# Focused Liquid Pinching in Coaxial Drop Capsule Generation

## TL;DR

This paper studies how an inner drop pinches faster in a coaxial setup due to flow focusing from the outer drop's contraction.

## Contribution

The study reveals a new focusing effect in coaxial drop pinching dynamics when the inner-to-outer nozzle radius ratio exceeds 0.67.

## Key findings

- The inner drop pinches faster in a coaxial setup compared to a single drop in a liquid medium.
- The thinning rate depends on the outer nozzle size when the radius ratio R̃ exceeds 0.67.
- Satellite droplets form when the outer drop squeezes the inner filament above its minimum neck location.

## Abstract

The pinching dynamics of an inviscid inner drop in a
coaxial pendant
drop structure have been investigated here both experimentally and
numerically. The thinning rate of the inner drop, when it pinches
in an inertial regime in this configuration, is found to be faster
than that of a single drop pinching in a liquid medium. This is attributed
to a focusing of the flow between the inner and outer drop interfaces
induced by the contraction of the outer drop during its own pinching
process. Our results reveal that this focusing effect increases dramatically
when the ratio of the inner to outer nozzle radii, R̃, in a coaxial nozzle configuration exceeds 0.67. Beyond this value,
the thinning rate becomes dependent on the outer nozzle size. Furthermore,
the difference between the minimum neck radii of the inner and outer
drop, denoted as Δh
min, serves as
a reliable predictor of the inner drop’s thinning rate, even
for different outer liquid viscosities, and helps identify the conditions
under which the satellite droplets form. Satellite droplets are observed
when the outer drop squeezes the inner filament above its minimum
neck location, which occurs when Δh
min ranges between 0.3% and 1% of the capillary length.