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On the long-time persistence of hydrodynamic memory
1Departamento de física Aplicada, Facultad de Ingeniería, Universidad Central de Venezuela, Caracas, Venezuela. miguel.villegas.diaz@gmail.com.
The European Physical Journal. E, Soft Matter
|November 24, 2021
Summary
This study introduces a fractional generalized Basset-Boussinesq-Oseen equation to model particle motion with complex shapes. The findings reveal that memory effects in particle dynamics persist indefinitely, even under general driving conditions.
Area of Science:
- Fluid dynamics
- Particle dynamics
- Rheology
Background:
- The Basset-Boussinesq-Oseen (BBO) equation models nonuniform motion of spherical particles at low Reynolds numbers.
- It incorporates a singular integral term for vorticity diffusion and historical effects.
- Deviations from spherical shape or rigidity necessitate additional history force terms.
Purpose of the Study:
- To introduce a fractional generalized Basset-Boussinesq-Oseen equation.
- To incorporate both singular and non-singular history terms as fractional derivatives.
- To analyze the long-term memory effects in particle motion.
Main Methods:
- Development of a fractional generalized Basset-Boussinesq-Oseen equation.
- Application of the Laplace transform technique.
- Derivation of an integral representation for the solution.
Main Results:
- The fractional generalized BBO equation effectively models particles with complex shapes and compositions.
- An integral solution was obtained using the Laplace transform.
- Memory effects were shown to persist indefinitely for a driven single particle.
Conclusions:
- The fractional generalization of the BBO equation provides a more comprehensive model for particle dynamics.
- The study highlights the enduring nature of memory effects in particle motion.
- This framework offers insights into the behavior of non-spherical and non-rigid particles in fluid flow.
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