Instantaneous Mass Transfer Coefficient By Penetration Theory Calculator

Penetration Theory Formula:

\[ k = \sqrt{\frac{D}{\pi t}} \]

Mass Transfer Coefficient (k):

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1. What is the Penetration Theory?

The Penetration Theory, proposed by Higbie, describes mass transfer at fluid interfaces where fresh fluid elements are continuously exposed to the interface for short contact times. It provides the instantaneous mass transfer coefficient based on unsteady-state diffusion.

2. How Does the Calculator Work?

The calculator uses the Penetration Theory equation:

\[ k = \sqrt{\frac{D}{\pi t}} \]

Where:

\( k \) — Instantaneous mass transfer coefficient (m/s)
\( D \) — Diffusion coefficient (m²/s)
\( t \) — Time of exposure (s)
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: The equation shows that the mass transfer coefficient decreases with increasing exposure time and increases with higher diffusion rates.

3. Importance of Mass Transfer Coefficient

Details: The mass transfer coefficient is crucial for designing separation processes, predicting reaction rates in heterogeneous systems, and optimizing industrial processes involving gas-liquid or liquid-liquid mass transfer.

4. Using the Calculator

Tips: Enter diffusion coefficient in m²/s and time in seconds. Both values must be positive numbers. The calculator provides the instantaneous mass transfer coefficient in m/s.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for diffusion coefficients?
A: Diffusion coefficients typically range from 10⁻⁹ to 10⁻⁵ m²/s, with gases having higher values than liquids.

Q2: How does time affect the mass transfer coefficient?
A: The mass transfer coefficient decreases with the square root of time, meaning it's highest at very short contact times.

Q3: What are the limitations of penetration theory?
A: It assumes constant exposure time for all fluid elements and neglects velocity gradients near the interface.

Q4: How is this different from film theory?
A: Unlike film theory which assumes steady-state conditions, penetration theory accounts for unsteady-state diffusion during short contact times.

Q5: What industrial applications use penetration theory?
A: It's used in gas absorption, distillation, extraction, and other separation processes where short contact times are involved.