Mass Transfer Coefficient given Mass Flux Density and Concentration Gradient Calculator

Mass Transfer Coefficient Formula:

\[ k_d = \frac{m}{c - c_i} \]

Mass Density of Crystal Surface:

kg/(s·m²)

Bulk Solution Concentration:

kg/m³

Interface Concentration:

kg/m³

Mass Transfer Coefficient (m/s):

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1. What is Mass Transfer Coefficient?

Definition: The Mass Transfer Coefficient is defined as the rate at which solute molecules are transported from the bulk solution to the surface of growing crystals or vice versa.

Purpose: This calculator helps determine the mass transfer coefficient based on mass flux density and concentration gradient, which is crucial in crystallization and other mass transfer processes.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ k_d = \frac{m}{c - c_i} \]

Where:

\( k_d \) — Mass Transfer Coefficient (m/s)
\( m \) — Mass Density of Crystal Surface (kg/(s·m²))
\( c \) — Bulk Solution Concentration (kg/m³)
\( c_i \) — Interface Concentration (kg/m³)

Explanation: The mass transfer coefficient is calculated by dividing the mass flux density by the concentration difference between the bulk solution and the interface.

3. Importance of Mass Transfer Coefficient

Details: Understanding and calculating the mass transfer coefficient is essential for designing and optimizing processes like crystallization, distillation, absorption, and other separation processes.

4. Using the Calculator

Tips: Enter the mass density of crystal surface in kg/(s·m²), bulk solution concentration in kg/m³, and interface concentration in kg/m³. All values must be ≥ 0.

5. Frequently Asked Questions (FAQ)

Q1: What is typical range for mass transfer coefficients?
A: Mass transfer coefficients typically range from 10⁻⁶ to 10⁻³ m/s depending on the system and conditions.

Q2: What happens when bulk and interface concentrations are equal?
A: When c = ci, the denominator becomes zero, making the mass transfer coefficient undefined as there would be no driving force for mass transfer.

Q3: How is mass density of crystal surface measured?
A: It's typically determined experimentally by measuring the mass deposition rate per unit surface area of the crystal.

Q4: What factors affect the mass transfer coefficient?
A: Factors include fluid velocity, temperature, system geometry, and physical properties of the fluid and solute.

Q5: Can this calculator be used for gases?
A: Yes, but ensure consistent units (e.g., kg/m³ for concentration) and note that typical values differ significantly for gas-phase systems.