NUMERICAL TREATMENT OF THE INSTABILITY AND THE BREAKUP OF A LIQUID CAPILLARY COLUMN IN A BOUNDED IMMISCIBLE PHASE

The capillary instability of an infinite axisymmetric viscous liquid c olumn in an immiscible medium is investigated. The process of disinteg ration is simulated numerically using a (second-order) finite-differen ce method applied to the 'vorticity-stream function' formulation of th e Navier-Stokes equations. These equations and corresponding boundary conditions are written in there detailed form including convective ter ms in Navier-Stokes equations and nonlinear terms in the mass and mome ntum conservation equations at the unknown interface. Then the evoluti on in time of a given cosinusoidal disturbance is studied subjected to the action of the nonlinear effects. In these conditions the formatio n of a satellite drop attached to the main drop is observed. In the ca se where the liquid column is submerged into a low density inviscid fl uid, the basic characteristics of the column disintegration such as dr ops sizes and breakup time are in a good agreement with those calculat ed by previous authors. New results are obtained for the instability p arameters of a liquid column surrounded by another viscous fluid. (C) 1997 Elsevier Science Ltd.