A surface renewal model for unsteady-state mass transfer using the generalized Danckwerts age distribution function

Area of Science:

• Environmental Engineering
• Fluid Dynamics
• Mass Transfer

Background:

• The generalized Danckwerts age distribution is crucial for understanding air-water interfacial processes.
• Previous models focused on steady-state conditions, limiting their application to dynamic scenarios.

Purpose of the Study:

• To extend the steady-state generalized Danckwerts age distribution to unsteady-state conditions.
• To analyze the impact of wind speed on gas absorption and mass transfer coefficients.
• To validate theoretical predictions with experimental data.

Main Methods:

• Mathematical extension of the Danckwerts age distribution model.
• Simulations using data from the Heidelberg Aeolotron for air-water heat exchange.
• Calculation of gas absorption and dissolved-gas transfer coefficients for oxygen in water.
• Comparison of theoretical predictions with experimental measurements for the nitrous oxide-water system.

Main Results:

• The age distribution transitions from a sharp peak to a bell shape over time, influenced by wind speed.
• Mean eddy renewal time increases with time but asymptotically approaches a wind-speed-dependent steady-state value.
• Gas absorption and dissolved-gas transfer coefficients exhibit inverse behavior under unsteady conditions, converging as steady state is approached.
• Theoretical predictions for the steady-state mass-transfer coefficient showed an average absolute error of 18.1% against experimental data.

Conclusions:

• The extended Danckwerts age distribution effectively models unsteady-state gas absorption.
• Wind speed is a critical factor influencing gas transfer dynamics and interfacial renewal.
• The study provides valuable insights for optimizing gas absorption processes in dynamic environments.