Flicks diffusion equation - metabolism rate

In summary, the conversation discusses the diffusion and metabolism of an organic chemical in a bio-film reactor, with a concentration of 2mg/L being diffused at a rate of 20 m^3/hr. The concentration is represented by C1 in the reactor and C3 in the bio-film. The equation for diffusion is governed by Fick's law and includes constants e (porosity), d (diffusion coefficient), and R (metabolism rate). The solution involves finding a particular solution using separation of variables and solving the heat equation.
  • #1
gladerider
1
0
So i have an organic chemical in a bio-film reactor being diffused into a bio-film and also being metabolized at constant rate R by bacteria.

the concentration into the reactor Cin = 2mg/L with f-in at 20 m^3/hr
the concentration in the reactor is C1
C3 is the concentration in the bio-film

flicks law of diffusion:

e*dc/dt = d*(d^2C/Dz^2) - R where c = C3

where e, d, and R are constants.
e-porosity
d - diffusion coefficient

with bc's ;
dC3/dz = 0 @ z = 2micrometers
C3 = C1(.005mg/l) @ z = 0


I've was trying to solve with separation of variables but I'm rusty and running into some problems... Please help!
 
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  • #2
The general solution will be a particular solution + the general solution of the heat equation. I hope we can find a particular solution (even approximate) in polynomials is z,t .
 

1. What is Fick's diffusion equation?

Fick's diffusion equation is a mathematical formula that describes the rate of diffusion of a substance across a membrane or through a medium. It takes into account factors such as concentration gradient, diffusion coefficient, and surface area to determine the rate at which molecules will move from an area of high concentration to an area of low concentration.

2. How is Fick's diffusion equation related to metabolism rate?

Fick's diffusion equation is often used in the field of metabolism to study the rate at which nutrients and waste products are exchanged between cells and their surrounding environment. Metabolic rate is influenced by the diffusion of these molecules, as well as other factors such as enzyme activity and cellular respiration.

3. What factors affect the diffusion coefficient in Fick's equation?

The diffusion coefficient in Fick's equation is affected by temperature, molecular weight, and the properties of the medium through which diffusion is occurring. For example, diffusion through a liquid will have a different coefficient than diffusion through a gas.

4. Can Fick's diffusion equation be applied to biological systems?

Yes, Fick's diffusion equation can be applied to biological systems, as it is often used to study the exchange of molecules between cells and their environment. However, it should be noted that biological systems can be complex and may require additional factors to be considered in the equation.

5. What are some real-world applications of Fick's diffusion equation?

Fick's diffusion equation has many real-world applications, including in the fields of pharmacology, biochemistry, and environmental science. It is used to understand and predict the movement of molecules in various systems, such as drug absorption in the body, gas exchange in the lungs, and nutrient transport in plants.

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