# MSE 201 S21 Lecture 17 - Module 1 - Steady-State Diffusion

TLDRThis lecture delves into steady-state diffusion, a fundamental concept in mass transfer. Flux, the rate of mass or moles per unit area over time, is introduced as a key measure. The driving force behind diffusion is the concentration gradient, which is the difference in concentration over an area. Fick's first law of diffusion is discussed, relating flux to the negative concentration gradient through the diffusion coefficient, a material-specific property. An example of butyl rubber gloves protecting against methylene chloride illustrates the practical application of steady-state diffusion, emphasizing the importance of flux in determining the effectiveness of protective materials.

### Takeaways

- 😀 Steady-state diffusion is the simplest case of diffusion where the rate of mass transfer does not change over time.
- 📚 The concept of mass transfer is quantified by the rate of mass transfer per unit surface area, known as flux.
- 🔍 Flux is defined as the mass or moles moving through a given area per unit of time, with units of mass or moles per area squared per second.
- 🧪 The driving force behind diffusion is a concentration gradient, where mass moves from an area of high concentration to one of low concentration.
- 🌐 Fick's first law of diffusion relates the flux to the concentration gradient, with the flux being proportional to the negative of the concentration gradient.
- ⚖️ The negative sign in Fick's first law indicates that the flux moves from high to low concentration, which is the natural direction of diffusion.
- 🔑 The diffusion coefficient (D) is a material property that quantifies the rate of diffusion for a substance through a particular medium.
- 🧤 An example of steady-state diffusion is the use of rubber gloves to protect against the diffusion of chemicals like methylene chloride through the skin.
- 📉 The flux across a material can be calculated by considering the diffusion coefficient, the concentration gradient, and the thickness of the material.
- 🛡️ A lower flux indicates a better barrier material, as it means less of the substance is diffusing through to the other side.
- 🔬 Understanding and calculating flux is crucial for applications such as material science, environmental science, and chemical engineering where controlling the rate of diffusion is important.

### Q & A

### What is the concept of steady-state diffusion?

-Steady-state diffusion refers to a situation where the rate of mass transfer does not change with time. It is characterized by a constant flux, which is the amount of mass or moles passing through a given area over a length of time.

### What is the definition of flux in the context of diffusion?

-Flux is defined as the rate of mass transfer per unit surface area. It measures how much mass or moles move through a given area over a specific length of time, and is typically measured in units of kilograms or grams per square meter per second.

### What is the driving force behind the diffusion process?

-The driving force behind diffusion is the concentration gradient, which is the difference in concentration of a substance from one side of a medium to the other. This gradient causes the substance to move from an area of high concentration to an area of low concentration.

### What is Fick's first law of diffusion, and how does it relate to steady-state diffusion?

-Fick's first law of diffusion states that the flux is proportional to the concentration gradient. In the context of steady-state diffusion, this law formalizes the relationship between the constant flux and the concentration gradient, indicating that the flux is equal to the negative product of the diffusion coefficient and the concentration gradient.

### Why is the negative sign used in Fick's first law of diffusion?

-The negative sign in Fick's first law indicates the direction of the flux, which is from the region of higher concentration to the region of lower concentration. It signifies the natural tendency of substances to diffuse towards areas of lower concentration.

### What is the role of the diffusion coefficient (D) in Fick's first law?

-The diffusion coefficient (D) in Fick's first law is a material property that quantifies the tendency of a substance to diffuse through a medium. It is a constant that relates the flux to the concentration gradient for a given material under steady-state conditions.

### How can the concentration gradient be empirically measured in an experiment?

-The concentration gradient can be empirically measured by setting up an experiment with a known area and imposing a concentration gradient across a thin film or membrane. By observing how fast atoms or molecules diffuse across the membrane, the concentration gradient can be determined.

### What is an example of a practical application of steady-state diffusion?

-A practical application of steady-state diffusion is the use of rubber gloves to protect hands from chemicals, such as methylene chloride, which is a common paint remover. The flux across the glove material can be calculated to determine how much of the chemical might come into contact with the skin.

### Why is it important to calculate the flux when comparing different types of gloves for chemical protection?

-Calculating the flux is important because it provides a measure of how much of a potentially harmful chemical can pass through the glove material. A lower flux indicates better protection, as it means less of the chemical is reaching the skin.

### What is the significance of the assumption of a linear concentration gradient in the context of steady-state diffusion?

-Assuming a linear concentration gradient simplifies the calculation of the concentration gradient as the difference in concentration divided by the distance between the two areas. This assumption is valid when the change in concentration is gradual and uniform over the distance considered.

### Outlines

### 🔬 Introduction to Steady State Diffusion

The script begins with an introduction to the concept of steady state diffusion, a fundamental aspect of the diffusion process. It explains the importance of mass transfer and the quantification of this transfer through the rate of mass transfer per unit surface area, termed as 'flux.' Flux is defined as the amount of mass or moles moving through a given area over time, with units of mass or moles per square meter per second. The driving force behind diffusion is identified as a concentration gradient, where mass naturally moves from an area of high concentration to one of low concentration. The script uses the example of coffee to illustrate this concept, highlighting the diffusion of coffee molecules into water. The steady state diffusion is characterized by a time-independent rate, meaning the rate of diffusion does not change over time, which is a key feature of the experiments discussed in the script.

### 🧪 Steady State Diffusion and Fick's First Law

This paragraph delves deeper into steady state diffusion, introducing Fick's first law as a formal expression that relates the flux to the concentration gradient. The concentration gradient is defined as the change in concentration over the change in thickness (dc/dx), and the flux is shown to be proportional to this gradient, with a negative sign indicating the direction of mass movement from high to low concentration. The diffusion coefficient (D) is introduced as a material property that influences the rate of diffusion. The paragraph provides a practical example involving butyl rubber gloves and the diffusion of methylene chloride, a common paint remover and irritant. By calculating the flux using the given diffusion coefficient, concentrations, and the thickness of the gloves, the script illustrates how to determine the rate at which the chemical can potentially pass through the gloves, emphasizing the importance of selecting gloves with the lowest flux to protect against irritants.

### 📚 Conclusion and Transition to Non-Steady State Diffusion

The final paragraph of the script serves as a conclusion to the discussion on steady state diffusion and a transition to the next topic, non-steady state diffusion. It briefly mentions that the next module will explore scenarios where the assumption of a constant rate of diffusion is not appropriate, indicating a shift in focus to more complex diffusion processes. This sets the stage for further exploration of diffusion dynamics where the rate of mass transfer is not time-independent, likely involving more intricate experimental setups and calculations.

### Mindmap

### Keywords

### 💡Diffusion

### 💡Steady-State Diffusion

### 💡Flux

### 💡Concentration Gradient

### 💡Membranes

### 💡Fick's First Law of Diffusion

### 💡Diffusion Coefficient

### 💡Methylene Chloride

### 💡Butyl Rubber Gloves

### 💡Non-Steady State Diffusion

### Highlights

Introduction to steady-state diffusion and its importance in mass transfer.

Definition of flux as the rate of mass transfer per unit surface area over time.

Flux is a key concept in understanding diffusion processes, with units of mass per area per time.

The role of concentration gradients as the driving force behind diffusion.

Experiment setup to measure the rate of diffusion across a membrane.

Concept of steady-state diffusion where the rate of diffusion does not change over time.

Fick's first law of diffusion and its relation to the concentration gradient.

The negative sign in Fick's first law indicating the direction of mass movement from high to low concentration.

The diffusion coefficient (D) as a material property that influences the rate of diffusion.

Calculating the concentration gradient for a linearly varying concentration profile.

Practical application of steady-state diffusion in the context of protective gloves against chemicals.

Example calculation of flux for butyl rubber gloves to determine chemical permeation rate.

Importance of flux in selecting gloves with the lowest permeation rate for safety.

Assumption of constant flux in steady-state diffusion experiments and its implications.

Introduction to non-steady-state diffusion and its differences from steady-state diffusion.

Upcoming module on non-steady-state diffusion and its significance in various applications.