Experimental investigation on the history force acting on oscillating fluid spheres at low Reynolds number

This paper reports an experimental investigation of isolated fluid particles rising (or falling) in a quiescent viscous liquid placed in an oscillating frame. Our goal is to carry out the first quantitative analysis of the effect of the history force on clean and spherical drops and bubbles. The average terminal Reynolds number is less than 0.5, the Strouhal number ranges from 1 to 25, and the Weber number ranges from 0.006 to 0.5. The particle motion is tracked by using a high-speed video camera and an accurate image processing facility. The average terminal velocity, the oscillation magnitude, and the phase shift with the oscillating frame are measured and compared with theoretical predictions. The comparison is made by solving the equation of motion of the sphere with and without the history force. Agreement between experiments and theory is observed when the history force corresponding to the creeping flow limit is taken into account. This experimental setup provides credible results, which confirm the fact that the history force given by the creeping flow theory remains still valid in these conditions, and brings non-negligible contribution into the momentum balance of small fluid inclusions moving in unsteady flows.