Models for Facilitated Transport Membranes: A Review

Area of Science:

• Membrane science and separation technology
• Chemical engineering
• Materials science

Background:

• Facilitated transport membranes offer a promising alternative to traditional solution-diffusion membranes, potentially overcoming inherent trade-offs.
• Reaction-activated transport involves complex simultaneous mechanisms often overlooked in favor of material development.
• A rigorous theoretical framework is essential for understanding and optimizing these systems.

Purpose of the Study:

• To review and present key mathematical models for facilitated transport in both mobile and fixed carrier systems under steady-state conditions.
• To provide a comprehensive overview of existing mathematical tools for analyzing facilitated transport.
• To guide the selection of appropriate models for developing new facilitated transport systems and materials.

Main Methods:

• Literature review and analysis of established mathematical models for facilitated transport.
• Examination of models describing mobile and fixed facilitated transport systems.
• Assessment of model assumptions, approximations, applicability, precision, and flexibility.

Main Results:

• Analytical solutions are often unattainable, even for simple facilitated transport systems like oxygen-hemoglobin.
• Modeling studies provide approximate analytical solutions, validated against experimental data and numerical calculations.
• Specific models by Teramoto, Morales-Cabrera et al. (mobile carriers), and Noble et al. (fixed carriers) are identified as particularly flexible and comprehensive.

Conclusions:

• Mathematical modeling is crucial for advancing facilitated transport membrane technology.
• The reviewed models offer valuable insights into the behavior of mobile and fixed carrier systems.
• Selecting the right mathematical tools is essential for the effective design and development of next-generation separation membranes.