Average Mass Transfer Coefficient by Penetration Theory Calculator

Average Convective Mass Transfer Coefficient Formula:

\[ k_{L(Avg)} = 2 \times \sqrt{\frac{D_{AB}}{\pi \times t_c}} \]

Average Mass Transfer Coefficient (k_L(Avg)):

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1. What is Average Mass Transfer Coefficient by Penetration Theory?

Definition: This calculator estimates the average convective mass transfer coefficient based on the penetration theory, which considers the diffusion coefficient and contact time.

Purpose: It helps chemical engineers and researchers determine the mass transfer coefficient for fluid-fluid interfaces in absorption, distillation, and extraction processes.

2. How Does the Calculator Work?

The calculator uses the penetration theory formula:

\[ k_{L(Avg)} = 2 \times \sqrt{\frac{D_{AB}}{\pi \times t_c}} \]

Where:

\( k_{L(Avg)} \) — Average convective mass transfer coefficient (m/s)
\( D_{AB} \) — Diffusion coefficient (m²/s)
\( t_c \) — Average contact time between phases (seconds)
\( \pi \) — Mathematical constant (3.14159...)

Explanation: The formula shows that the mass transfer coefficient is proportional to the square root of the diffusion coefficient and inversely proportional to the square root of contact time.

3. Importance of Mass Transfer Coefficient Calculation

Details: Accurate calculation of mass transfer coefficients is crucial for designing efficient separation processes and predicting mass transfer rates in chemical engineering applications.

4. Using the Calculator

Tips: Enter the diffusion coefficient (D_AB) in m²/s and average contact time (t_c) in seconds. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is penetration theory?
A: Penetration theory models mass transfer at fluid interfaces assuming unsteady-state diffusion into a semi-infinite medium during short contact times.

Q2: How do I determine the diffusion coefficient?
A: Diffusion coefficients can be found experimentally or estimated using empirical correlations based on the properties of the system.

Q3: What affects the contact time in mass transfer?
A: Contact time depends on fluid dynamics, system geometry, and operating conditions like flow rates and agitation.

Q4: Why is the coefficient proportional to √D?
A: This relationship comes from the fundamental solution to Fick's second law of diffusion for short contact times.

Q5: What are typical values for k_L?
A: Values typically range from 10^-5 to 10^-3 m/s depending on the system and conditions.