A slender-body theory for low-viscosity drops in shear-flow between parallel walls

A slender-body analysis is presented for the deformation and break-up of a highly confined and highly elongated low-viscosity drop in shear flow between two parallel walls that are separated by a distance less than the drop length. The analysis is simplified by the assumption that the drop has a circular cross section. The results show that confinement enhances the alignment of a low-viscosity drop with the imposed flow, thereby reducing its deformation and increasing the critical flow strength required for breakup. In the intermediate limit, where the wall separation is small compared with the drop length but large compared with its width, the dynamics can be related to that of an unconfined drop at a shear rate reduced by a factor of v3. Under these corresponding conditions, the drop length and cross-section profile are the same for both cases, whereas the centerline deflection of the confined drop is reduced relative to the unconfined case by v3. In the intermediate limit of wall separations, the critical flow strength for a confined drop is v3 times larger than that for an unconfined drop