M. Chacha et al., NUMERICAL TREATMENT OF THE INSTABILITY AND THE BREAKUP OF A LIQUID CAPILLARY COLUMN IN A BOUNDED IMMISCIBLE PHASE, International journal of multiphase flow, 23(2), 1997, pp. 377-395
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.