer       - How to use mass transfer coefficients for different phases (gas, liquid, solid) - How convective fluid transport is expressed using coefficients - How to perform mass transfer analysis based on transfer coefficients