Dynamics of a periodically forced spheroid in a quiescent fluid in the limit of low Reynolds numbers

A set of ordinary differential equations governing the migration of an arbitrary forced spheroid in a quiescent flow at low Reynolds number is formulated and discussed, assuming a sufficiently diluted suspension to neglect the particle-particle interactions. The equations are non-linear and contain a history term of all the past position and velocity and hence impossible to solve symbolically. The spheroid transport is numerically investigated by varying Reynolds numbers, particle aspect ratios, and external forces. Interestingly, the size of the attractor increases as aspect ratio or/and force increases, whereas it decreases as Reynolds number increases. This decrement is due to the increase in the particle inertia. A delay with the velocity at maximum position is observed as evident from the respective time series. The reason for the delay could be the fact that in the absence of inertia, the time at which the velocity reaches its maximum, the position is at its minimum and when the particle experiences its maximum deviation, the velocity is at its minimum. Since position variation is almost sinusoidal, the velocity will also be sinusoidal with a phase shift of nearly π/2. The net migration at zero Reynolds number will be negligible and should increase with the number increases. Inertia should change this to a larger extent at higher values of Reynolds number. The dependence of the position and velocity on the parameters can be characterized for making use it as a potential application to particle separation.