Lecture Notes: Fick's Law and Diffusion

Introduction to Adolf Fick

• Adolf Fick is a notable historical figure in the field of science.
• Known for developing essential scientific laws, particularly in diffusion.

Fick's Law Overview

• Fick’s Law describes the rate of diffusion of particles.
• The law is crucial for understanding the movement of particles over time and space in various scientific contexts.

Conceptual Experiment

• Imagine a box with molecules and a challenge to maximize the number of particles crossing from one side to the other (side 1 to side 2).
• Reward: $5 for each particle that crosses the back wall in a set period.
• Objective: Maximize profits by increasing the number of particles crossing.

Strategies to Maximize Diffusion

1. Reduce Thickness of the Wall

   • Bring the back wall closer to the front.
   • Less distance for molecules to travel increases the crossing rate.

2. Use Smaller Molecular Weight Molecules

   • Smaller molecules have a higher diffusion rate (as per Graham's Law).
   • Faster diffusion leads to more particles crossing.

3. Increase Pressure at the Start (Side 1)

   • More molecules initially on side 1 elevate the pressure.
   • Higher pressure boosts the likelihood of molecules crossing.

4. Enlarge Surface Area

   • Expand the box dimensions to increase the area.
   • Greater area provides more opportunities for molecules to cross.

Fick's Law Formula

• General Formula:

  [ \dot{V} = \frac{A \cdot (P1 - P2) \cdot D}{T} ]

  • (\dot{V}): Rate of particles moving (volume or amount per time)
  • (A): Surface area
  • (P1 - P2): Pressure difference between sides 1 and 2
  • (D): Diffusion constant
  • (T): Thickness of the wall

Related Concepts

• Diffusion Constant (D)

  • Related to Henry's Law (solubility) and Graham’s Law (molecular weight impact).
  • Smaller molecular weight increases diffusion rate.

• Thickness (T)

  • Thicker walls reduce the rate of diffusion.

Alternative Representation of Fick’s Law

• Flux and Gradient Approach:

  1. Flux: Net rate of particles moving through an area.
  2. Gradient: Change in pressure over a distance.

• Formula:

  [ \text{Flux} = \text{Gradient} \times D ]

Summary

• Fick's Law is intuitive and can be derived through logical thinking about particle diffusion.
• It’s often expressed in different formats, but the core principles remain consistent.