Formula & Calculator
Gas-Phase Mass Transfer Rate (Two-Film Theory)
Estimates the rate of mass transfer of a species across a gas-liquid interface using an overall gas-phase mass transfer coefficient and driving force.
Interpretation
Two‑film theory: N_A = K_y·a·(y − y*), where K_y is mass transfer coefficient, a is interfacial area, and driving force is concentration difference. Example: K_y=0.1, a=10, y−y*=0.05 → N_A=0.05 mol/(m³·s).
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| N_A | Molar mass transfer rate per volume | mol/m3.s |
| Ky | Overall gas-phase mass transfer coefficient | mol/m2.s |
| a | Interfacial area per unit volume | m2/m3 |
| y | Bulk gas-phase mole fraction | |
| y* | Gas-phase mole fraction in equilibrium with the bulk liquid |
What it means
The two‑film theory is a simple model for mass transfer across a phase interface (e.g., gas‑liquid). It assumes that the resistance to mass transfer is confined to two stagnant films (one on each side of the interface), and that the bulk fluids are well‑mixed. The overall mass transfer rate N_A (per unit volume) is given by N_A = K_y a (y − y*), where K_y is the overall gas‑phase mass transfer coefficient, a is the interfacial area per unit volume, y is the mole fraction of the transferring component in the bulk gas, and y* is the mole fraction in equilibrium with the bulk liquid. This equation is used in the design of packed columns, tray columns, and other gas‑liquid contactors. The overall coefficient K_y combines the individual film coefficients for gas and liquid phases. The driving force is the difference between actual and equilibrium composition. The two‑film theory is a cornerstone of absorption, stripping, and distillation design. Although simplified, it provides a practical framework for estimating mass transfer rates and is widely used in chemical engineering practice.
Worked example
Mass Transfer Rate – Two Examples
Real‑World| Parameter | Value |
|---|---|
| Ky | 0.05 |
| a | 100 |
| y | 0.05 |
| y* | 0.02 |
| Parameter | Value |
|---|---|
| Ky | 0.03 |
| a | 150 |
| y | 0.1 |
| y* | 0.04 |
Common mistakes
- Mass transfer coefficient K_y: Based on gas‑phase driving force (y − y*). Units: mol/(m²·s) or kmol/(m²·s) – check.
- Interfacial area a: Specific interfacial area per unit volume (m²/m³). For packed columns, depends on packing.
- Driving force (y − y*): y is bulk gas mole fraction, y* is equilibrium mole fraction at the interface.
- Two‑film theory: Assumes equilibrium at the interface and steady state; for fast reactions, modify.
- Units: N_A in mol/(m³·s) if a is per volume; or in mol/(m²·s) if area is total.
Applications
The two‑film theory describes mass transfer between a gas and a liquid, with the transfer rate given by N_A = K_y·a·(y − y*). This equation is used to design gas absorption, stripping, and humidification equipment. The overall mass transfer coefficient K_y accounts for resistances in both gas and liquid films, while the interfacial area a is provided by the contacting device (packing, trays). Engineers use this formula to size absorption towers, to evaluate the performance of packed columns, and to optimise operating conditions. It is also applied in environmental engineering for air stripping of volatile organics. By understanding mass transfer, professionals can achieve efficient separation and pollution control.
- Design of gas absorption columns (e.g., CO₂, SO₂, NH₃ removal)
- Sizing of stripping columns for volatile contaminants
- Design of humidifiers, dehumidifiers, and cooling towers
- Selection of packing or tray types for gas‑liquid contactors
- Environmental control of industrial emissions
Frequently Asked Questions
The two‑film theory assumes a stagnant gas film and a stagnant liquid film at the interface. The mass transfer rate of a species is N_A = K_y · a · (y – y*), where K_y is the overall gas‑phase mass transfer coefficient (based on mole fraction driving force), a is the interfacial area per volume, y is the bulk gas mole fraction, and y* is the equilibrium mole fraction at the interface.
- Mixing gas‑phase and liquid‑phase coefficients – use consistent driving forces (e.g., gas‑phase coefficients with gas‑phase mole fractions).
- Using the wrong equilibrium relation (e.g., Henry's law for y*).
- Not including the interfacial area a – some equations use flux per unit area (N_A = K_y·(y – y*)) without a; include it correctly.
It is the reciprocal of the sum of resistances: 1/K_y = 1/k_y + H/(k_x) (if equilibrium is y* = m·x, with m = H/P). K_y accounts for both gas‑film and liquid‑film resistances.
It provides a simple framework for mass transfer in gas‑liquid contactors. It is used in design of absorption, stripping, and distillation columns, though more detailed models exist (e.g., penetration theory).
They are obtained from correlations, typically functions of Re, Sc, and geometry (e.g., packed column, tray column). Sherwood numbers for the gas and liquid phases are used.
It is the mole fraction in the gas that would be in equilibrium with the liquid bulk composition. It is calculated using the equilibrium relationship (e.g., Raoult's law or Henry's law).
- Sizing of absorption columns (removing CO₂, SO₂).
- Design of air strippers for water treatment.
- Distillation (though more complex).