Diffusivity By Average Contact Time In Penetration Theory Calculator

Penetration Theory Formula:

\[ D_{AB} = \frac{t_c \cdot (k_{L,avg})^2 \cdot \pi}{4} \]

Diffusion Coefficient (D_AB):

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1. What is Penetration Theory?

Penetration Theory, developed by Higbie, describes mass transfer at fluid interfaces where eddies bring fluid elements to the interface for a short, constant contact time before being replaced. It's particularly useful for gas-liquid mass transfer systems.

2. How Does the Calculator Work?

The calculator uses the Penetration Theory formula:

\[ D_{AB} = \frac{t_c \cdot (k_{L,avg})^2 \cdot \pi}{4} \]

Where:

\( D_{AB} \) — Diffusion coefficient (m²/s)
\( t_c \) — Average contact time (s)
\( k_{L,avg} \) — Average convective mass transfer coefficient (m/s)
\( \pi \) — Mathematical constant pi (approximately 3.1416)

Explanation: The equation relates the diffusion coefficient to the contact time and mass transfer coefficient, based on the assumption of unsteady-state diffusion during the brief contact period.

3. Importance of Diffusion Coefficient Calculation

Details: The diffusion coefficient is crucial for designing mass transfer equipment, predicting reaction rates, and understanding transport phenomena in chemical processes, environmental engineering, and biological systems.

4. Using the Calculator

Tips: Enter average contact time in seconds and average convective mass transfer coefficient in m/s. Both values must be positive numbers for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of diffusion coefficients?
A: Diffusion coefficients typically range from 10⁻⁹ to 10⁻⁵ m²/s for gases and 10⁻¹⁰ to 10⁻⁹ m²/s for liquids.

Q2: When is Penetration Theory most applicable?
A: Penetration Theory is most applicable to systems with short contact times and when the mass transfer resistance is primarily in the liquid phase.

Q3: How does contact time affect diffusion?
A: Shorter contact times generally lead to higher mass transfer rates per unit time, as fresh fluid is constantly brought to the interface.

Q4: What are the limitations of Penetration Theory?
A: The theory assumes constant contact time for all fluid elements, which may not be realistic in many practical systems with varying flow patterns.

Q5: How is this different from other mass transfer theories?
A: Unlike film theory which assumes steady-state conditions, penetration theory accounts for the unsteady-state nature of mass transfer at fluid interfaces.