### Dynamics of inertial particles with memory: an application of fractional calculus

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, November 17, 2014 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Dr. Mohammad Farazmand – GA Tech Physics

Recent experimental and numerical observations have shown the significance
of the Basset--Boussinesq memory term on the dynamics of small spherical
rigid particles (or inertial particles) suspended in an ambient fluid flow.
These observations suggest an algebraic decay to an asymptotic state, as
opposed to the exponential convergence in the absence of the memory term.
I discuss the governing equations of motion for the inertial particles,
i.e. the Maxey-Riley equation, including a fractional order derivative in
time. Then I show that the observed algebraic decay is a universal property
of the Maxey--Riley equation. Specifically, the particle velocity decays
algebraically in time to a limit that is O(\epsilon)-close to the fluid
velocity, where 0<\epsilon<<1 is proportional to the square of the ratio of
the particle radius to the fluid characteristic length-scale. These results
follows from a sharp analytic upper bound that we derive for the particle
velocity.