(128i) Noncoalescence Of Drops In An Ambient Flow: Stability Of Stationary States

An axisymmetric thin-film formulation for the near-contact motion of drops in the presence of ambient flow has been developed for small-deformation conditions. The influence of flow on the film drainage is characterized by a single dimensionless flow-strength parameter. Our analysis shows that the film drainage is qualitatively affected by the presence of flow at long times. Two distinct behaviors occur, depending on the direction of the drop-scale stresses induced by the ambient flow. For drop-scale stresses that are radially-inward in the near-contact region, film drainage is arrested, leading to a stationary film profile. For values of the flow-strength parameter below a critical value, the film profile exhibits sustained temporal oscillations. For drop-scale stresses that are radially-outward in the near-contact region, the film is exponentially accelerated; an analytical solution is obtained for the accelerated near-contact motion of a drop toward a rigid surface. Qualitative agreement is found between the evolution predicted by our thin-film simulations and exact results obtained from axisymmetric boundary integral simulations under finite-deformation conditions. Trajectory calculations indicate that an ambient flow can also affect offset drop collisions.