The Maxey-Riley-Gatignol Equation (1983) describes the behavior of a spherical rigid particle carried by a fluid. The dispersed phase dynamics is generally modeled by this lagrangian approach which takes into account various types of forces: fluid acceleration, buoyancy, added mass, drag force. So what is the physical interpretation of the added mass in the equation of motion?
Previous answer is correct. It seems that in the term you presented the authors used the value 1/2 which means the added mass of a small sphere.
Dear Abdallah,
I agree with Mostafa and Alex.
Please see your equation again, this seems to be the relative acceleration particule (p) and whole fluid (f). If you need more detailed information about conservative equations in fluid see : http://www.lfpn.ds.mpg.de/turbulence/documents/Dipl-thesis-SimonKlein.pdf.
Good luck
Thank you Mostafa/Alex/Abel for your answers. Yes the particles are supposed to be very heavy spheres with a radius much smaller that the Kolmogorov dissipative scale. I can clearly now understand the meaning of the minus in the added mass term due to the work of particles on the carrying fluid. I think that the added mass term was well written.
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