Deformation of a Capsule in a Power-Law Shear Flow

Area of Science:

• Computational fluid dynamics
• Non-Newtonian fluid mechanics
• Biophysics

Background:

• Modeling fluid-structure interactions (FSI) with non-Newtonian fluids is crucial for understanding biological and industrial processes.
• Existing methods often struggle to accurately capture the complex rheology of shear-thinning or shear-thickening fluids.
• Simulating deformable structures like capsules in such flows presents significant computational challenges.

Purpose of the Study:

• To develop and validate a novel immersed boundary-lattice Boltzmann method (IB-LBM) for simulating FSI involving power-law fluids.
• To investigate the deformation of a capsule in a power-law shear flow under varying conditions.
• To analyze the influence of key parameters such as Reynolds number, dimensionless shear rate, and power-law index on capsule behavior.

Main Methods:

• Coupling the immersed boundary method (IBM) for structure dynamics with the lattice Boltzmann equation (LBE) for fluid dynamics.
• Implementing a shear rate-dependent relaxation time in the LBE to accurately represent non-Newtonian (power-law) fluid rheology.
• Validating the in-house solver using a benchmark problem: power-law flow in a straight channel against analytical solutions.
• Performing simulations of a capsule's deformation in a power-law shear flow across a range of Reynolds numbers, shear rates, and power-law indices.

Main Results:

• The IB-LBM solver demonstrated good agreement with analytical solutions for power-law flow in a straight channel.
• Capsule deformation was found to increase with the power-law index across various Reynolds numbers and dimensionless shear rates.
• The effect of Reynolds number on capsule deformation was found to be negligible within the studied flow regime.
• The influence of the power-law index on capsule deformation was more pronounced at higher dimensionless shear rates.

Conclusions:

• The developed IB-LBM is a robust and accurate tool for simulating FSI in non-Newtonian power-law fluids.
• Capsule deformation is significantly influenced by the fluid's non-Newtonian properties (power-law index), particularly at higher shear rates.
• The findings provide valuable insights into the behavior of deformable capsules in complex fluid environments, relevant for microfluidics and biomedical applications.