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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Equilibrium theory-based analysis of nonlinear waves in separation processes.

Marco Mazzotti¹, Arvind Rajendran

¹ETH Zurich, Institute of Process Engineering, Zurich, Switzerland. marco.mazzotti@ipe.mavt.ethz.ch

Annual Review of Chemical and Biomolecular Engineering

|March 5, 2013

Summary

Mathematical models accurately predict composition fronts in one-dimensional, nonstationary separation processes. This equilibrium theory approach offers insights for adsorption, chromatography, and distillation applications.

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Area of Science:

Engineering
Separation Process Technology
Applied Mathematics

Background:

One-dimensional, nonstationary processes are common in engineering, particularly in separation technologies.
These processes are often modeled using systems of first-order partial differential equations, assuming negligible dispersion and transport resistances.
The behavior of these systems is characterized by propagating composition or thermal fronts.

Purpose of the Study:

To present the equilibrium theory as a method for solving model equations for one-dimensional, nonstationary processes.
To demonstrate how mathematical insights can enhance understanding of engineering aspects in separation processes.
To guide researchers in understanding fundamental properties and discovering new phenomena in these systems.

Main Methods:

Utilizing mathematical models based on systems of first-order partial differential equations.
Applying the equilibrium theory to predict the behavior of composition and thermal fronts.
Analyzing the accuracy of the equilibrium theory despite simplifying assumptions.

Main Results:

The equilibrium theory accurately predicts the behavior of continuous and discontinuous fronts in separation processes.
The study highlights applications in adsorption, chromatography, ion-exchange, distillation, gas injection, heat storage, sedimentation, precipitation, and dissolution waves.
Mathematical analysis reveals fundamental properties and potential for discovering new phenomena.

Conclusions:

The equilibrium theory provides a powerful and accurate tool for analyzing one-dimensional, nonstationary separation processes.
Mathematics offers valuable insights into complex engineering challenges, aiding researchers and practitioners.
The presented tools and understanding are beneficial for educators, researchers, and industry professionals.