Research Paper#Fluid Dynamics, Chemotaxis, Mass Transport, Mathematical Modeling🔬 ResearchAnalyzed: Jan 3, 2026 19:52
Thermodynamically Consistent Model for Two-Phase Flows with Chemotaxis
Published:Dec 27, 2025 13:19
•1 min read
•ArXiv
Analysis
This paper presents a novel diffuse-interface model for simulating two-phase flows, incorporating chemotaxis and mass transport. The model is derived from a thermodynamically consistent framework, ensuring physical realism. The authors establish the existence and uniqueness of solutions, including strong solutions for regular initial data, and demonstrate the boundedness of the chemical substance's density, preventing concentration singularities. This work is significant because it provides a robust and well-behaved model for complex fluid dynamics problems, potentially applicable to biological systems and other areas where chemotaxis and mass transport are important.
Key Takeaways
- •Presents a thermodynamically consistent diffuse-interface model for two-phase flows with chemotaxis and mass transport.
- •Proves the existence and uniqueness of solutions, including strong solutions for regular initial data.
- •Demonstrates the boundedness of the chemical substance's density, preventing concentration singularities.
- •Offers a robust model with potential applications in biological systems and related fields.
Reference
“The density of the chemical substance stays bounded for all time if its initial datum is bounded. This implies a significant distinction from the classical Keller--Segel system: diffusion driven by the chemical potential gradient can prevent the formation of concentration singularities.”