A Hybrid Reactive Multiphasic Mixture With a Compressible Fluid Solvent.

Area of Science:

• Biomechanics
• Biophysics
• Computational Fluid Dynamics

Background:

• Standard multiphasic mixture frameworks lack dynamics of viscous fluids and fluid compressibility.
• This limits finite element implementation in computational fluid dynamics solvers for biological systems.

Purpose of the Study:

• To formulate governing equations for reactive multiphasic mixtures with viscous and compressible interstitial fluid.
• To develop a hybrid framework enhancing biomechanical and biophysical modeling capabilities.

Main Methods:

• Developed a hybrid reactive multiphasic framework with state variables including deformation gradient, volumetric strain, and relative velocities.
• Formulated a state function for fluid pressure dependent on volumetric strain and solute concentrations, differing from standard Lagrange multipliers.

Main Results:

• The new framework accommodates viscous fluid dynamics and fluid compressibility.
• Demonstrated continuity of solvent volumetric strain across interfaces under isothermal conditions.
• The hybrid framework is consistent with existing multiphasic formulations.

Conclusions:

• The hybrid reactive multiphasic mixture theory expands the scope of problems addressable in biomechanics and mechanobiology.
• This enhanced framework supports more sophisticated modeling of biological tissues and cells.