Fick's 1st/2nd Law: Explaining the Sign Difference

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In summary, Fick's 1st law has a negative sign because it is looking at steady state diffusion and the concentration of the other substance decreases as you move further away. The 2nd law looks at concentration with respect to time and can be increasing or decreasing. The diffusion constant in the 1st law is a constant because it is used for steady state diffusion, while in the 2nd law it is a variable because it is used for non-steady state diffusion. The diffusion constant can depend on physical parameters such as temperature and molecular weight. The validity of Fick's laws depends on the boundary conditions, such as constant concentration or constant flux at the boundaries.
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Why does Fick's 1st law have a negative sign in the equation, but Fick's
2nd law doesn't?
 
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  • #2
also one more question:
Why's the D in Fick's 1st law a constant, but a variable in Fick's 2nd law?
 
  • #3
hmm

far from an expert, but here is my best guess

for your first question:

in the 1st law, we're looking at steady state diffusion, and how the concentrations vary with respect to position

so, the concentration of the other substance will be decreasing as you go further and furthery away from it, hence the negative sign

in the 2nd law, we are looking at concertration with respect to time and it may be increasing or decreasing
for your second question:

the 1st law is used for steady state diffusion (concentration does not change with respect to time), that's why D is a constant

2nd law is used for non-steady state diffusion, where the concentration does depend on time,
 
  • #4
wow! thank you very much! I've been thinking about that question for many days...
 
  • #5
what kind of diffusion constants do you know? what physical parameters does the diffusion constant depend on?
 
  • #6
what are the boundary condition of the validity of fick's first and 2nd law?
 

1. What is Fick's First Law and how does it explain the sign difference?

Fick's First Law is a mathematical equation that describes the diffusion of particles in a medium. It states that the rate of diffusion is directly proportional to the concentration gradient and the diffusion coefficient. The sign difference in Fick's First Law refers to the direction of diffusion, with a positive sign indicating diffusion from high concentration to low concentration and a negative sign indicating the opposite direction.

2. What is Fick's Second Law and how does it explain the sign difference?

Fick's Second Law is a differential equation that describes the change in concentration over time due to diffusion. It incorporates the diffusion coefficient, concentration gradient, and diffusion flux. The sign difference in Fick's Second Law is also related to the direction of diffusion, with a positive sign indicating an increase in concentration over time and a negative sign indicating a decrease in concentration.

3. Why is there a sign difference in Fick's Laws?

The sign difference in Fick's Laws is a result of the convention used to define the direction of diffusion. In Fick's First Law, the positive sign represents the direction of diffusion from high to low concentration, while in Fick's Second Law, the positive sign represents an increase in concentration over time. This convention is used to maintain consistency and avoid confusion in the interpretation of the equations.

4. How are Fick's Laws used in scientific research?

Fick's Laws are used in many different scientific fields to study the diffusion of particles, such as in the fields of chemistry, biology, and physics. They can be used to model the diffusion of substances in various mediums, such as gases, liquids, and solids. Additionally, Fick's Laws are used in the development of drug delivery systems and in understanding the movement of pollutants in the environment.

5. Are there any limitations to Fick's Laws?

While Fick's Laws are widely used and have been proven to accurately describe diffusion in many systems, there are some limitations to their applicability. For example, they assume that the diffusion coefficient is constant and that the concentration gradient is linear. In reality, these factors may vary depending on the system being studied. Additionally, Fick's Laws do not take into account other factors that may influence diffusion, such as temperature, pressure, and the presence of other substances in the medium.

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