Drop formation in viscous flows at a vertical capillary tube

Drop formation at the tip of a vertical, circular capillary tube immersed in a second immiscible fluid is studied numerically for low-Reynolds-number flows using the boundary integral method. The evolution and breakup of the drop fluid is considered to assess the influences of the viscosity ratio lambda, the Bond number B, and the capillary number C for 10(-2)less than or equal to lambda less than or equal to 10, 10(-2)less than or equal to C less than or equal to 1, and 0.1 less than or equal to B less than or equal to 5. For very small lambda, breakup occurs at shorter times, there is no detectable thread between the detaching drop and the remaining pendant fluid column, and thus no large satellite drops are formed. The distance to detachment increases monotonically with lambda and changes substantially for lambda>1, but the volume of the primary drop varies only slightly with lambda. An additional application of the numerical investigation is to consider the effect of imposing a uniform flow in the ambient fluid [e.g., Oguz and Prosperetti, J. Fluid Mech. 257, 111 (1993)], which is shown to lead to a smaller primary drop volume and a longer detachment length, as has been previously demonstrated primarily for high-Reynolds-number flows. (C) 1997 American Institute of Physics.