Force-moment line element method for flexible slender bodies in Stokes flow

Area of Science:

• Fluid Dynamics
• Biophysics
• Mechanical Engineering

Background:

• Understanding the movement of flexible slender bodies in fluid is crucial for various applications, including micro-robotics and biological systems.
• Accurate modeling of fluid-structure interaction is essential for predicting the behavior of these bodies.

Purpose of the Study:

• To develop and validate a novel numerical method for simulating the hydrodynamics of flexible slender bodies in Stokes flow.
• To investigate the fluid-structure interactions, including forces and moments, acting on these bodies.

Main Methods:

• The fluid dynamics were modeled using integral equations representing line sources of forces and moments.
• The flexible slender body was represented using finite beam elements.
• Interfacial continuity conditions linked the fluid and solid models, leading to a higher-order line element method.

Main Results:

• The developed higher-order line element method demonstrated efficiency and accuracy in solving slender-body hydrodynamics.
• Benchmark solutions were obtained for a flexible rod under torque and bending moment.
• The method successfully simulated the excitation of planar and spiral waves in a slender body under cyclic force and magnetic fields.

Conclusions:

• The presented higher-order line element method is a valid and efficient tool for analyzing the hydrodynamics of flexible slender bodies.
• The study provides insights into the complex fluid-structure interactions governing the motion of such bodies.
• The method's capability to simulate wave propagation opens possibilities for designing and controlling micro-scale devices.