Behavior of a drop (bubble) in a non-uniform pulsating flow Original Research Article

Behavior of a drop (bubble) in a non-uniform pulsating flow of a fluid with different density is studied. It is assumed that the pulsation frequency is high and amplitude is small. The gravity is absent. The drop (bubble) size is small in comparison with the characteristic scale of flow non-uniformity in the absence of inclusion and with the distance from the rigid walls. General formulas for the average force acting upon the drop (bubble) and for the average shape taken by the inclusion in a non-uniform pulsating flow of arbitrary kind are obtained. The average force is found to be determined by the velocity gradients of unperturbed flow and by the density ratio. This force vanishes for uniform pulsating flow. The deformation of average shape takes place for both uniform and non-uniform pulsating flows. For uniform pulsating flow, the drop (bubble) takes the shape of oblate spheroid. Non-uniformity of the pulsating flow results in more complex average shape of inclusion: the deviation of average shape from oblate spheroid is determined by velocity gradients of unperturbed flow. The calculations made for the pulsating flow generated by rotational vibrations in a narrow gap between two coaxial cylinders show that in this case the inclusion takes pear-shaped form extending to a surface of external cylinder. The average force acting upon inclusion from the pulsating flow is directed to the cylinder axis for the inclusion denser than the host fluid and in the opposite direction for less dense inclusion.