(24a) Dynamic Evolution of Drop in Miscible Liquid-Liquid Systems at Low Flow Rate

Title: Dynamic evolution of drop in miscible
liquid-liquid systems at low flow rate.

Abstract:

The
mechanisms of drop formation in immiscible liquid-liquid systems are very
important considering the aspects of drop on demand in chemical process industries,
emulsification, mixing, extraction etc. The present work describes the theoretical
model to predict the drop dynamics from a submerged nozzle. The resorted
semi-analytical and numerical techniques are able to predict the drop shape as
the liquid is injected from the submerged nozzle in immiscible environment. The
static formation of liquid drops emanating from a submerged nozzle was analysed
based on the principles of force balance. In the case of very small flow-rates
and constant flow conditions, the formation takes place in a quasi-static
manner and can thus be described by the Laplace equation as an equilibrium of
surface, pressure and gravitational forces acting on the drop surface. The
resulting ordinary differential equation then solved numerically to obtain the drop
characteristics such as shape, volume, and height and pressure variations at
the nozzle tip up to the limit of critical equilibrium of resistive and
disruptive forces. At this stage the drop reaches its maximum volume and will inevitably
disintegrate from the nozzle tip when further flow is added or if any small
perturbation is applied. Experiments are performed with cyclohexane as
dispersed phase and deionized water as quiescent fluid as shown in the figure.
The sequence of cyclohexane drop formation with a flow rate of 1.5 ml/min at
time 0.121, 0.449, 0.91 and 1.22 sec are compared with theoretical model. The comparison
with the experimental results are found in good agreement. Further details will
be given in full paper.

Key
word:       Drop formation, liquid-liquid interface, force
balance, immiscible systems.

Results

Figure
Cyclohexane drop formation sequence in water are shown at flow rate of Q=1.5ml/min,
through a nozzle: OD=0.56mm, ID=0.27mm). The left and right half are the corresponding
experimental and theoretical drop shape.